Citation
Augmentable object-oriented parallel processor architectures for real-time computer-generated imagery

Material Information

Title:
Augmentable object-oriented parallel processor architectures for real-time computer-generated imagery
Creator:
Fleischman, Ross Morris ( Dissertant )
Staudhammer, John ( Thesis advisor )
Doty, Keith L. ( Reviewer )
Smith, Jack R. ( Reviewer )
Principe, Jose C. ( Reviewer )
Duffy, Joseph ( Reviewer )
Place of Publication:
Gainesville, Fla.
Publisher:
University of Florida
Publication Date:
Copyright Date:
1988
Language:
English
Physical Description:
xii, 154 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Atmospheric attenuation ( jstor )
Block diagrams ( jstor )
Buffer storage ( jstor )
Display devices ( jstor )
Image processing ( jstor )
Integers ( jstor )
Opacity ( jstor )
Pixels ( jstor )
Rectangles ( jstor )
Simulations ( jstor )
Computer architecture ( lcsh )
Computer graphics ( lcsh )
Dissertations, Academic -- Electrical Engineering -- UF
Electrical Engineering thesis Ph. D
Parallel processing (Electronic computers) ( lcsh )
Three-dimensional display systems ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )
theses ( marcgt )

Notes

Abstract:
The hardware architecture of a system for real-time computer-generated imagery (CGI) is presented that combines augmentability, modularity, organizational simplicity, and parallelism. This architecture is a functional, highly-modular, parallel processor approach that is well suited for employing VLSI technology. It is a generic structure that can grow with technological advances and can accommodate a full range of CGI systems that demand different performance requirements through one basic set of modules. The CGI process contains five fundamental components: input, modeling, rendering, compositing, and output. This architectural approach extends specialized hardware into both the compositing and output components, which allows the definition of a generic framework for building systems appropriate for many simulations. The system architecture performs image synthesis in parallel by partitioning the image generation task in object space with each partition. assigned to an individual autonomous object generator. Objects are rendered independently from each other, and when complete they are automatically composited by the hardware for display. This process is repeated at a rate suitable for real-time animation. The picture representation accepts transparent, semi-transparent, and fully opaque surfaces. Hardware facilities perform automatic hidden surface removal with antialising and atmospheric attenuation inclusion. An approximation for surface intersection is performed, and a subpixel control mechanism is provided. The parallel hardware algorithm is classified as a compute-aggregate-broadcast paradigm: a compute phase generates objects, an aggregate phase combines the objects into a scene, and a broadcast phase displays the scene. Its system framework maintains a synchronous feed-through structure that allows enlargement by either dynamic or static additions. system improvement is accommodated by adding modules that incrementally improve system performance and scope. This reduces difficulties associated with the incorporation of new systems to introductions of new modules, thereby lengthening system life.
Thesis:
Thesis (Ph. D.)--University of Florida, 1988.
Bibliography:
Includes bibliographical references.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Ross Morris Fleischman.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
001123865 ( ALEPH )
20071125 ( OCLC )
AFM0917 ( NOTIS )

Downloads

This item has the following downloads:


Full Text















AUGMENTABLE OBJECT-ORIENTED
PARALLEL PROCESSOR ARCHITECTURES
FOR REAL-TIME COMPUTER-GENERATED IMAGERY
















BY

ROSS MORRIS FLEISCHMAN


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1988



































Copyright 1988

by

Ross Morris Fleischman












ACKNOWLEDGMENTS


I would like to express my appreciation to my advisor

and supervisory committee chairman, Dr. John Staudhammer,

for the guidance and encouragement he provided me on this

project. I am also grateful to the other members of my

supervisory committee, Dr. Keith L. Doty, Dr. Jack R.

Smith, Dr. Jose C. Principe, and Dr. Joseph Duffy, for

their commitment. I also wish to thank the members of the

UF Computer Graphics Research Group for their suggestions.

This dissertation is dedicated to my mother,

Ruth Koegel Fleischman, and to the memory of my father,

Erwin Lewis Fleischman.


iii












TABLE OF CONTENTS


Page
ACKNOWLEDGMENTS ... iii

LIST OF TABLES. ... .. .vii

LIST OF FIGURES ... .viii

LIST OF ABBREVIATIONS x

ABSTRACT. .. .xi


CHAPTERS

I INTRODUCTION. 1

Problem Definition. 2
Dissertation Project. 3
Overview of Dissertation. 4

II TYPICAL REAL-TIME CGI ARCHITECTURE. 5

Scene Manager 5
Geometric Processor. .. 8
Video Processor 9
Display Device .. 10

III ALTERNATE REAL-TIME CGI ARCHITECTURE. .. .12

System Model. .. 12
Underlying Idea .... 12
Supporting Architecture .. 15
Advantages of Approach. .. .19
Target Applications. .. 22

IV COMPOSITING NETWORK .. 23

Compositing Methodology 25
RGBZA Compositing Algorithm .. 33
Network Structure ... 40
Compositing Processing Node ....... 50
General Compositing Processing Node .... 54
Depth computation unit. .... 54
Opacity computation unit. ... .58
Color computation unit. .. ....... 63
Specialized Compositing Processing Node 70
Depth computation unit. .. .71
Color computation unit. .. .72
Analysis. ... 77












Complexity. 77
Performance ........ 84

V VIDEO GENERATION NODE ... 90

Configuration 90
Atmospheric Attenuation Unit. 92
Pixel Cache .. 95
Double-Buffered Frame Buffer. 96
Video Shift Registers ... 98
Color Palette .. 99
Digital-to-Analog Converters. .. 100
System Controller .. 100
Analysis. .. 101
Complexity. ... 101
Performance .. 102

VI DISPLAY DEVICE NODE .. 105

Display Device Approaches .. .105
Raster Scan Conversion. 106
Image Aspect Ratio. 107
Display Device Performance .. 107

VII OBJECT GENERATION NODE. 109

Configuration .. 110
Object Generation Node Nucleus. 110
Double-buffered image buffer. .. .112
Intensity multiplication unit .. .114
Nucleus controller. .. .115
Object Generation Unit. 118
Secondary Memory Unit 119
Analysis. 121
Complexity. .. .121
Performance .. .. 122

VIII MAINTENANCE MANAGEMENT NODE 124

Configuration 124
Operating Functions 125
System Boot Operation .. 125
System Normal Operation .. 126
Simulation Debugging. 127
Analysis. ... .. .127

IX CONCLUSION. .. .129

System Simulator. .... .... 129
System Simulation 130
Discussion of System Features ... .139
Summary .. .. .147













BIBLIOGRAPHY. .. 149

BIOGRAPHICAL SKETCH .................. 154












LIST OF TABLES


Table Page

4-1 Functional logic block equivalent of the
general CPN and the specialized CPN. .. 79

4-2 Pin requirement for the general CPN, the
specialized CPN, and each CPN computation
unit. 80

4-3 Gate equivalent and package pin count of
various functional logic blocks 81

4-4 Estimated complexity of the general CPN, the
specialized CPN, and each CPN computation
unit. 83

4-5 CPN processing-time for various image space
resolutions. The image update rate is 10
frames per second ... 86


vii












LIST OF FIGURES


Figure Page

2-1 Block diagram of a typical real-time CGI
system organization 6

3-1 Composition of an opaque background 3-D
object and an opaque foreground 3-D object
to produce a composite 3-D scene ...... 14

3-2 Block diagram of the proposed augmentable
real-time CGI system organization .. 17

4-1 Three distinct types of pixel coverage, with
respect to the ALPHA value: a) no coverage,
b) full coverage, and c) partial coverage.
The subpixel shape of the pixel with partial
coverage is arbitrary and is only shown in
this manner for conceptual clarity. ... 27

4-2 Two pixel opacity values are composite. The
values were derived from coverage information
from two different objects. The coverage
depictions are arbitrary, they are given
specific subpixel forms to clarify the
composite operation. The coverage areas are
actually averaged across the pixel. ... 35

4-3 The RGBZA Compositing Algorithm .. 39

4-4 A fully balanced three level compositing
tree ... .... 42

4-5 The general RGBZA compositing algorithm for a
fully balanced tree. Note that lower case
letters designate the product of intensity
and opacity. .. ... 47

4-6 The specialized RGBZ compositing algorithm of
a fully balanced tree .. 49

4-7 An iterative building block depiction of a
compositing processing node (CPN) .. .51

4-8 The algorithm performed by a general CPN
depth computation unit. ... 56

4-9 Block diagram of a general CPN depth computa-
tion unit ... 57


viii












4-10 The algorithm performed by a general CPN
opacity computation unit. .. 61

4-11 Block diagram of a general CPN opacity compu-
tation unit 62

4-12 The algorithm performed by a general CPN
color computation unit. 65

4-13 Block diagram of a general CPN color compu-
tation unit .. 66

4-14 The algorithm performed by a specialized CPN
color computation unit. 73

4-15 Block diagram of a specialized CPN color
computation unit. .. 74

5-1 Block diagram of a video generation node with
respect to its seven modules. .. 91

5-2 Block diagram of the atmospheric attenuation
unit, used to include atmospheric effects in
a scene ..... ......... 94

7-1 Block diagram of an object generation node
with respect to its three modules .. 111

7-2 Block diagram of the intensity multiplication
unit, used to condition the color and opacity
values for input to the compositing network 116

9-1 View of rectangle A and rectangle B in object
space .. .... 131

9-2 Contents of the simulated frame buffer of
OGN1 after scan converting rectangle A. ... .134

9-3 Contents of the simulated frame buffer of
OGN2 after scan converting rectangle B. ... 135

9-4 Contents of the simulated frame buffer of the
VGN for the first system simulation 136

9-5 Contents of the simulated frame buffer of the
VGN for the second system simulation. 137

9-6 Two system tree configurations: a) fully
balanced system tree and b) unbalanced system
tree. .. .. 144












LIST OF ABBREVIATIONS


2-D -------- Two-Dimensional
3-D -------- Three-Dimensional
AAU -------- Atmospheric Attenuation Unit
CGI -------- Computer-Generated Imagery
CN --------- Compositing Network
CPN -------- Compositing Processing Node
DAC -------- Digital-to-Analog Converter*
DDN -------- Display Device Node
I/O -------- Input/Output
IPU -------- Intensity Multiplication Unit
LSH -------- Least Significant Half
MSH -------- Most Significant Half
MMN -------- Maintanence Management Node
MMU -------- Maintanence Management Unit
OGN -------- Object Generation Node
OGNN ------- Object Generation Node Nucleus
OGU -------- Object Generation Unit
RGB -------- RED, GREEN, and BLUE
SMU -------- Secondary Memory Unit
VGN -------- Video Generation Node
VLSI ------- Very Large-Scale Integration












Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

AUGMENTABLE OBJECT-ORIENTED
PARALLEL PROCESSOR ARCHITECTURES
FOR REAL-TIME COMPUTER-GENERATED IMAGERY

By

Ross Morris Fleischman

December 1988

Chairman: Dr. John Staudhammer
Major Department: Electrical Engineering

The hardware architecture of a system for real-time

computer-generated imagery (CGI) is presented that combines

augmentability, modularity, organizational simplicity, and

parallelism. This architecture is a functional, highly-

modular, parallel processor approach that is well suited

for employing VLSI technology. It is a generic structure

that can grow with technological advances and can

accommodated a full range of CGI systems that demand

different performance requirements through one basic set of

modules.

The CGI process contains five fundamental components:

input, modeling, rendering, compositing, and output. This

architectural approach extends specialized hardware into

both the compositing and output components, which allows

the definition of a generic framework for building systems

appropriate for many simulations. The system architecture

performs image synthesis in parallel by partitioning the

image generation task in object space with each partition












assigned to an individual autonomous object generator.

Objects are rendered independently from each other, and

when complete they are automatically composite by the

hardware for display. This process is repeated at a rate

suitable for real-time animation.

The picture representation accepts transparent, semi-

transparent, and fully opaque surfaces. Hardware

facilities perform automatic hidden surface removal with

antialiasing and atmospheric attenuation inclusion. An

approximation for surface intersection is performed, and a

subpixel control mechanism is provided.

The parallel hardware algorithm is classified as a

compute-aggregate-broadcast paradigm: a compute phase

generates objects, an aggregate phase combines the objects

into a scene, and a broadcast phase displays the scene.

Its system framework maintains a synchronous feed-through

structure that allows enlargement by either dynamic or

static additions. System improvement is accommodated by

adding modules that incrementally improve system

performance and scope. This reduces difficulties

associated with the incorporation of new systems to

introductions of new modules, thereby lengthening system

life.


xii


















CHAPTER I
INTRODUCTION


A computer-generated imagery (CGI) system is a

specialized computer system that provides a visual simu-

lation of an artificial environment. Conceptually, a CGI

system consists of a window in multidimensional space with

which an observer may look into a world. The window is

presented by a computer driven display device, while the

world is modeled by a database that the computer can

access. Thus, the visual simulation may be regarded as a

generation of an out-the-window view, in real-time, ac-

cording to the simulated position and orientation of the

observer with respect to the simulated changes of the

artificial environment.

A popular application of real-time computer-generated

imagery visual simulators concerns vehicle training simu-

lation [FIS85, PAN86, SCH81, SCH83b, YAN85, ZYD88]. For

this application, an observer's visual experience is

created by a generated perspective projection of a 3-D

world rendered onto a 2-D display device [BEN83], with

associated special effects. Other simulation tasks [SUG83]

may have variations of the visual simulation requirement as












a function of the world structure, but the real-time per-

formance and rendering problems remain constant.

Real-time operation, which defines a computation

process where the execution time of the computer is syn-

chronized with the physical event time or wall-clock time,

is a major requirement of these systems [FOR83]. Also, the

associated image rendering problems are computationally

demanding. Thus, real-time CGI system organizations typi-

cally mandate custom-designed, special-purpose, high-speed

computers, with general-purpose computers for their control

[SCH81, SCH83b, YAN85].


Problem Definition

Traditional CGI architectures utilize both pipelining

and parallelism technologies to achieve real-time perfor-

mance for image synthesis. The system architectures are

usually highly specialized and constrain the types of

graphics primitives that can be employed [ENG86]. These

special-purpose architectures usually involve a fixed

graphics pipeline that is difficult to enhance for in-

creased performance or for inclusion of additional graphics

primitives.

The realization of major CGI architectural revisions

that exhibit improved performance with substantial hardware

reduction is a subject of research. Innovative CGI archi-

tectures will employ unique organizational structures that

realize algorithmic improvements with respect to imple-












mentation with massive memory, gate arrays, and custom

VLSI. Thus, improvements in both VLSI memory chips [COL87,

TUN87a] and VLSI computational chips [BUR87, COL87, GRI86,

MOK87], plus parallel processing trends [SCH87], are good

indicators that the evolution of CGI system organizational

philosophies will become VLSI-oriented through parallelism.


Dissertation Project

The general research objective is to develop the

guidelines and philosophies of a VLSI-oriented real-time

CGI architecture that combines augmentability, modularity,

organizational simplicity, and parallelism. This proposed

architecture will be a functional, highly-modular, parallel

processor approach that will be suited for employing VLSI

technology. It will be a generic structure that can grow

with technological advances. The investment in such a

system will hypothetically never be discarded; system

improvement can be accommodated by adding modules that

incrementally improve the performance and scope of a sys-

tem. The introduction of new systems will be reduced to

introductions of new modules, thereby resisting system

obsolescence. Therefore, such a system will be continu-

ously expandable and never totally outmoded, thus providing

performance, development, and economic benefits.











Overview of Dissertation

This dissertation is organized into nine chapters.

Chapter I is an introductory chapter that covers objectives

and background about the dissertation subject. Chapter II

describes a typical real-time CGI architecture. Chapter

III presents an overview and introduction of the proposed

augmentable CGI architectures, along with the fundamental

driving idea for the approach. Chapters IV through VIII

describes each major subsystem of the augmentable CGI

architectural approach. Chapter IV describes the compos-

iting network. Chapter V describes the video generation

node. Chapter VI describes the display device node.

Chapter VII describes the object generation node. Chapter

VIII describes the maintenance management node. Chapter IX

is a concluding chapter that contains a discussion of the

system simulation, along with a summary of the dissertation

results.

















CHAPTER II
TYPICAL REAL-TIME CGI ARCHITECTURE


A typical real-time CGI system organization, popular

among vehicle training simulators, is shown in Figure 2-1.

This structure provides a single field-of-view of the

artificial environment, termed a channel. Its organization

consists of a cascade of four major subsystems: the scene

manager, the geometric processor, the video processor, and

the display device [SCH83b, YAN85]. The first three sub-

systems form a specialized computer graphics pipeline for

image rendering. The last subsystem provides a specialized

display for viewing.


Scene Manager

The overall function of the scene manager is to

provide scene elements to the system pipeline that lie in

the observer's field-of-view, within the artificial envi-

ronment, given observer position and orientation. Observer

position and orientation information are provided to the

scene manager by a host simulator [FOR83, SCH83b]. This

information directs dynamic extraction of database scene

elements from mass storage that are loaded into an active

database memory for sorting [PAN86]. These scene elements

represent the observer's panorama and are examined to











Data From Host
Simulator


3-D Data
Blocks


3-D Data
Blocks


Blocks


3-D


Analog
Video


Figure 2-1. Block diagram of a
system organization.


typical real-time CGI













determine if they are potentially visible within the field-

of-view of the observer [PAN86, YAN85]. Scene elements

satisfying this condition are provided with an appropriate

level-of-detail, while the remainder are culled [PAN86,

YAN85].

The resultant scene elements are sent down the system

pipeline, at the image update rate, to the geometric

processor [YAN85]. Subsystem processing load is continu-

ously monitored by the scene manager to avoid overloading

the processing capacity of the pipeline. Processing load

reduction techniques utilize various dynamic scene content-

control mechanisms that usually degrade image quality

gracefully [SCH83a, YAN85].

The mass storage device contains a database, which

models an artificial environment, that drives the hardware.

Features of a simulated scene (natural and cultural) are

modeled to be of the same size, shape, location, and color

as their real-world counterparts [SCH81, SCH83a]. Database

modeling primitives for the typical CGI system consist of

planar polygons as a major primitive and quadric surfaces

as an option for both man-made curved objects and natural

curvilinear objects [YAN85]. The database also contains

scene element attributes such as color and texture.












Geometric Processor

The geometric processor is a special-purpose pipelined

computer that operates on the scene element output from the

scene manager. These operations usually produce the pro-

jected geometry of the scene with associated geometric

gradient and color gradient parameters. In general, the

fixed coordinate system of the scene elements are trans-

formed (via translation, rotation, and scaling) to the

momentary eye-based coordinate system (origin located at

the observer's eye). Within the eye-based coordinate

system, a visibility frustrum is defined. Then, a 3-D

clipping algorithm is applied to determine where the 3-D

scene intersects the bounding planes of the visibility

frustrum. Scene parts within the visibility frustrum are

projected to the image plane with the computed geometric

gradient and color gradient parameters, while the rest are

deleted [BEN83].

Issues relating to color can be found in Rogers

[ROG85]. A matrix multiplier was presented by Meares et

al. [MEA74] and a three-dimensional coordinate transforma-

tion device was presented by Newarikar [NEW82]. Clipping

algorithms, geometric transformations, and perspective

projection can be found in Rogers [ROG85] with an interest-

ing VLSI solution presented by Clark [CLA82]. Clark

discusses a four-component vector, floating point VLSI












processor for accomplishing matrix transformations, clip-

ping, and mapping to output device coordinates.


Video Processor

The video processor is a special-purpose computer that

operates on the resultant projected geometry, geometric

gradient, and color gradient output from the geometric

processor for subsequent display. The video processor

computes each pixel color produced on the picture plane

representing visible portions of scene element surfaces

[SCH83b, YAN85]. Pixel color computation is a function of

various items: geometric gradient parameters (surface

normals), color gradient parameters (scene element native

color), texture maps, atmospheric attenuation (haze color),

scene element illumination (both natural and cultural light

sources), antialiasing techniques, shadows, and shading

techniques. During, before, or after pixel computation,

visible portions of the scene are identified through a

hidden surface removal technique.

This processor also provides timing and control of the

display device, which relate to the video processor organ-

izational philosophy [YAN85]: scan-line-based or frame-

buffer-based. Scan-line-based units perform video pro-

cessing one scan-line at a time in synchronism with each

raster of the display device; one row of the visible

scene's pixel codes are stored. Frame-buffer-based units

perform video processing independent of the raster display;












complete frame of the visible scene's pixel codes are

stored.

Algorithms and techniques used by the video processor

are well known and can be found in the literature, such as

Rogers [ROG85]. Examples of antialiasing include Booth's

[B0087] presentation concerning the human factors relation

to antialiasing and Carpenter's [CAR84] presentation of an

interesting A-buffer approach. Real-time hardware ap-

proaches to texture mapping can be found in the literature,

such as one approach presented by Fant [FAN86].


Display Device

Display device technology primarily consists of two

variations: calligraphic displays and raster displays

[SCH83a]. The color calligraphic display is characterized

by a continuous layered phosphor surface (RED and GREEN

phosphor layers) used to present a color picture with beam

penetration control (electron beam velocity) of sequen-

tially refreshed straight lines (vectors or strokes) and

points (zero length vectors). The raster display contains

a regular grid of phosphor triads (RED, GREEN, and BLUE)

that are used to present a color picture by modulated

illumination of each phosphor triad point (pixel) with

refresh in a regular pattern. Calligraphic systems main-

tain high quality light points with color limitations,









11


while raster systems maintain high quality painted faces

without color limitations [YAN85, SCH83a].

















CHAPTER III
ALTERNATE REAL-TIME CGI ARCHITECTURE


This chapter presents an alternate real-time CGI

architectural approach as compared to the traditional

approach briefly presented in Chapter II. This discussion

is meant as an overview to give an understanding of the new

approach before delving into its details. The system model

is presented to illustrate the underlying idea and its

supporting architecture. Following, is a discussion of the

advantages of the new approach and typical applications.


System Model

A system model is presented that exhibits the premise

of this research. First, the underlying idea with respect

to the image generation problem is presented. Second, the

supporting architecture that can realize the underlying

idea is described.


Underlying Idea

This field of architectural research is driven by the

fundamental idea that an individual scene is composed of

separable objects. Therefore, a scene can be produced from

the summation of every object existing in that scene; this

process is called compositing. An example of compositing











is presented in Figure 3-1, which illustrates the composite

of two opaque 3-D objects. As shown, an opaque background

3-D object and an opaque foreground 3-D object are merged

to form a composite 3-D scene. This process indicates that

there is an alternative to producing an entire complex

scene directly. The generation of simpler objects can be

done individually, followed by compositing the simpler

objects to produce an entire complex scene [POR84, STA83].

The approach taken by this research separates the

image compositing process from the image synthesis process

of the image generation problem. The compositing is

reduced to the pixel level, where a procedure is defined

that can blend images through a pixel-by-pixel process.

This compositing process is extended further, at the pixel

level, to include the effect of atmospheric attenuation.

The compositing process performs antialiased blending

of images utilizing a mixing factor. This mixing factor

defines the average opacity of a pixel, which defines the

average pixel reflectivity. It is useful for performing

surface edge antialiasing and for rendering surfaces that

are either transparent, semi-transparent, or opaque. Along

with the mixing factor is the depth value for determining

the depth location of a pixel in space. This information

is used for a comparison to determine whether a pixel, as

compared to another pixel, is in front of, behind, or at

the same distance. Also, the horizontal and vertical












Background 3-D Object


Composite 3-D Scene




Figure 3-1. Composition of an opaque background 3-D object
and an opaque foreground 3-D object to
produce a composite 3-D scene.


Foreground 3-D Object











position is determined by the pixel location in the image

array and the color value is defined as the additive tri-

stimulus colors: RED, GREEN, and BLUE.

The atmospheric attenuation process is performed by a

procedure that calculates attenuation as a function of

distance from the viewpoint with respect to a fading

constant and a horizon color. The fading constant is

adjusted for varying atmospheric conditions such as foggy,

hazy, and murky atmospheres. The horizon color is adjusted

for varying background lighting conditions. This process

is performed following the compositing process, which

results in a pixel value representing the composite tri-

stimulus color value with the effect of atmospheric

attenuation included.


Supporting Architecture

The fundamental idea of compositing focuses on allow-

ing a scene to be blended by computer. Hypothetically, the

objects would be visually computer-generated in their

proper position and orientation, then they would be merged

by computer for display. Therefore, instead of having an

individual total database for an artificial environment,

the total database would be partitioned by objects to

provide multiple partial databases. This would allow each

object or group of similar objects in a scene to be

assigned an individual processor, which would have the

advantage of distributing the image generation task, thus













reducing the performance requirement for each processor and

secondary memory unit. Also, the task of merging or

compositing the collection of objects would be performed by

separate processors. As a result, an organization of this

nature would produce multiple data-streams and multiple

instruction-streams, thereby speeding-up both computational

processing and I/O processing. Also, the separable nature

of objects existing in a scene points to the goal of

expandability without affecting other elements of the

system.

The abstract organization of the proposed augmentable

CGI architecture, which logically follows from the above

discussion, is illustrated in Figure 3-2. Major components

of the proposed real-time CGI machine consists of multiple

object generation nodes (OGNs), a compositing network (CN),

a video generation node (VGN), a display device node (DDN),

and a maintenance management node (MMN). This system can

handle opaque, transparent, and semi-transparent images. A

short description of each subsystem is discussed below with

a more detailed discussion of each subsystem presented

subsequently in Chapters IV through VIII.

The object generation node is a VLSI-oriented image

synthesis processor with an optional local secondary

memory, which can execute computer graphics algorithms to

render an assigned object. OGNs operate autonomously and

concurrently with respect to the complete system, but in























Compositing
Network


NGeneral
Communications



Figure 3-2. Block diagram of the proposed augmentable
real-time CGI system organization.












synchronism with it. They are assigned a partition, termed

an object, of the entire image generation task. An OGN

interfaces to the compositing network through its image

memory, which contains an image space view of the assigned

object. Each element of the image memory contains three

pixel attributes: color, opacity, and depth. The X, Y

coordinates are derived from a pixel's position in the

image memory.

The compositing network is a pixel-by-pixel hardware

compositor, which is an expandable ensemble of intercon-

nected compositing processing nodes, that produces a

computer graphics picture through blending independently

rendered objects into a full image. This network is a

synchronous feed-forward structure. It simultaneously

reads each image memory area, of every OGN, pixel-by-pixel

in a row-by-row manner and writes the composite result to

the VGN pixel-by-pixel.

The video generation node processes composite object

digital image data from the compositing network and then

converts it to analog video data for display. Pixels are

individually received from the compositing network. While

pixels are received, the VGN includes the effect of

atmospheric attenuation to each pixel and then writes the

result to its frame buffer pixel-by-pixel in a row-by-row

manner. Simultaneously, the frame buffer data is read and

converted to analog data for driving the display device













node. Also, the timing of the entire system is derived

from the VGN.

The display device node is a raster scan type monitor.

It receives three primary colors from the VGN: RED, GREEN,

and BLUE. The video timing of the monitor is also control-

led directly from the VGN.

The maintenance management node provides central

control and health assurance of the system. It is an

autonomous processor that provides self-maintenance

operations and system support functions. Included is a

computational unit, a secondary memory unit, and a con-

sole. The MMN communications to and from the nodes of the

system is provided by a general interface from which all

system nodes are connected.


Advantages of Approach

The improvements of this CGI architectural approach as

compared to existing CGI architectural approaches encompass

a reduced complexity of the individual image synthesis

processors, ease of system expansion, ease of including

different graphic primitives, decoupling of the rendering

process from the compositing process, and ease of system

understanding. The reduced complexity of image synthesis

processors is due to three factors: 1) the image genera-

tion task is distributed among many processors (OGNs), 2)

the hidden surface removal with antialiasing is included in












the architectural structure (compositing network), and 3)

the effect of atmospheric attenuation is included in the

architectural structure (VGN). The automatic processing of

2 and 3 above is relegated to the machine structure and

the distributed processing of 1 above is shared among many

image synthesis processors. The result is a simplified

database and a reduction of the amount of geometry required

to render an object. This relieves individual processing

performance requirements of each object generation node,

thus allowing modest processors, e.g., off-the-shelf VLSI,

to perform their image synthesis tasks. Thus, OGNs do not

have to be the same type. The decoupling of the rendering

process from the compositing process is done though

independent memory areas; this enhances system performance

by keeping both processes running in parallel. The system

expansion is eased, since it is done by merely adding

additional CPNs and OGNs. New graphics primitives can be

easily added to the system by additional OGNs that have

special hardware. The basic goal, which may raise load

balance issues, is to add more processors when performance

demands increase. The system understanding is simplified,

since the complex task of merging many objects is done

through the generic machine structure.

An underlying advantage is the trivial pixel level

solution to the intersection problem. A solution to a set

of simultaneous equations is usually done to solve the











intersection of two or more surfaces. This would require a

large amount of calculations. The pixel level approach of

this new architecture reduces the geometry that is

typically involved for solving intersection problems to the

comparison of depth values. The solution is an approxima-

tion, however it is visually correct. Also, the hidden

surface problem is solved in a similar pixel level manner.

Since reflectivity is handled by a mixing factor, the

opaque, transparency, semi-transparency and edge-anti-

aliasing problems associated with computer graphics are

also consolidated to the pixel level. Along with this is

the inclusion, at the pixel level, of the atmospheric

attenuation effects. Thus, a compact pixel-by-pixel method

allows the solution to complex geometrical problems and the

inclusion of complex realistic image effects.

This organization will allow a full range of CGI

systems that demand different performance requirements to

be accommodated through one basic set of modules. It will

be a generic structure that can grow with technological

advances. System improvement is accommodated by adding

modules as opposed to a system redesign that is usually

associated with typical real-time CGI systems. Thus, in

contrast to current fixed performance brute-force real-time

CGI architectures, a variable performance and expandable

real-time CGI architectural approach is presented here.












Target Applications

Target applications of this device will not be

restricted to any specific real-time simulation task, i.e.,

vehicle simulation. A goal of this research is to extend

the architecture for inclusion of.other real-time simu-

lation applications, e.g., process and system simulations.

It will be a general purpose framework to simulate many

things, in real-time, with visual output.

In short, the object generation nodes can be thought

of as processing logical objects. Objects can be a single

item or a collection of items. For instance, an object is

abstract: blade of grass, total field of grass, or physical

object. Therefore, some or all of the tasks of simulation

can be moved to each object, so long as these tasks are

separable. However, the tasks do not have to be cleanly

separable. For instance, overlaps could exist, which would

be resolved in compositing. This would allow simple

splitting of some objects into two somewhat overlapping

ones without the need of calculating new intersections due

to an artificial division cut. Also, true-color, pseudo-

color, or both can be applied for the visual simulation

with respect to the problem domain.

















CHAPTER IV
COMPOSITING NETWORK


The compositing network (CN) is a hardware compositor

that produces a computer graphics picture through blending

heterogenously rendered objects into a full image. These

separately rendered objects are reductions of a total

modeled environment into pieces that rely on compositing

techniques for accumulation. Each object is produced by an

individual object generation node (OGN), which is in itself

a computer image generation device. The network configura-

tion is in the form of a synchronous feed-forward tree that

is connected to a multiplicity of object generation nodes

(OGNs) for input and to a single video generation node

(VGN) for output. Therefore, many object images are com-

posited simultaneously. The composite of additional object

images is done through enlarging the compositing network

and through including additional object generation nodes.

There is no fixed configuration, but rather a general

framework to configure a compositing network utilizing a

collection of basic building blocks, called compositing

processing nodes (CPNs).

The compositing network operation requires the simul-

taneous input of all instances of pixels with the same X











and Y cartesian coordinate per unit time. Each instance of

a pixel is part of an individual object rendered by an

object generation node. These pixel values flow in a

synchronous feed-forward manner through the compositing

network, while being merged pixel-by-pixel at particular

stages. The last stage of the network provides a single

surviving pixel as output, which has an implied X coordi-

nate and Y coordinate.

To summarize, the compositing process is carried-out

pixel-by-pixel through three steps: 1) every pixel value is

simultaneously read from each image array of the object

generation nodes at a specified X coordinate and Y coordi-

nate, 2) the compositing process operates on the collection

of pixel values read from the OGNs to produce a single

composite pixel resultant, and 3) the single composite

pixel resultant is written to the resident image array of

the video generation node at the same X coordinate and Y

coordinate used for the read operation. This process is

repeated at every X coordinate and Y coordinate of the

image array to produce every composite pixel value of the

image array within the video generation node.

The entire compositing network action, for each

collection of pixels, can be generally characterized by


Pc = oper(P1, P2, P3,..'* Pi) (1)

at every pixel with identical X, Y cartesian coordinates in











the i image arrays. The value Pc represent a single sur-

viving pixel after compositing. The "oper" operator is a

general operation that symbolizes the compositing action

due to the entire compositing network. Specifics of the

compositing algorithm that the compositing network realizes

are developed and described in the following sections.


Compositing Methodology

Guidelines for the generation of 2-D pictures and

arithmetic for their 2-D compositing were discussed by

Porter and Duff [POR84]. Their compositing method produced

antialiased composite images through a pixel-by-pixel

process. The antialiased composite or antialiased blending

of images requires information about the subpixel overlap

and object opacity. This information, as discussed by

Porter and Duff [POR84], is given by adding a mixing factor

to the color channels, which is called an ALPHA value.

Therefore, a pixel is defined by four independent varia-

bles: RED, GREEN, BLUE, and ALPHA. Thus, the interplay of

alpha values must be considered for compositing objects to

accumulate a final image [POR84].

The ALPHA portion of an object representation provides

two pieces of information for compositing: 1) the single

ALPHA value represents the extent of coverage of an object

within a pixel and 2) the collection of ALPHA values repre-

senting an object provides coverage information that desig-

nates the shape of an object within the image space. The












pixel coverage information provides a mixing factor to

control linear interpolation of foreground and background

colors at every pixel. The object shape information, which

is termed a matte, identifies the object from what is not

the object within an isolated image array.

The ALPHA value represents the opacity of a pixel,

which is a fractional value that ranges from zero to one.

The antithesis of ALPHA, which is the transparency of a

pixel, is defined as (1-ALPHA). Therefore, the transpar-

ency value also ranges from zero to one. Figure 4-1 illus-

trates this coverage information, pictorially, for three

distinct coverage types of opacity: no coverage, full

coverage, and partial coverage. As shown, no coverage is

indicated by an ALPHA value of zero, full coverage is

indicated by an ALPHA value of one, and partial coverage is

indicated by a fractional ALPHA value between zero and one

[POR84].

The pixel coverage information consists of an average

value of opacity. Therefore, the subpixel distribution of

opacity is not known or, in other words, the subpixel shape

is not known. Thus, some pixel coverage information is

missing, but the ALPHA value information is still useful

for rendering transparent objects, semi-transparent ob-

jects, and performing non-commutative object edge anti-

aliasing for rendering opaque, semi-transparent, or trans-

parent objects. Also, since the ALPHA value represents















ALPHA = 0


a) No Coverage


ALPHA = 1


b) Full Coverage


0 < ALPHA < 1


c) Partial Coverage
(arbitrary depiction)


Figure 4-1. Three distinct types of pixel coverage, with
respect to the ALPHA value: a) no coverage, b)
full coverage, and c) partial coverage. The
subpixel shape of the pixel with partial
coverage is arbitrary and is only shown in
this manner for conceptual clarity.












the average coverage of an object within a pixel, the pixel

color is determined by the product of ALPHA and the

object's true color.

Porter and Duff [POR84] discussed many operators for

the compositing of two-dimensional images. The operator

of interest to this research is the "over" operator. This

operator computes a composite pixel color due to one pixel

in front of another. The composite pixel color is given by


cc = Cf + (1 Af)cb (2)


and the composite opacity


Ac = Af + (1 Af)Ab (3)


where c denotes one of three tri-stimulus color values, A

denotes the opacity value ALPHA, the subscript c denotes

the composite, subscript f denotes the foreground, and

subscript b denotes the background. Also, the true fore-

ground color Cf is multiplied by the foreground opacity Af

to produce cf and the true background color Cb is multi-

plied by the background opacity Ab to produce cb. This is

done to keep the computation of cc similar to the computa-

tion of Ac. The derivation of the "over" operator is

presented by Porter and Duff [POR84]. A similar develop-

ment of "over," adjusted for this research, is presented

in the following section of this chapter.












Porter and Duff's approach has a drawback of requiring

the priority of images to be manually entered. Therefore,

Duff [DUF85] introduced the depth variable, Z, as an ex-

tension to the earlier image composition algorithm to

correct this drawback. The approach extended each pixel

in the image space to contain five independent variables:

RED, GREEN, BLUE, ALPHA, and Z. From this representation

an RGBAZ algorithm was developed that combined the "over"

operator of Porter and Duff [POR84] with a Z-buffer algo-

rithm. Before discussing Duff's [DUF85] approach, the Z-

buffer algorithm is presented and discussed.

A Z-buffer is a depth buffer that stores the Z car-

tesian coordinate, which is also termed the depth coordi-

nate, of every visible pixel in image space. It is used in

conjunction with a frame buffer, which is an attribute

buffer that stores the intensity of each pixel in image

space. A Z-buffer algorithm is a hidden-surface algorithm

that operates on the RGB intensity information and the

depth coordinate, Z, stored at each pixel in image space.

The Z-buffer algorithm is described by Catmull [CAT74]. It

functions by comparing the depth value of a new pixel,

which is to be written into the frame buffer, with the

depth value of the pixel that is currently stored in the Z-

buffer. If the comparison indicates that the new pixel is

closer to the viewpoint than the current pixel, then the

new pixel's intensity value is written into the frame












buffer and its depth value is written into the Z-buffer

[ROG85]. If the comparison does not indicate the new pixel

is closer to the viewpoint than the current pixel, then the

current pixel values remain in the frame buffer and in the

Z-buffer.

To recapitulate, the Z-buffer algorithm is a search

over X, Y in 3-D space for the value of Z(X,Y) that is

closest to the viewpoint in image space. The Z-buffer

operation can be defined as RGBZ = zmin(L,M), where L is an

image array, M is an image array, and RGBZ is the survivor

pixel from either M or L according to the algorithm. The

collection of resultant RGBZ survivors over X, Y produces

an image space that is a composite image of the rendered

objects. This composite operation [DUF85] is more com-

pactly characterized as


Zc = zmin(ZL, ZM) (4)

RGBc = RGBL, if ZL = zmin, else RGBM (5)


at every pixel in the two image arrays. The subscript c

denotes the composite. Two properties of the "zmin" oper-

ator is that it is both commutative and associative.

The Z-buffer algorithm allows pixels to be written

into the frame buffer in arbitrary order. Therefore, the

computation time associated with a depth sort operation is

eliminated [ROG85]. Unfortunately, the algorithm has

inherent aliasing problems due to its point sampling nature












[DUF85]. It also fails for rendering transparent objects,

but it is fast and simple [CAR84].

Duff's approach utilized the depth value at each of

the four corners of a pixel to compute a fraction called

BETA. This value is computed through linearly interpolat-

ing the four depth corner values. The composite color is

computed by


cc = B(cf over cb) + (1 B)(cb over cf) (6)

and

Zc = min(Zf, Zb) (7)


where c denotes one of three tri-stimulus color values

multiplied by its respective opacity value, Z denotes the

depth value, B denotes Duff's BETA value, the subscript c

denotes the composite, subscript f denotes the foreground,

and subscript b denotes the background. This approach

combines the pixels by area sampling. A drawback of this

3-D compositing approach and of the previously discussed 2-

D compositing approach is that they do not apply when the

edges of more than one object are projected onto a single

pixel. The compositing algorithm developed in this re-

search, which is discussed in the following section of this

chapter, addresses this problem.

Another interesting approach to compositing was dis-

cussed by Carpenter [CAR84], with the introduction of the

A-buffer. An A-buffer is an antialiased hidden surface












mechanism that is an enhancement to the Z-buffer through

inclusion of a mask that contains subpixel coverage infor-

mation. Therefore, the mask provides more pixel coverage

information than the ALPHA value, but it is more memory

intensive.

The compositing techniques specified in the reviewed

literature had specific idealic objectives, which are

listed as follows:


1. Must not induce spatial aliasing in the image,

which implies that soft edges of objects must be

respected in computing the final image [POR84].


2. Provide facilities for arbitrary dissolves, fades,

darkening, and attenuation of objects [POR84].


3. Exploit the full associativity of the compositing

process, which implies accumulation of several

foreground objects into an aggregate foreground can

be inspected over different backgrounds [POR84].


4. Allow various object representations: transparent,

semi-transparent, and opaque [POR84].


5. Visibility technique must support all conceivable

geometric modeling primitives: polygons, quadrics,

patches, fractals, and so on [CAR84, DUF85].












6. Must handle opaque intersecting surfaces and trans-

parent intersecting surfaces [CAR84].


7. Must handle hidden surface removal [CAR84, DUF85].


The proposed new architectural approach attempts to

satisfy these compositing technique objectives. Unfortu-

nately, due to trade-offs taken to keep the approach within

hardware limits, some of these objectives are not entirely

met. The constraints and trade-offs associated with the

approach addressed through this research, which concern the

stated idealic objectives, are discussed in later sections

and chapters.


RGBAZ Compositing Algorithm

The proposed compositing method is developed to allow

any number of images to be composite with hidden surface

removal and antialiasing. The compositing algorithm real-

ized by the compositing network is based on Porter and

Duff's [POR84] "over" operator, but is modified through the

introduction of the depth value. This rendition modifies

the "over" operator through incorporating the "zmin" oper-

ator for identifying the foreground pixel from the back-

ground pixel. The algorithm is labeled an RGBAZ algorithm,

as was Duff's [DUF85], but differs from that formulation.

It is developed and described in the subsequent paragraphs.

Consider opacity values, A1 and A2, belonging to a

pair of semi-transparent pixels, P1 and P2, that have












identical X and Y coordinates, but differ in the Z coordi-

nate where the Z1 value is less than that of the Z2

value. The composite Z value for this situation, in ac-

cordance with the Z-buffer algorithm utilizing Equation 4,

is given by


Zc = Z1 (8)

where Z denotes the depth value, and subscript c identifies

the composite resultant.

The depth comparison identifies pixel P1 as being

closer to the viewpoint than pixel P2. Therefore, pixel P1

is identified as the foreground pixel and pixel P2 is

identified as the background pixel. The opacity represen-

tation designates the opaqueness of pixel P1 as A1 and its

clearness as (1 AI). Likewise, the opaqueness of pixel

P2 is A2 and its clearness is (1 A2). This implies that
the composite opacity, according to the "over" operator, of

the two pixels is given by


Ac = Al + (1 A1)A2 (9)


where A denotes the opacity value. An example of this

situation is depicted in Figure 4-2.

The composite color is calculated by realizing that

pixel P1 allows (1 AI) of its background light through

and reflects A1 of its color. Likewise, pixel P2 allows (1

- A2) of its background light through and reflects A2 of


















I
A2 (1


I I
A1 (1-A


I I
A1 (1-A 1


Figure 4-2.


Background Object
(partial pixel coverage)




-A 2)





Foreground Object
(partial pixel coverage)




1)





Composited Objects
(shared partial pixel coverage)




N2 (1-A 1 )(1-A2)


Two pixel opacity values are composite. The
values were derived from coverage information
from two different objects. The coverage
depictions are arbitrary, they are given
specific subpixel forms to clarify the
composite operation. The coverage areas are
actually averaged across the pixel.













its color. Therefore, P1 reflects A1 of its color and lets

(1 A1) of P2's reflected color through. This implies

that the composite color, according to the "over" operator,

of the two pixels is given by


cc = A1C1 + (1 A1)A2C2 (10)


where C represents the tri-stimulus colors: RED, GREEN, and

BLUE. The upper case C is used to designate the true

color, which occurs when the pixel is 100% overlapped by

the object. The lower case color c depicts the true color

value multiplied by its opacity value, which is given by


cc = AcCc (11)


A similar argument follows, as presented above, when

Z2 is less then Z1. For this condition, substitute pixel

subscript identifiers "2" for "1" and "1" for "2" in the

development presented above. The composite depth, opacity,

and color would then be given by


zc = z2 (12)

Ac = A2 + (1 A2)A1 (13)

cc = A2C2 + (1 A2)A1C1 (14)

respectively.

The incorporation of the "zmin" operator with the

"over" operator requires an additional development for the

effects of two pixels with equal depth values. This condi-












tion implies that two objects are occupying the same voxel

in space. Therefore, both objects contribute to the in-

tensity of the resultant pixel, but the intensity contribu-

tion due to each of these objects is nebulous. This

condition can be understood by considering the quantization

error due to the use of finite depth values. The opacity

contributions from the input pixels may be due to pixel

overlap. But, the foreground and background object can not

be discerned, since the difference in depth is within the

limits of the quantization error.

The development of this condition will consider the

pixel as a small cubic volume, instead of a small surface.

This model will allow the edges of two objects to be

projected into its space. The viewable or reflective front

surface of this small cubic volume is only of interest for

determination of the opacity and color values.

The composite opacity is found by first considering

the condition, Z1 < Z2, where (Z2 Z1) is within the

quantization error. The composite opacity would then be

equal to Equation 9. Now, consider the condition, Z1 >

Z2, where (Z1 Z2) is within the quantization error. The

composite opacity would then be equal to Equation 13. The

probability of either of these conditions occurring within

the small cubic volume are equal. Therefore, the composite

opacity and color values are computed through a simple

average of the two possible conditions, which are given by













Ac = [(A1 + (1 A1)A2) + (A2 + (1 A2)A1)]/2

= Al + A2 A1A2 (15)


and


cc = [(A1C1 + (1 A1)A2C2) + (A2C2 + (1 A2)A1C1)]/2

= A1C1 + A2C2 (C1 + C2)A1A2/2 (16)


Also, the composite depth is given by


Zc = Zi = Z2 (17)


It is interesting to note that Equations 9, 13, and 15 are

equal.

Boundary analysis of Equation 16 is performed to check

its validity, which is presented as follows:


Cc = A1C1, if A2 = 0 (18)

Cc = A2C2, if A1 = 0 (19)

Cc = (C1 + C2)/2, if A1 = A2 = 1 (20)

The first two boundary examples demonstrate a reduction to

a single pixel case, which is to be expected. The last

boundary example reduces to an average color that does not

become amplified, which is also to be expected. A psueoo-

code outline of this RGBZA compositing algorithm with

respect to a pair of image arrays is given in Figure 4-3.

As shown, each pixel of the two image arrays are compos-

ited to produce a composite image array for display. The



















RGBZA Compositing Algorithm
given
An array RGBZAl[x,y]
An array RGBZA2[x,y]
An array rgbZAc[x,y]
begin
for each element(x,y) of array rgbZAC[x,y] do
AC = Al + A AIA2
f Z1 < Z2 henA
rc = A1R1 + (1-A1)A2R2
gc = AG1 + (1-AI)A2G2
bc = AiB1 + (1-AI)A2B2
Z = Z1
endif
if > Z2 then
rc = A2R2 + (1-A2)A1R1
c = A2G2 + (1-A2)A1G1
bc = A2B2 + (1-A2)A1B1
Z = Z2
endif
if Z = Z2 then
rc = AIR1 + A2R2 (R1 + R2)AIA2/2
gc = A1G1 + A2G2 (GI + G2)A1A2/2
bc = A1B1 + A2B2 (B1 + B2)AIA2/2
Z = Z1
endif
endfor
Display rgbc array of the rgbZAc array
end


Figure 4-3. The RGBZA Compositing Algorithm.












composite opacity and depth values are not needed for

display; they are included so that the resultant image

array can be composite with other image arrays. This

subject is discussed in the following section.


Network Structure

The compositing operation described in the previous

section dealt with compositing two pixels, each produced

from two separate objects, to form a single composite pixel

as a result. A method of compositing many pixels, where

each pixel is produced from many objects, would be to

create a hierarchy of compositing operations. At the

bottom of the hierarchy, compositing operations would

simultaneously accept pixel values from separate image

arrays as input. The multiple outputs of the bottom level

in the hierarchy would be used as inputs to the next level

in the hierarchy. This process would continue until an

individual output is produced at the top of the hierarchy

of compositing operations. The result would be a composite

pixel value of every pixel value used as input to the

lowest level of the hierarchy. This composite pixel value

would then be written into an image array at the same X, Y

coordinate that was used for the input pixels. The same

procedure would be done for all succeeding composite pixel

value outputs of the hierarchy, which would produce a

complete composite image array of many objects.












A hardware synthesis of the hypothetical hierarchy of

compositing operations is what defines the compositing

network. It is created through interconnecting an ensemble

of fundamental hardware compositing units that realize the

compositing operation. These units are termed compositing

processing nodes (CPNs). The defined function of a CPN is

to produce a single composite pixel value from a pair of

input pixel values. It maintains a 2-to-1 configuration,

where the output of one CPN can supply an input to a suc-

ceeding CPN. This is an iterative property, which is the

property required to realize the hierarchy of compositing

operations in hardware. The structure of the entire

compositing network is driven by the structure of an

individual CPN. Therefore, the interconnection of CPNs

forms a binary tree, which realizes the compositing net-

work. A depiction of this structure is shown in Figure 4-

4, which illustrates a fully balanced 3 level compositing

tree that has 7 CPNs and 8 connections for deeper CPN

levels or for terminal OGN connection. The general struc-

ture for a fully balanced tree with N terminal connections

maintains n=log2N levels with N-l CPNs for the network

configuration. However, the compositing network does not

have to be a fully balanced tree. It can be unbalanced as

long as all of the OGNs are connected at the same level

within the system tree.











To Video Generation Node (VGN)


Level 1









Level 2









Level 3


1 2 3 4 5 6 7 8

From deeper levels of Compositing Processing Nodes (CPNs)
or from eight Object Generation Nodes (OGNs)


Figure 4-4.


A fully balanced three level compos-
iting tree.












The compositing network can be modeled as a pipelined

machine, where each level in the system's binary tree

structure is a pipeline stage. At every machine cycle, a

collection of pixels, with identical X, Y coordinates, are

routed to the nodes within the lowest level of the system

tree. The machine operation proceeds in a synchronous

feed-through manner for every machine cycle, where a col-

lection of pixels at a particular level in the system tree

is computed to produce a collection of composite pixel

values as a result. These results are routed, before the

next machine cycle, to the inputs of a succeeding level in

the system tree. Therefore, each succeeding level in the

system tree produces half the amount of pixel values (fully

balanced tree) then were provided for input. The output of

this machine provides a single composite pixel value as a

result, which is produced from the highest level of the

system tree.

This structure is classified as a synchronous feed-

forward configuration, where CPN operation is synchronous

with the image update rate. Therefore, the machine cycle-

time is a function of both the image space resolution and

the image update rate. The pipeline is considered full

when every CPN in the system tree has a valid input.

During a full pipeline state, each level of the tree is

processing a set of pixels that have identical X, Y coordi-

nates. Therefore, the start-up time through a tree will be











a function of the tree depth and the number of pipeline

stages within an individual CPN.

The effect of the feed-through structure, of the

compositing network, has to be considered regarding the

RGBZA algorithm. This structure has a cumulative affect

that directly influences the compositing operation. There-

fore, the RGBZA algorithm has to be adjusted to accommodate

this fact.

The compositing network is a subtree of the system

tree and the OGNs are terminal nodes of the system tree

that provide input to the compositing network. Now, con-

sider the evaluation of the composite opacity value from a

fully balanced system tree with i CPNs and i+l OGNs, where

the total number of tree nodes is 2i+l. The CPNs are

located at binary tree positions 1 through i. The OGNs are

located at binary tree positions i+l through 2i+l. Note

that a fully balanced system tree is used to simplify this

development. However, the system tree can be unbalanced to

accommodate a collection of OGNs that are not a binary

multiple. The criteria is for all of the OGNs to exist at

the same level within the system tree. This subject is

discussed further in the system features discussion of the

conclusion. For the fully balanced system tree, the

composite opacity defined at the first CPN or root node,

1, to the last CPN, i, for all cases, is given as follows












Al = A2 + A3 A2A3

A2 = A4 + A5 A4A5
A3 = A6 + A7 A6A7


Ai = A2i + A2i+l A2iA2i+l (21)

where the subscript identifies the tree node number. The

result is a recursive relation for the evaluation of the

opacity value. The composite color value and depth value

are defined through the use of a similar development for

each of the three depth value comparisons. The condition

Z2i < Z2i+l gives

Zi = Z2i (22)

ci = c2i + (1 A2i)c2i+l (23)

and the condition Z2i > Z2i+l gives


Zi = Z2i+l (24)

ci = c2i+l + (1 A2i+l)c2i (25)

and the condition Z2i = Z2i+ gives


Zi = Z2i = Z2i+1 (26)

ci = c2i + c2i+l (A2ic2i+l + A2i+lc2i)/2 (27)

where the lower case color "c" depicts the true color value

multiplied by its opacity value. This form of the compos-

iting functions require each color value entering the











compositing network to be multiplied by its respective

opacity. Also, each composite color value exiting the

network will be the composite color multiplied by its

composite opacity.

The recursive relations are handled by iterative

techniques utilizing CPNs. The RGBZA compositing algorithm

that each CPN should execute is depicted in Figure 4-5.

This algorithm, which is termed the general RGBZA compos-

iting algorithm, includes the image arrays and the multi-

plication operation of the OGN's. It also includes the

image array of the VGN and a reference to the DDN. The

second loop within the main loop is the actual network

algorithm. This task inputs a collection of pixel values

for processing, according to their respective depth re-

lationship, to produce a single surviving composite pixel

value for output. The loop counts down in order to obviate

the start-up time that would be associated with a hardware

pipeline.

The operation of the entire compositing network action

is reduced to a special case when only opaque objects are

involved without the inclusion of special effects (e.g.,

dissolves, darkening, antialiasing, etc.). This is given

as follows


{Z2i, if Z2i < Z2i+l
c = Z2i+l if Z2i > Zi+l (28)
(Z2i, if Z2i = Z2i+













General RGBZA Compositing Algorithm
const
n = total number of CPNs in tree
given
Array rgbZAi, where i=1,2,3,...,2n+l {node registers}
Array RGBZAjy, where j=l,2,3,...,n+l {OGN Memory}
Array rgb x' {VGN Memory}
begin
for each element(x,y) of RGBZA8 x and rgby do
for i=n+l to 2n+l do {load 6N'utput registers}
j =i-n
ri = AjYjY

A = Aj=
-i -jx,yGjIx~y

end or {end load OGN output registers}
for i=n downto 1 do (CPN compositing operation)
A = A2i + A2i+ A2i(A2i+)
if Z < 22i+1 then
ri =r2i + (l-A2i)r2i+l
gi= g2i + (1-A2i)92i+l
bi = b2i + (l-A2i)b2i+l
Zi Z2i
endif
if Z2i > Z2i+l then
i = r2i+l + (l-A2i+l)r2i
gi = g2i+1 + (1-A2i+1)92i
bi = b2i+l + (l-A2i+l)b2i
Zi Z2i+l
endif
if Z2i = Zi+l then
ri = r2i + r2i+l (A2ir2i+l + A2i+lr2i)/2
i = g2i + g2i+ (A2ig2i+l + A2i+192i)/2
bi = b2i + b2i+l (A2ib2i+l + A2i+1b2i)/2
Zi = Z2i
endif
endfor {end CPN compositing operation}
rgbxy = rgbi {write composite result to VGN}
endfor
Display rgbxy array {DDN}
end



Figure 4-5. The general RGBZA compositing algorithm for a
fully balanced tree. Note that lower case
letters designate the product of intensity and
opacity.












C2i, if Z2i < Z2i+
C= {C2i+1 if Zi > +1 (29)
{(C2i + C2i+1)/2, if Z2i Z2i+1

at every pixel in the i+l image arrays. The composite

pixel has either full coverage or no coverage. Therefore,

the opacity information is not needed. Also, the matte

information is implied by a depth value that is not the

maximum. The specialized RGBZ algorithm is presented in

Figure 4-6. As for Figure 4-5, the second loop within the

main loop is the actual network algorithm. This task

inputs a collection of pixel values for processing, ac-

cording to their respective depth relationship, to produce

a single surviving composite pixel value for output. A

mixture of both the specialized and the general forms of

the compositing algorithm for CPNs can compose a

compositing network. The OGNs can be specialized for

opaque objects without antialiasing and special effects.

These nodes would be assigned to the section of the tree

that contain the specialized CPNs. Also, OGNs that process

objects with antialiasing and special effects can be

assigned to the section of the tree that contain the

general CPNs. Configurations could include a mix of

general and specialized CPNs. The purpose of mixing CPNs

would be to reduce the system complexity, since the

specialized CPNs are of a simpler form than the general

CPNs.















Specialized RGBZ Compositing Algorithm
const
n = total number of CPNs in tree
given
Array RGBZi, where i=1,2,3,...,2n+l {node registers)
Array RGBZj ,,, where j=l,2,3,...,n+l {OGN Memory)
Array RGBxy {VGN Memory)
begin
for each element(x,y) of RGBZ and RGB do
for i=n+l to 2n+l do {load 6GN output re4gsters)
j =i-n
Ri = R
Gi = Gj,x,y
Bi =Bjx,y
B = B*'x'Y
i ),x,y
Z = Z.
end or {end load OGN output registers)
for i=n downto 1 do {CPN compositing operation}
if Z2i < Z2i+l then
Ri = R2i
Gi = G2i
Bi = B2i
zi = Z2i
endif
if Z2i > Z2i+ then
Ri = R2i+1
Gi = G2i+1
Bi = B2i+
Z = Z2i+
endif
if Z2i = Z2i+ then
Ri = (R2i + R2i+i)/2
Gi = (G2i + G2i+i)/2
Bi = (B2i + B2i+i)/2
Z = Z2i
endif
endfor (end CPN compositing operation)
RGBy = RGB1 {write composite result to VGN}
endfor
Display RGBx y array {DDN}
end





Figure 4-6. The specialized RGBZ compositing algorithm of
a fully balanced tree.













Compositing Processing Node

The purpose of a CPN is to perform pixel-by-pixel

compositing. It is a fundamental iterative hardware build-

ing block used to construct a CN tree. A generic CPN

configuration is depicted in Figure 4-7. The subscript "i"

is a node number that identifies a node within the system

tree, which consists of CPNs, OGNs, and a VGN. The CN is a

subset of the system tree that contains only CPNs. The

OGNs are the terminal nodes of the system tree. The VGN is

connected to the root node of the CN and is identified

through node number zero of the system tree. As shown, the

CPN structure maintains a 2-to-1 configuration. The data

inputs consists of two pixel values P2i and P2i+lr which

can be routed to the CPN by either two preceding CPNs or by

two preceding OGNs. The data output consists of a single

pixel value, which can be routed to the input of a suc-

ceeding CPN or to the input of a video generation node.

The CPN input clock, CLK, is driven by a system clock that

synchronizes the internal CPN operation with the entire

system. This signal is provided by the video generation

node (VGN), which maintains the entire system timing and

control.

A pixel is represented by five independent variables:

RED, GREEN, BLUE, ALPHA, and Z. The tri-stimulus color or

intensity is represented by the values of RED, GREEN, and

BLUE. The ALPHA value represents the average opaqueness of












Pixel output to next
stage of system tree


System
Clock
From
VGN


Pixel input from Pixel input from
previous stage previous stage
of system tree of system tree
where,
P. ={ri, g bi, Ai, Zi}

P2i ={r2i' 2i, b2i A2i Z 2

P2i+1 ={r2i+1 g 2i+1' b2i+1, A 2i+1' Z2i+1
CPNi is a CPN located in the CN at node position "i."

CLK is the system timing input.


Figure 4-7.


An iterative building block depiction of a
compositing processing node (CPN).













the pixel or the average light blocking characteristic of

the material that the pixel represents. The Z value repre-

sents the Z coordinate, in cartesian space, where the pixel

exists. The X, Y cartesian coordinates are implied as

identical for both input pixels, but may be different

within the same clock cycle for the single output pixel due

to the hardware pipeline approach.

Schemes for realizing the previously discussed RGBAZ

compositing algorithms are developed that are fast and

inexpensive to implement in hardware, but which produces

results of numerically high quality. These schemes honors

two considerations: machine and numerical considerations.

Machine considerations concern speed and cost of the physi-

cal device. Numerical considerations concern the closest

approximations to the exact numbers. The schemes attempt

to maintain a balance between both. Also, the effects of

roundoff error accumulation due to the feed-through opera-

tion of the binary tree of CPNs are taken into consider-

ation.

Finite precision fixed-point numbers are used in this

machine for representation of the pixel values. This

representation allows storage of pixel values within the

local image buffers of the OGNs and of the VGN to be inte-

gers, which simplifies the image buffer organization.

Also, the hardware complexity for realization of the com-

positing algorithms and of the video generation processing












algorithms is reduced, along with accommodation of faster

cycle times for an implementation. Therefore, the compos-

iting algorithms that are depicted in Figures 4-5 and 4-6

must be adjusted to accommodate the fixed-point repre-

sentation of a pixel value, which relates to the machine

precision of a number represented within and operated by a

CPN.

The tri-stimulus color variables RED, GREEN, and BLUE,

are usually represented in rendering algorithms as fixed-

point numbers. Therefore, they do not create an initial

problem. But, roundoff error amplification can occur due

to the repetitive modification of these values through the

compositing network. Therefore, to enhance the numeric

accuracy of the final result, the roundoff error has to be

controlled. Representation of the opacity value, ALPHA,

presents a similar problem, but differs slightly since its

initial value is defined as a fractional number. The depth

variable, Z, is usually represented within a rendering

algorithm as a floating-point number. The compositing

network handles the depth value as an integer and does not

modify its value, therefore its floating-point value can be

rounded or truncated.

The algorithm modification and the CPN conceptual

hardware organization are discussed in the following

sections. Two CPN organizations are presented: the general

CPN and the specialized CPN. The combinatorial hardware












layout of the conceptual block diagrams consist of breaks

in the logic for registers, termed stages. This is done to

maintain a pipeline of partial operations, which enhances

performance. Maximum system performance is then achieved

by matching the clock cycle to the longest delay through

the slowest stage. The stage delay is calculated by

totaling the delay through the logic and conductors that

exist between the two registers of a stage. Also, the

stage with the longest delay becomes the bandwidth limiting

section.


General Compositing Processing Node

A general CPN performs pixel-by-pixel compositing of

various object types: opaque, transparent, and semi-trans-

parent. It also handles antialiasing and special effects,

such as fade-outs and fade-ins. The hardware organization

contains three distinct functional units: the depth compu-

tation unit, the opacity computation unit, and the color

computation unit. These functional units are discussed

with respect to finite fixed-point pixel value repre-

sentation. The algorithm and the conceptual hardware

organization of each unit is presented.

Depth computation unit

The depth computation unit discerns the foreground

pixel from the background pixel or identifies both as

foreground pixels. This unit functions according to the











algorithm presented in Figure 4-8, which is a subset of the

general RGBZA compositing algorithm of Figure 4-5. The

depth value, Z, is represented by a single z-bit integer,

where 0 S Z < (22-1). Therefore, the floating point repre-

sentation of this value is initially truncated or rounded.

The task performed by this unit, as the algorithm indi-

cates, consists of 1) receiving a pair of depth values, 2)

performing a comparison of depth values, 3) providing

status information, and 4) outputting the smallest depth

value. Status information consists of the LESS bit and

EQUAL bit, which are used by the color computation unit.

The LESS bit, when set, indicates that the Z2i value is

smaller then the Z2i+l value. The EQUAL bit, when set,

indicates that the Z2i value and Z2i+l value are equal in

magnitude.

A block diagram of the CPN depth computation unit is

depicted in Figure 4-9. Stage 1 performs an initial load

of the incoming pair of depth values from the CPN intercon-

nect. Stage 2 performs a comparison of the two depth

values for status information and passes the two depth

values along with the status information. Stage 3 routes

the surviving depth value, which is the composite depth

value, to succeeding stages utilizing a 2:1 multiplexer

with the LESS status bit as a selector. The succeeding

stages are waiting stages that allow a final result to



























CPN Depth Computation Unit Algorithm


given
literal Z2i
literal Z2i+l

begin
EQUAL = 0
if Z2i < Z2i+l then
Z. =Z
ESS =2
else

ii Z 26+1
if Z E = Z2i+1 then
EQUAL = 1
endif
endif
end


{z-bit integer)
(z-bit integer}












{result is a z-bit integer}


Figure 4-8. The algorithm performed by a general CPN depth
computation unit.








































Comparator Symbol
In A In B





V II A

Note: Registers are clocked
at image update rate.


Figure 4-9. Block diagram of a general CPN depth computa-
tion unit.


Z2i Z2i+1












occur simultaneously with the remaining CPN computation

unit results.

Opacity computation unit

The opacity computation unit produces a single com-

posite opacity value from two opacity values that are

provided as input. The opacity is defined as a positive

fractional value that ranges from zero to one. Each opac-

ity value is stored in the image buffers of this machine as

fixed-point binary numbers. Therefore, the opacity value,

A, is represented by a positive fixed-fractional value

given by


A
0 ---- 1 (30)
Amax

where A is a binary integer such that 0 < A < Amax, and

Amax is a constant that defines the range of opacity. The
local image buffers store the integer value, A, while the

fixed-fractional value is incorporated by the hardware.

Substituting the opacity representation of Equation 30 into

Equation 21 and collecting terms, gives


(Amax A2i)A2i+l
Ai = A2i + ---------- (31)
Amax

The division required in Equation 31 is eliminated by

defining Amax as 2m-1, where m is the number of bits in A.

This transforms the division operation to a shift opera-












tion. A trade-off occurs with this technique, since each

image buffer, within the OGNs, will require an extra bit-

plane and an extra signal line to represent the opacity

value for a particular range. Substituting the value of

Amax into Equation 31, gives


Ai = A2i + -----m-------- (32)


In order to have a more accurate result, the hardware unit

represents each opacity value as a higher precision number,

which reduces the roundoff error accumulation through the

compositing network. This is shown by multiplying both

sides of Equation 32 with 2m and adjusting the product

term, which gives

(22m-1 2mA2i)2mA2i+l
2mAi = 2mA ----------------- (33)
22m-1

Equation 33 shows that the opacity value can be handled as

a double precision number, if the opacity value is shifted

left by m bits and if the least-significant-half of the

word is padded with zeroes before entering the CN tree.

Therefore, the opacity computation with the opacity values

defined as double precision numbers is given by

(22m-1 A2i)A2i+1
Ai = A2i + ----22----- --- (34)
22m-1












where the opacity value, Ai, is a binary integer such that

0 < Ai < 22m-l

The opacity computation unit functions according to

the algorithm presented in Figure 4-10, which follows the

developed relations. The task performed by this unit

consists of 1) receiving a pair of opacity values, 2)

performing an opacity compositing operation, and 3) output-

ting the composite opacity result.

A block diagram of the compositing computation unit

is depicted in Figure 4-11. Stage 1 performs an initial

load of the pair of opacity values from the CPN intercon-

nect. Stage 2 performs a subtraction operation and passes

the two opacity values along with the subtraction result.

Stage 3 performs a multiplication of the subtraction

result with the A2i+l opacity value and shifts the multi-

plication result right by 2m-2 bits (division). It also

passes the A2i opacity value along with the shifted multi-

plication result. Stage 4 sums the A2i value with the

shifted multiplication result and performs rounding, which

produces the composite opacity. Note that eliminating the

signal input to the carry bit and setting the carry bit to

0 will cause chopping of the multiplication result, instead

of rounding. The succeeding stages are waiting stages that

allow a final result to occur simultaneously with the

remaining CPN computation unit results.

























CPN Opacity Computation Unit Algorithm

const
m = number of bits of initially stored opacity value

given
literal A2i (2m-bit integer}
literal A2i+1 {2m-bit integer)

begin
Ai = A2i + [(22m-1 A2i)A2i+1] shr 2m-l

if [(22m-1 A2i)A2i+ AND 22m-2] = 22m-2 then
Ai = Ai + 1 (roundoff error)
endif
end {result is a 2m-bit integer)



















Figure 4-10. The algorithm performed by a general CPN
opacity computation unit.












A2i A2i+1


22m-1


A2i
A2i+1


LSB


Note: Registers are clocked
at image update rate.
reg


reg


Aj


Figure 4-11. Block diagram of a general CPN opacity compu-
tation unit.


Adder Symbol
InA InB


Overflow Carry In

Result











Color computation unit

The color computation unit produces a composite color

value from two color values that are provided as input.

The color values are defined as the true tri-stimulus color

values multiplied by their respective opacity value. Each

primary color (intensity) value, c, is stored in the

machine's image buffers as an n-bit integer, where 0 < c <

2n-l. But, this hardware unit handles the opacity and the

color values as higher precision numbers (2m and m+n-1 bits

respectfully) in order to reduce the roundoff error

accumulation through the compositing network.

The composite color operation for the Z2i < Z2+1

condition is developed by substituting the higher preci-

sion representations of both the intensity and the opacity

values into Equation 23, which gives


(22m-1 A2i)c2i+l
ci = c2i + ---- m-----(35)


where each primary color value, c, is defined as an n+m-1

bit value within the CN tree. Therefore, each n-bit prima-

ry color value requires multiplication by the m-bit opacity

value before entering the CN tree. When exiting the CN

tree, each color value requires shifting right by m-1 bits

with rounding or chopping to provide an n-bit result.

The Z2i > Z2i+1 condition is obtained through a simi-

lar development as above, but with the use of Equation 25.












It is given in final form by

(22m1 A2i+l)c2i
ci = c2i+1 + ------2------ (36)



The Z2i = Z2i+ condition is also obtained through a

similar development as above, but with the use of Equation

27. It is given in final form by

(22m-1 A2i+1/2)c2i (A2i/2)c2i+1
ci = c2i+1 + ----------- --- (37)
22m-1 22m-1


Note that the first two terms of Equation 37 are similar to

Equation 36. This reduces the hardware requirement for a

realization.

The color computation unit functions according to the

algorithm presented in Figure 4-12, which follows the

developed relations, where the color triad is represented

by c. The task performed by this unit consists of 1)

receiving a pair of color triads, a pair of opacity values,

and status information, 2) performing a compositing opera-

tion according to the depth comparison, and 3) outputting

the result.

A block diagram of the color computation unit is

depicted in Figure 4-13. Stage 1 performs an initial load

of the incoming pair of color values from the CPN intercon-

nect. Stage 2 is a waiting stage for the status result of

the depth computation unit. Stage 3 routes the color and













CPN Color Computation Unit Algorithm

const
n = number of bits of initially stored intensity value
m = number of bits of initially stored opacity value


given
literal c2i
literal c2i+1
literal A2i
literal A2i+l
literal LESS
literal EQUAL


{m+n-1 bit integer: red, green, or blue)
{m+n-1 bit integer: red, green, or blue)
(2m bit integer)
{2m bit integer)
(1 bit}
(1 bit}


begin
if LESS = 1 then2m 2i < Z2i+1)
ci = c2i + [(22- A2i)c2i+l] shr 2m-1
if [(22m-1 A2i)c2i+l AND 22m-2] = 22m-2
ci = ci + 1 {roundoff error)
endif
else
if EQUAL = 1 then {Z(i = Z2i+I
ci = c2i+ + [(22m- 2i+ sr l)c2i]
[(A2i shr l)c2i+1] shr 2m-1


then



shr 2m-1


if [(22m-1 A2i+1 shr 1)c2i AND 22m-2] = 22m-2 then
c = c, + 1 (roundoff error)
endif 2m-
if [(A2i shr l)c2i+1 AND 22m-2] = 22m-2 then
ci = ci 1 {roundoff error)
endif
else 2m Z2i > Z2i+}
ci = c2i+1 + [(2 A2i+l)c2i] shr 2m-1
if [(22m- A2i+l)c2 AND 22m-2] = 22m-2 then
c = c + 1 {roundoff error)
endif
endif
endif
end {result is an m+n-1 bit integer)






Figure 4-12. The algorithm performed by a general CPN
color computation unit.
















A2i A24~1


LESS
EQUAL


Adder Symbol
InA In B


Overflow + Carry In

Result
Note: Registers are clocked
at image update rate.


Transparency








Figure 4-13. Block diagram of a general CPN color compu-
tation unit.
































TRANSPARENCY


Figure 4-13--Continued

































TRANSPARENCY


Figure 4-13--Continued
































TRANSPARENCY


Figure 4-13--Continued













opacity values according to their depth priority. It also

shifts the routed opacity value right by 1, if the two

depth values are equal. Included is the multiplication of

the c2i+l color value with the halved A2i opacity value.

Also, the multiplication result is shifted right by 2m-2

bits (division). Stage 4 performs the opacity subtraction

operation and rounds the shifted multiplication result of

stage 3. It also, passes the routed color values, the

EQUAL status bit, and the subtraction result (transpar-

ency). Stage 5 performs a multiplication of the subtrac-

tion result (transparency) with a routed color value along

and passes a routed color value. Included is shifting the

multiplication result by 2m-2 bits (division). It also

routes the rounded value of stage 4, if the two depth

values are equal, but routes all zeroes, if the two depth

values are not equal. Stage 6 sums the shifted multipli-

cation result with the passed color value along with

rounding and passes the multiplexer result of stage 5.

Stage 7 subtracts the multiplexer result from the addition

result of stage 6, which produces the composite color

value.


Specialized Compositing Processing Node

A specialized CPN performs pixel-by-pixel compositing

of opaque objects without antialiasing or special effects.

The hardware organization contains two distinct functional












units: the depth computation unit and the color computation

unit. An opacity computation unit is unnecessary, since

this specialized CPN does not incorporate antialiasing,

semi-transparency, transparency, and special effects.

These two computation units are discussed with respect to

finite fixed-point pixel value representation. The algo-

rithm and the conceptual hardware organization of each unit

is presented.

Depth computation unit

The depth computation unit discerns the foreground

pixel from the background pixel or identifies both as

foreground pixels. This unit conceptually functions iden-

tically to the depth computation unit of the general CPN.

Therefore, it functions according to the algorithm pre-

sented in Figure 4-8. As for the general CPN, the depth

value, Z, is represented by a single z-bit integer, where 0

< Z < (2Z-1). Therefore, the floating point repre-

sentation of this value is initially truncated or rounded.

The algorithm discussion can be found in the general CPN

section.

The block diagram of the depth computation unit is

identical to the unit of the general CPN. Therefore, its

depiction is shown in Figure 4-9. The hardware discussion

can be found in the general CPN section.











Color computation unit

The color computation unit produces a single composite

color value from the pixel values that are provided as

input. The color value, C, is defined as the true tri-

stimulus color values. This machine stores each primary

color (intensity) value in its image buffers as an n-bit

integer, where 0 < C < 2n-1. The color value is passed as

an n-bit integer in the hardware; therefore no shifting is

necessary before entering a specialized CPN. The unit

functions according to the algorithm presented in Figure 4-

14, which follows the relations developed in Equation 29,

where the color triad is represented by C, and each color

is an n-bit integer. The task performed by this unit

consists of 1) receiving a pair of color triad values and

status information, 2) performing a composite operation of

the color triad according to the depth comparison, and 3)

outputting the result.

A block diagram of the color computation unit is

depicted in Figure 4-15. Stage 1 performs an initial load

of the incoming pair of color values from the CPN intercon-

nect. Stage 2 sums both color values along with shifting

the result right by one. It is also a waiting stage for

the status result of the depth computation unit. Stage 3

routes a color triad according to its depth priority

utilizing a 4:1 multiplexer with both the LESS and EQUAL

status bits as selectors. The succeeding stages are



























CPN Color Computation Unit Algorithm


given
literal C2i
literal C2i+l

begin
if LESS = 1 then
Ci = C2i
else
if EQUAL = 1 then
Ci = (C2i + C2i+l)
else
Ci = C2i+1
endif
end


{n-bit integer)
{n-bit integer}


{Z2i < Z2i+)


{z2i =Z2i+l)
shr 1
(Z2i > Z2i+l)


{result is an n-bit integer)


Figure 4-14. The algorithm performed by a specialized CPN
color computation unit.


































LESS -
EQUAL-


Adder Symbol
In A In B



Overflow Carry In

Result

Note: Registers are clocked
at image update rate.


Figure 4-15. Block diagram of a specialized
computation unit.


CPN color






























































Figure 4-15--Continued































LESS -
EQUAL


Figure 4-15--Continued












waiting stages that allow a final result to occur simulta-

neously with the general CPNs. The result is a point

sampled composite color.


Analysis

The compositing network analysis examines two areas:

complexity and performance. Complexity is estimated for

discrete construction, for VLSI fabrication, and for gate-

array construction. Performance is examined with respect

to image space resolution, CPN processing speed, and

compositing network tree depth.


Complexity

The compositing network complexity is a function of

both the CPN complexity and the quantity of CPNs config-

uring a network. CPN complexity is measured utilizing two

metrics: gate count estimate and I/O signal pin count

estimate. The gate count estimate is determined through

partitioning the CPN conceptual hardware organization into

individual functional logic blocks, which are off-the-self

SSI, MSI, and LSI components. Then, the estimated gate

count of each functional logic block is determined and

totaled to provide a gate count estimate of a CPN. This

technique provides an estimate of expected complexity for

integrated circuit fabrication. It also provides an

estimate of board-level complexity for an off-the-shelf

integrated circuit implementation, which is determined











through totaling the functional logic block package types

used. It should be noted that performance is usually

enhanced for a realization by judicious use of additional

gating, which may alter the estimated gate count.

The partitioning of the design into functional logic

blocks allows the examination of implementation trade-offs

that are offered between different technologies. It

reduces the organization to a logic format that can be

matched to the logic resources of a target device. The

hardware synthesis can be individually optimized around

each vendor's library and design rule guidelines for a VLSI

or a gate-array realization.

The functional block equivalent is listed in Table 4-

1, the I/O pin count is listed in Table 4-2, and the gate

equivalent of various standard size functional logic blocks

are listed in Table 4-3. The functional block equivalent

and I/O pin counts were compiled from the conceptual

hardware organizations. The standard logic device gate

counts were estimated by counting the gates within the

functional block diagrams given in TTL data books [FAI84,

SIG84]. The gate count of the 16-bit multiplier was esti-

mated by considering it to be a full adder tree without

input and output registers [KUC78]. This was done since

the input and output registers are taken into account when

estimating gate equivalences of the staging registers.

These gate counts are expected to be close to an upper-









79














Table 4-1. Functional logic block equivalent of the
general CPN and the specialized CPN.

Logic General CPN Specialized CPN
Function DCU OCU CCU DCU CCU

Comparator (z-bit) 1 0 0 1 0

Adder (m-bit) 0 4 8 0 0

Adder (n-bit) 0 0 6 0 3

2:1 Multiplexer z 0 6m+6n-6 z 0

4:1 Multiplexer 0 0 5m+3n-3 0 3n

D Flip-Flop 9z+2 22m+l 52m+48n-34 9z+2 30n

Multiplier (2mX2m) 0 1 0 0 0

Multiplier 0 0 6 0 0
((m+n-l)X2m)

Note: Inverters are not included, since inversion can be
produced through flip-flop output selection.










80


Table 4-2. Pin requirement for the general CPN, the
specialized CPN, and each CPN computation unit.

Signal General CPN Specialized CPN I
Name DCU OCU CCU GCPN DCU CCU SCPN


RED2i

GREEN2i

BLUE2i

Z2i

ALPHA2 i

RED2i+1

GREEN2i+l

BLUE2i+1

Z2i+1

ALPHA2i+1

REDi

GREENi

BLUEi

zi

ALPHAi

CLK

LESS

EQUAL

POWER

GROUND


0 0 m+n-1 m+n-1

0 0 m+n-1 m+n-1

0 0 m+n-1 m+n-1


z 0

0 2m


0 z


0 0 m+n-1 m+n-1

0 0 m+n-1 m+n-1

0 0 m+n-1 m+n-1


z 0

0 2m


0 z


0 0 m+n-1 m+n-1

0 0 m+n-1 m+n-1

0 0 m+n-1 m+n-1


z 0

0 2m

1 1

1 0

1 0

1 1

1 1


0 2m

1 1

1 0

1 0

1 1

1 1


n n

n n

n n


0 z

0 0

n n

n n

n n


0 z

0 0

n n

n n

n n

0 z

0 0

1 1

1 0

1 0

1 1

1 1


total pins 3z 6m 9n 9n 3z 9n 9n
+5 +3 +13m +15m +5 +5 +3z
-4 +3z +3
-6




















Table 4-3. Gate equivalent and package pin count of
various functional logic blocks.

Logic Package Gate
Function Pins Equivalent

4-bit Magnitude Comparator (74F85) 16 31

4-bit Binary Full Adder (74F283) 16 36

Quad 2:1 Multiplexer (74F157) 16 15

Dual 4:1 Multiplexer (74F153) 16 16

Octal D-Type Flip-Flop (74F273) 20 48

16x16 Bit Multiplier (29517A) 64 4320*

This approximate number excludes the input and output
registers, which would account for about 288 additional
gate equivalent units.












bound. The procedure for estimating the total gate count

for a specific design is found utilizing the tables

subsequent to determining the CPN parameter values: m, n,

and z. The total CPN gate count can be estimated for a

different set of functional blocks by changing Table 4-3,

followed by performing the suggested procedure.

A graphics system is defined to exemplify the sug-

gested technique for estimation of CPN complexity. The

graphics device has three criteria: it will be a full-color

system, it will have better than one-percent incremental

change in opacity, and it will have a high-precision depth

resolution. A full-color device requires the tri-stimulus

colors to provide 16.7 million simultaneous colors, which

is about at the human visual perception limits [ROG85].

Therefore, the required value of n is 8, which provides 8

bits for each primary color: RED, GREEN, and BLUE. The

resolution of opacity that would provide better than a

one-percent incremental change requires m to equal 8, since

its range would be 127 (0 < A < 2m-l). The value of z is

selected as 24, since the depth resolution of 24-bits is

satisfactory for high-end graphics devices. Relating these

selected parameter values of m, n, and z with Tables 4-1

through Table 4-3 produces the specified system estimated

complexity, which is presented in Table 4-4.

The general CPN has a complexity of about 12 times

that of the specialized CPN. Therefore, a compositing























Table 4-4. Estimated complexity of the general CPN, the
specialized CPN, and each CPN computation unit.

Type of General CPN Specialized CPN
Count DCU OCU CCU GCPN DCU CCU SCPN

Pins 77 51 172 258 77 77 147

Gates 1585 5670 33362 40617 1585 1848 3433

Packages 40 32 251 323 40 48 88
16-Pin 12 8 149 169 12 18 30
20-Pin 28 23 96 147 28 30 58
64-Pin 0 1 6 7 0 0 0

Note: The CPN parameters for m, n, and z, are 8, 8, and 24.












network that can utilize a mixture of both the general and

the specialized CPNs would be the most efficient configura-

tion. Table 4-4 indicates that a board level CPN imple-

mentation would have a reasonable package count for the

general CPN and a very reasonable package count for the

specialized CPN. This indicates that a CPN implemented

using off-the-shelf parts is within bounds. At the time of

this writing, a 16,000-gate bipolar ECL/TTL array with 100-

ps delays and 292 input/output cells was available [COL88].

Chip densities of HCMOS arrays are as high as 237,000

gates, with 400-ps switching delays [BUR88]. Therefore,

the CPN gate counts and pin counts are within bounds for a

single chip VLSI implementation or a single-chip gate-array

implementation.


Performance

The CPN performs pixel-by-pixel processing that is

independent of scene complexity. Therefore, its pro-

cessing-time is a function of both the image space reso-

lution and the image update rate, which is given by


1
Processing-Time = ----------------------------- (38)
(Image Update Rate)(Resolution)


The image update rate is considered real-time at 10 frames

per second, since images sequenced at this rate appear to

have a smooth visual flow. The image space resolution is

defined as the total number of visible pixels. The CPN













processing-time for various image space resolutions is

presented in Table 4-5. As shown, to double the final

resolution while maintaining the same level of performance,

the speed of the CPNs must be increased by a factor of

four.

The CPNs of the compositing network operate in lock-

step. When the tree structure is maximally unbalanced so

that each node has a left descendant but none has a right

one, the compositing network degenerates into a linear

pipeline. This implies that each stage of the linear

pipeline must perform its function within the CPN pro-

cessing-time to successfully composite a collection of

pixels. Therefore, the slowest stage in the pipeline is

what determines the peak performance of the compositing

network. This is the multiplication stage for the general

CPN, which implies that the multiplier parts are what

determine the compositing network performance if any CPN is

of the general type. In contrast, the comparator stage

determines the compositing network performance if all CPN's

are of the specialized type.

Consider the example of the constraints section, where

all of the CPN's are of the general type. The 16-bit

multiplier, which had been specified, maintains a 45-ns

multiply time (including set-up time) [ADV85]. This part

has internal input and output registers, therefore the

multiply time can be considered the total pipeline stage



















Table 4-5. CPN processing-time for various image space
resolutions. The image update rate is 10
frames per second.

Image Space Resolution CPN Processing-Time
(pixels) (ns)

640 X 480 325.5

1280 X 960 81.4

1280 X 1024 76.3

1600 X 1280 48.8

2048 X 2048 23.8













time. Therefore, the compositing network would have a

maximum bandwidth of 22.2 million results per second. From

Table 4-5, all but the last entry could be supported with a

single compositing network. The last entry could be sup-

ported if two CN's were used, where each CN would be

dedicated to a separate half of the image array, while

operating at half the image update rate.

The computational performance of a compositing network

that is configured with all general CPNs is measured

through calculating the total number of additions and

multiplications that every general CPN performs per unit

time. A general CPN performs, as a lower bound (all Z's

not equal), eight additions and four multiplications. As

an upper bound (all Z's equal), a general CPN performs

eleven additions and seven multiplications. Therefore, the

range of computational performance for a compositing net-

work configured with all general CPNs is given by


8(CPNs)(BW) < additions/s < 11(CPNs)(BW) (39)

4(CPNs)(BW) < multiplications/s < 7(CPNs)(BW) (40)

12(CPNs)(BW) < operations/s < 18(CPNs)(BW) (41)


where BW refers to the general CPN bandwidth or general CPN

results per second. The CPNs refer to the total number of

compositing processing nodes that comprise a compositing

network.











For example, consider an augmentable system archi-

tecture configured with a three level CN tree with all

general CPNs and a 1600 X 1280 resolution display device

node. It will maintain a CN processing performance of

between 1720-MOPS and 2580-MOPS (million operations per

second). This throughput is what supercomputers provide,

which demonstrates the potential of distributed simulta-

neous calculations.

The performance of a CN configured with all special-

ized CPNs is measured through the total bandwidth of the

CN, which is equal to the bandwidth of a unitary special-

ized CPN. This metric is used since specialized CPNs

primarily route data, as apposed to performing a computa-

tion with regards to the data. If all depth values are

equal, each specialized CPN will perform one addition.

This will provide an additions per second rate that is

computed through the product of the number of CPNs

configured and the CPN bandwidth. The performance limiting

stage of a specialized CPN is its comparison stage, but

depending on word size it could be the addition stage

instead.

Consider* the example presented in the constraints

section, but where all of the CPN's are of the specialized

type. The comparison stage, utilizing the components

specified in Table 4-3, maintains a 42-ns propagation delay

from clock to output. Therefore, the system would have a




Full Text

PAGE 1

$8*0(17$%/( 2%-(&725,(17(' 3$5$//(/ 352&(6625 $5&+,7(&785(6 )25 5($/7,0( &20387(5*(1(5$7(' ,0$*(5< %< 5266 0255,6 )/(,6&+0$1 $ ',66(57$7,21 35(6(17(' 72 7+( *5$'8$7( 6&+22/ 2) 7+( 81,9(56,7< 2) )/25,'$ ,1 3$57,$/ )25 7+( )8/),//0(17 2) 7+( 5(48,5(0(176 '(*5(( 2) '2&725 2) 3+,/2623+< 81,9(56,7< 2) )/25,'$

PAGE 2

&RS\ULJKW E\ 5RVV 0RUULV )OHLVFKPDQ

PAGE 3

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

PAGE 4

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

PAGE 5

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

PAGE 6

%,%/,2*5$3+< %,2*5$3+,&$/ 6.(7&+ ? YL

PAGE 7

/,67 2) 7$%/(6 7DEOH 3DJH )XQFWLRQDO ORJLF EORFN HTXLYDOHQW RI WKH JHQHUDO &31 DQG WKH VSHFLDOL]HG &31 3LQ UHTXLUHPHQW IRU WKH JHQHUDO &31 WKH VSHFLDOL]HG &31 DQG HDFK &31 FRPSXWDWLRQ XQLW *DWH HTXLYDOHQW DQG SDFNDJH SLQ FRXQW RI YDULRXV IXQFWLRQDO ORJLF EORFNV (VWLPDWHG FRPSOH[LW\ RI WKH JHQHUDO &31 WKH VSHFLDOL]HG &31 DQG HDFK &31 FRPSXWDWLRQ XQLW &31 SURFHVVLQJWLPH IRU YDULRXV LPDJH VSDFH UHVROXWLRQV 7KH LPDJH XSGDWH UDWH LV IUDPHV SHU VHFRQG YLL

PAGE 8

/,67 2) ),*85(6 )LJXUH 3DJH %ORFN GLDJUDP RI D W\SLFDO UHDOWLPH &*, V\VWHP RUJDQL]DWLRQ &RPSRVLWLRQ RI DQ RSDTXH EDFNJURXQG REMHFW DQG DQ RSDTXH IRUHJURXQG REMHFW WR SURGXFH D FRPSRVLWH VFHQH %ORFN GLDJUDP RI WKH SURSRVHG DXJPHQWDEOH UHDOWLPH &*, V\VWHP RUJDQL]DWLRQ 7KUHH GLVWLQFW W\SHV RI SL[HO FRYHUDJH ZLWK UHVSHFW WR WKH $/3+$ YDOXH Df QR FRYHUDJH Ef IXOO FRYHUDJH DQG Ff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f 7KH DOJRULWKP SHUIRUPHG E\ D JHQHUDO &31 GHSWK FRPSXWDWLRQ XQLW %ORFN GLDJUDP RI D JHQHUDO &31 GHSWK FRPSXWDn WLRQ XQLW YLLL

PAGE 9

7KH DOJRULWKP SHUIRUPHG E\ D JHQHUDO &31 RSDFLW\ FRPSXWDWLRQ XQLW %ORFN GLDJUDP RI D JHQHUDO &31 RSDFLW\ FRPSXn WDWLRQ XQLW 7KH DOJRULWKP SHUIRUPHG E\ D JHQHUDO &31 FRORU FRPSXWDWLRQ XQLW %ORFN GLDJUDP RI D JHQHUDO &31 FRORU FRPSXn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f IXOO\ EDODQFHG V\VWHP WUHH DQG Ef XQEDODQFHG V\VWHP WUHH L[

PAGE 10

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

PAGE 11

$EVWUDFW RI 'LVVHUWDWLRQ 3UHVHQWHG WR WKH *UDGXDWH 6FKRRO RI WKH 8QLYHUVLW\ RI )ORULGD LQ 3DUWLDO )XOILOOPHQW RI WKH 5HTXLUHPHQWV IRU WKH 'HJUHH RI 'RFWRU RI 3KLORVRSK\ $8*0(17$%/( 2%-(&725,(17(' 3$5$//(/ 352&(6625 $5&+,7(&785(6 )25 5($/7,0( &20387(5*(1(5$7(' ,0$*(5< %\ 5RVV 0RUULV )OHLVFKPDQ 'HFHPEHU &KDLUPDQ 'U -RKQ 6WDXGKDPPHU 0DMRU 'HSDUWPHQW (OHFWULFDO (QJLQHHULQJ 7KH KDUGZDUH DUFKLWHFWXUH RI D V\VWHP IRU UHDOWLPH FRPSXWHUJHQHUDWHG LPDJHU\ &*,f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

PAGE 12

DVVLJQHG WR DQ LQGLYLGXDO DXWRQRPRXV REMHFW JHQHUDWRU 2EMHFWV DUH UHQGHUHG LQGHSHQGHQWO\ IURP HDFK RWKHU DQG ZKHQ FRPSOHWH WKH\ DUH DXWRPDWLFDOO\ FRPSRVLWHG E\ WKH KDUGZDUH IRU GLVSOD\ 7KLV SURFHVV LV UHSHDWHG DW D UDWH VXLWDEOH IRU UHDOWLPH DQLPDWLRQ 7KH SLFWXUH UHSUHVHQWDWLRQ DFFHSWV WUDQVSDUHQW VHPLn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

PAGE 13

&+$37(5 ,1752'8&7,21 $ FRPSXWHUJHQHUDWHG LPDJHU\ &*,f V\VWHP LV D VSHFLDOL]HG FRPSXWHU V\VWHP WKDW SURYLGHV D YLVXDO VLPXn ODWLRQ RI DQ DUWLILFLDO HQYLURQPHQW &RQFHSWXDOO\ D &*, V\VWHP FRQVLVWV RI D ZLQGRZ LQ PXOWLGLPHQVLRQDO VSDFH ZLWK ZKLFK DQ REVHUYHU PD\ ORRN LQWR D ZRUOG 7KH ZLQGRZ LV SUHVHQWHG E\ D FRPSXWHU GULYHQ GLVSOD\ GHYLFH ZKLOH WKH ZRUOG LV PRGHOHG E\ D GDWDEDVH WKDW WKH FRPSXWHU FDQ DFFHVV 7KXV WKH YLVXDO VLPXODWLRQ PD\ EH UHJDUGHG DV D JHQHUDWLRQ RI DQ RXWWKHZLQGRZ YLHZ LQ UHDOWLPH DFn FRUGLQJ WR WKH VLPXODWHG SRVLWLRQ DQG RULHQWDWLRQ RI WKH REVHUYHU ZLWK UHVSHFW WR WKH VLPXODWHG FKDQJHV RI WKH DUWLILFLDO HQYLURQPHQW $ SRSXODU DSSOLFDWLRQ RI UHDOWLPH FRPSXWHUJHQHUDWHG LPDJHU\ YLVXDO VLPXODWRUV FRQFHUQV YHKLFOH WUDLQLQJ VLPXn ODWLRQ >),6 3$1 6&+ 6&+E <$1 =<'@ )RU WKLV DSSOLFDWLRQ DQ REVHUYHUnV YLVXDO H[SHULHQFH LV FUHDWHG E\ D JHQHUDWHG SHUVSHFWLYH SURMHFWLRQ RI D ZRUOG UHQGHUHG RQWR D GLVSOD\ GHYLFH >%(1@ ZLWK DVVRFLDWHG VSHFLDO HIIHFWV 2WKHU VLPXODWLRQ WDVNV >68*@ PD\ KDYH YDULDWLRQV RI WKH YLVXDO VLPXODWLRQ UHTXLUHPHQW DV

PAGE 14

D IXQFWLRQ RI WKH ZRUOG VWUXFWXUH EXW WKH UHDOWLPH SHUn IRUPDQFH DQG UHQGHULQJ SUREOHPV UHPDLQ FRQVWDQW 5HDOWLPH RSHUDWLRQ ZKLFK GHILQHV D FRPSXWDWLRQ SURFHVV ZKHUH WKH H[HFXWLRQ WLPH RI WKH FRPSXWHU LV V\Qn FKURQL]HG ZLWK WKH SK\VLFDO HYHQW WLPH RU ZDOOFORFN WLPH LV D PDMRU UHTXLUHPHQW RI WKHVH V\VWHPV >)25@ $OVR WKH DVVRFLDWHG LPDJH UHQGHULQJ SUREOHPV DUH FRPSXWDWLRQDOO\ GHPDQGLQJ 7KXV UHDOWLPH &*, V\VWHP RUJDQL]DWLRQV W\SLn FDOO\ PDQGDWH FXVWRPGHVLJQHG VSHFLDOSXUSRVH KLJKVSHHG FRPSXWHUV ZLWK JHQHUDOSXUSRVH FRPSXWHUV IRU WKHLU FRQWURO >6&+ 6&+E <$1@ 3UREOHP 'HILQLWLRQ 7UDGLWLRQDO &*, DUFKLWHFWXUHV XWLOL]H ERWK SLSHOLQLQJ DQG SDUDOOHOLVP WHFKQRORJLHV WR DFKLHYH UHDOWLPH SHUIRUn PDQFH IRU LPDJH V\QWKHVLV 7KH V\VWHP DUFKLWHFWXUHV DUH XVXDOO\ KLJKO\ VSHFLDOL]HG DQG FRQVWUDLQ WKH W\SHV RI JUDSKLFV SULPLWLYHV WKDW FDQ EH HPSOR\HG >(1*@ 7KHVH VSHFLDOSXUSRVH DUFKLWHFWXUHV XVXDOO\ LQYROYH D IL[HG JUDSKLFV SLSHOLQH WKDW LV GLIILFXOW WR HQKDQFH IRU LQn FUHDVHG SHUIRUPDQFH RU IRU LQFOXVLRQ RI DGGLWLRQDO JUDSKLFV SULPLWLYHV 7KH UHDOL]DWLRQ RI PDMRU &*, DUFKLWHFWXUDO UHYLVLRQV WKDW H[KLELW LPSURYHG SHUIRUPDQFH ZLWK VXEVWDQWLDO KDUGZDUH UHGXFWLRQ LV D VXEMHFW RI UHVHDUFK ,QQRYDWLYH &*, DUFKLn WHFWXUHV ZLOO HPSOR\ XQLTXH RUJDQL]DWLRQDO VWUXFWXUHV WKDW UHDOL]H DOJRULWKPLF LPSURYHPHQWV ZLWK UHVSHFW WR LPSOH

PAGE 15

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n WHP 7KH LQWURGXFWLRQ RI QHZ V\VWHPV ZLOO EH UHGXFHG WR LQWURGXFWLRQV RI QHZ PRGXOHV WKHUHE\ UHVLVWLQJ V\VWHP REVROHVFHQFH 7KHUHIRUH VXFK D V\VWHP ZLOO EH FRQWLQXn RXVO\ H[SDQGDEOH DQG QHYHU WRWDOO\ RXWPRGHG WKXV SURYLGLQJ SHUIRUPDQFH GHYHORSPHQW DQG HFRQRPLF EHQHILWV

PAGE 16

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n LWLQJ QHWZRUN &KDSWHU 9 GHVFULEHV WKH YLGHR JHQHUDWLRQ QRGH &KDSWHU 9, GHVFULEHV WKH GLVSOD\ GHYLFH QRGH &KDSWHU 9,, GHVFULEHV WKH REMHFW JHQHUDWLRQ QRGH &KDSWHU 9,,, GHVFULEHV WKH PDLQWHQDQFH PDQDJHPHQW QRGH &KDSWHU ,; LV D FRQFOXGLQJ FKDSWHU WKDW FRQWDLQV D GLVFXVVLRQ RI WKH V\VWHP VLPXODWLRQ DORQJ ZLWK D VXPPDU\ RI WKH GLVVHUWDWLRQ UHVXOWV

PAGE 17

&+$37(5 ,, 7<3,&$/ 5($/7,0( &*, $5&+,7(&785( $ W\SLFDO UHDOWLPH &*, V\VWHP RUJDQL]DWLRQ SRSXODU DPRQJ YHKLFOH WUDLQLQJ VLPXODWRUV LV VKRZQ LQ )LJXUH 7KLV VWUXFWXUH SURYLGHV D VLQJOH ILHOGRIYLHZ RI WKH DUWLILFLDO HQYLURQPHQW WHUPHG D FKDQQHO ,WV RUJDQL]DWLRQ FRQVLVWV RI D FDVFDGH RI IRXU PDMRU VXEV\VWHPV WKH VFHQH PDQDJHU WKH JHRPHWULF SURFHVVRU WKH YLGHR SURFHVVRU DQG WKH GLVSOD\ GHYLFH >6&+E <$1@ 7KH ILUVW WKUHH VXEn V\VWHPV IRUP D VSHFLDOL]HG FRPSXWHU JUDSKLFV SLSHOLQH IRU LPDJH UHQGHULQJ 7KH ODVW VXEV\VWHP SURYLGHV D VSHFLDOL]HG GLVSOD\ IRU YLHZLQJ 6FHQH 0DQDJHU 7KH RYHUDOO IXQFWLRQ RI WKH VFHQH PDQDJHU LV WR SURYLGH VFHQH HOHPHQWV WR WKH V\VWHP SLSHOLQH WKDW OLH LQ WKH REVHUYHUnV ILHOGRIYLHZ ZLWKLQ WKH DUWLILFLDO HQYLn URQPHQW JLYHQ REVHUYHU SRVLWLRQ DQG RULHQWDWLRQ 2EVHUYHU SRVLWLRQ DQG RULHQWDWLRQ LQIRUPDWLRQ DUH SURYLGHG WR WKH VFHQH PDQDJHU E\ D KRVW VLPXODWRU >)25 6&+E@ 7KLV LQIRUPDWLRQ GLUHFWV G\QDPLF H[WUDFWLRQ RI GDWDEDVH VFHQH HOHPHQWV IURP PDVV VWRUDJH WKDW DUH ORDGHG LQWR DQ DFWLYH GDWDEDVH PHPRU\ IRU VRUWLQJ >3$1@ 7KHVH VFHQH HOHPHQWV UHSUHVHQW WKH REVHUYHUnV SDQRUDPD DQG DUH H[DPLQHG WR

PAGE 18

'DWD )URP +RVW 6LPXODWRU 'DWD %ORFNV DQG ,QVWUXFWLRQV 9LGHR 3URFHVVRU $QDORJ 9LGHR )LJXUH %ORFN GLDJUDP RI D W\SLFDO UHDOWLPH &*, V\VWHP RUJDQL]DWLRQ

PAGE 19

GHWHUPLQH LI WKH\ DUH SRWHQWLDOO\ YLVLEOH ZLWKLQ WKH ILHOG RIYLHZ RI WKH REVHUYHU >3$1 <$1@ 6FHQH HOHPHQWV VDWLVI\LQJ WKLV FRQGLWLRQ DUH SURYLGHG ZLWK DQ DSSURSULDWH OHYHORIGHWDLO ZKLOH WKH UHPDLQGHU DUH FXOOHG >3$1 <$1@ 7KH UHVXOWDQW VFHQH HOHPHQWV DUH VHQW GRZQ WKH V\VWHP SLSHOLQH DW WKH LPDJH XSGDWH UDWH WR WKH JHRPHWULF SURFHVVRU ><$1@ 6XEV\VWHP SURFHVVLQJ ORDG LV FRQWLQXn RXVO\ PRQLWRUHG E\ WKH VFHQH PDQDJHU WR DYRLG RYHUORDGLQJ WKH SURFHVVLQJ FDSDFLW\ RI WKH SLSHOLQH 3URFHVVLQJ ORDG UHGXFWLRQ WHFKQLTXHV XWLOL]H YDULRXV G\QDPLF VFHQH FRQWHQW FRQWURO PHFKDQLVPV WKDW XVXDOO\ GHJUDGH LPDJH TXDOLW\ JUDFHIXOO\ >6&+D <$1@ 7KH PDVV VWRUDJH GHYLFH FRQWDLQV D GDWDEDVH ZKLFK PRGHOV DQ DUWLILFLDO HQYLURQPHQW WKDW GULYHV WKH KDUGZDUH )HDWXUHV RI D VLPXODWHG VFHQH QDWXUDO DQG FXOWXUDOf DUH PRGHOHG WR EH RI WKH VDPH VL]H VKDSH ORFDWLRQ DQG FRORU DV WKHLU UHDOZRUOG FRXQWHUSDUWV >6&+ 6&+D@ 'DWDEDVH PRGHOLQJ SULPLWLYHV IRU WKH W\SLFDO &*, V\VWHP FRQVLVW RI SODQDU SRO\JRQV DV D PDMRU SULPLWLYH DQG TXDGULF VXUIDFHV DV DQ RSWLRQ IRU ERWK PDQPDGH FXUYHG REMHFWV DQG QDWXUDO FXUYLOLQHDU REMHFWV ><$1@ 7KH GDWDEDVH DOVR FRQWDLQV VFHQH HOHPHQW DWWULEXWHV VXFK DV FRORU DQG WH[WXUH

PAGE 20

*HRPHWULF 3URFHVVRU 7KH JHRPHWULF SURFHVVRU LV D VSHFLDOSXUSRVH SLSHOLQHG FRPSXWHU WKDW RSHUDWHV RQ WKH VFHQH HOHPHQW RXWSXW IURP WKH VFHQH PDQDJHU 7KHVH RSHUDWLRQV XVXDOO\ SURGXFH WKH SURn MHFWHG JHRPHWU\ RI WKH VFHQH ZLWK DVVRFLDWHG JHRPHWULF JUDGLHQW DQG FRORU JUDGLHQW SDUDPHWHUV ,Q JHQHUDO WKH IL[HG FRRUGLQDWH V\VWHP RI WKH VFHQH HOHPHQWV DUH WUDQVn IRUPHG YLD WUDQVODWLRQ URWDWLRQ DQG VFDOLQJf WR WKH PRPHQWDU\ H\HEDVHG FRRUGLQDWH V\VWHP RULJLQ ORFDWHG DW WKH REVHUYHUnV H\Hf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n WLRQ GHYLFH ZDV SUHVHQWHG E\ 1HZDULNDU >1(:@ &OLSSLQJ DOJRULWKPV JHRPHWULF WUDQVIRUPDWLRQV DQG SHUVSHFWLYH SURMHFWLRQ FDQ EH IRXQG LQ 5RJHUV >5*@ ZLWK DQ LQWHUHVWn LQJ 9/6, VROXWLRQ SUHVHQWHG E\ &ODUN >&/$@ &ODUN GLVFXVVHV D IRXUFRPSRQHQW YHFWRU IORDWLQJ SRLQW 9/6,

PAGE 21

SURFHVVRU IRU DFFRPSOLVKLQJ PDWUL[ WUDQVIRUPDWLRQV FOLSn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f FRORU JUDGLHQW SDUDPHWHUV VFHQH HOHPHQW QDWLYH FRORUf WH[WXUH PDSV DWPRVSKHULF DWWHQXDWLRQ KD]H FRORUf VFHQH HOHPHQW LOOXPLQDWLRQ ERWK QDWXUDO DQG FXOWXUDO OLJKW VRXUFHVf DQWLDOLDVLQJ WHFKQLTXHV VKDGRZV DQG VKDGLQJ WHFKQLTXHV 'XULQJ EHIRUH RU DIWHU SL[HO FRPSXWDWLRQ YLVLEOH SRUWLRQV RI WKH VFHQH DUH LGHQWLILHG WKURXJK D KLGGHQ VXUIDFH UHPRYDO WHFKQLTXH 7KLV SURFHVVRU DOVR SURYLGHV WLPLQJ DQG FRQWURO RI WKH GLVSOD\ GHYLFH ZKLFK UHODWH WR WKH YLGHR SURFHVVRU RUJDQn L]DWLRQDO SKLORVRSK\ ><$1@ VFDQOLQHEDVHG RU IUDPHn EXIIHUEDVHG 6FDQOLQHEDVHG XQLWV SHUIRUP YLGHR SURn FHVVLQJ RQH VFDQOLQH DW D WLPH LQ V\QFKURQLVP ZLWK HDFK UDVWHU RI WKH GLVSOD\ GHYLFH RQH URZ RI WKH YLVLEOH VFHQHnV SL[HO FRGHV DUH VWRUHG )UDPHEXIIHUEDVHG XQLWV SHUIRUP YLGHR SURFHVVLQJ LQGHSHQGHQW RI WKH UDVWHU GLVSOD\

PAGE 22

FRPSOHWH IUDPH RI WKH YLVLEOH VFHQHnV SL[HO FRGHV DUH VWRUHG $OJRULWKPV DQG WHFKQLTXHV XVHG E\ WKH YLGHR SURFHVVRU DUH ZHOO NQRZQ DQG FDQ EH IRXQG LQ WKH OLWHUDWXUH VXFK DV 5RJHUV >52*@ ([DPSOHV RI DQWLDOLDVLQJ LQFOXGH %RRWKnV >%@ SUHVHQWDWLRQ FRQFHUQLQJ WKH KXPDQ IDFWRUV UHODWLRQ WR DQWLDOLDVLQJ DQG &DUSHQWHUnV >&$5@ SUHVHQWDWLRQ RI DQ LQWHUHVWLQJ $EXIIHU DSSURDFK 5HDOWLPH KDUGZDUH DSn SURDFKHV WR WH[WXUH PDSSLQJ FDQ EH IRXQG LQ WKH OLWHUDWXUH VXFK DV RQH DSSURDFK SUHVHQWHG E\ )DQW >)$1@ 'LVSOD\ 'HYLFH 'LVSOD\ GHYLFH WHFKQRORJ\ SULPDULO\ FRQVLVWV RI WZR YDULDWLRQV FDOOLJUDSKLF GLVSOD\V DQG UDVWHU GLVSOD\V >6&+D@ 7KH FRORU FDOOLJUDSKLF GLVSOD\ LV FKDUDFWHUL]HG E\ D FRQWLQXRXV OD\HUHG SKRVSKRU VXUIDFH 5(' DQG *5((1 SKRVSKRU OD\HUVf XVHG WR SUHVHQW D FRORU SLFWXUH ZLWK EHDP SHQHWUDWLRQ FRQWURO HOHFWURQ EHDP YHORFLW\f RI VHTXHQn WLDOO\ UHIUHVKHG VWUDLJKW OLQHV YHFWRUV RU VWURNHVf DQG SRLQWV ]HUR OHQJWK YHFWRUVf 7KH UDVWHU GLVSOD\ FRQWDLQV D UHJXODU JULG RI SKRVSKRU WULDGV 5(' *5((1 DQG %/8(f WKDW DUH XVHG WR SUHVHQW D FRORU SLFWXUH E\ PRGXODWHG LOOXPLQDWLRQ RI HDFK SKRVSKRU WULDG SRLQW SL[HOf ZLWK UHIUHVK LQ D UHJXODU SDWWHUQ &DOOLJUDSKLF V\VWHPV PDLQn WDLQ KLJK TXDOLW\ OLJKW SRLQWV ZLWK FRORU OLPLWDWLRQV

PAGE 23

ZKLOH UDVWHU V\VWHPV PDLQWDLQ KLJK TXDOLW\ SDLQWHG IDFHV ZLWKRXW FRORU OLPLWDWLRQV ><$1 6&+D@

PAGE 24

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

PAGE 25

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

PAGE 26

%DFNJURXQG 2EMHFW )RUHJURXQG 2EMHFW &RPSRVLWH 6FHQH )LJXUH &RPSRVLWLRQ RI DQ RSDTXH EDFNJURXQG REMHFW DQG DQ RSDTXH IRUHJURXQG REMHFW WR SURGXFH D FRPSRVLWH VFHQH

PAGE 27

SRVLWLRQ LV GHWHUPLQHG E\ WKH SL[HO ORFDWLRQ LQ WKH LPDJH DUUD\ DQG WKH FRORU YDOXH LV GHILQHG DV WKH DGGLWLYH WULn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n VWLPXOXV FRORU YDOXH ZLWK WKH HIIHFW RI DWPRVSKHULF DWWHQXDWLRQ LQFOXGHG 6XSSRUWLQJ $UFKLWHFWXUH 7KH IXQGDPHQWDO LGHD RI FRPSRVLWLQJ IRFXVHV RQ DOORZn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

PAGE 28

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f D FRPSRVLWLQJ QHWZRUN &1f D YLGHR JHQHUDWLRQ QRGH 9*1f D GLVSOD\ GHYLFH QRGH ''1f DQG D PDLQWHQDQFH PDQDJHPHQW QRGH 001f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

PAGE 29

B 9LGHR 3URFHVVLQJ 1RGH 0DLQWHQDQFH 0DQDJHPHQW 1RGH QU *HQHUDO &RPPXQLFDWLRQV %ORFN GLDJUDP RI WKH SURSRVHG DXJPHQWDEOH UHDOWLPH &*, V\VWHP RUJDQL]DWLRQ )LJXUH

PAGE 30

V\QFKURQLVP ZLWK LW 7KH\ DUH DVVLJQHG D SDUWLWLRQ WHUPHG DQ REMHFW RI WKH HQWLUH LPDJH JHQHUDWLRQ WDVN $Q 2*1 LQWHUIDFHV WR WKH FRPSRVLWLQJ QHWZRUN WKURXJK LWV LPDJH PHPRU\ ZKLFK FRQWDLQV DQ LPDJH VSDFH YLHZ RI WKH DVVLJQHG REMHFW (DFK HOHPHQW RI WKH LPDJH PHPRU\ FRQWDLQV WKUHH SL[HO DWWULEXWHV FRORU RSDFLW\ DQG GHSWK 7KH ; < FRRUGLQDWHV DUH GHULYHG IURP D SL[HOnV SRVLWLRQ LQ WKH LPDJH PHPRU\ 7KH FRPSRVLWLQJ QHWZRUN LV D SL[HOE\SL[HO KDUGZDUH FRPSRVLWRU ZKLFK LV DQ H[SDQGDEOH HQVHPEOH RI LQWHUFRQn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

PAGE 31

QRGH $OVR WKH WLPLQJ RI WKH HQWLUH V\VWHP LV GHULYHG IURP WKH 9*1 7KH GLVSOD\ GHYLFH QRGH LV D UDVWHU VFDQ W\SH PRQLWRU ,W UHFHLYHV WKUHH SULPDU\ FRORUV IURP WKH 9*1 5(' *5((1 DQG %/8( 7KH YLGHR WLPLQJ RI WKH PRQLWRU LV DOVR FRQWUROn OHG GLUHFWO\ IURP WKH 9*1 7KH PDLQWHQDQFH PDQDJHPHQW QRGH SURYLGHV FHQWUDO FRQWURO DQG KHDOWK DVVXUDQFH RI WKH V\VWHP ,W LV DQ DXWRQRPRXV SURFHVVRU WKDW SURYLGHV VHOIPDLQWHQDQFH RSHUDWLRQV DQG V\VWHP VXSSRUW IXQFWLRQV ,QFOXGHG LV D FRPSXWDWLRQDO XQLW D VHFRQGDU\ PHPRU\ XQLW DQG D FRQn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f WKH LPDJH JHQHUDn WLRQ WDVN LV GLVWULEXWHG DPRQJ PDQ\ SURFHVVRUV 2*1Vf f WKH KLGGHQ VXUIDFH UHPRYDO ZLWK DQWLDOLDVLQJ LV LQFOXGHG LQ

PAGE 32

WKH DUFKLWHFWXUDO VWUXFWXUH FRPSRVLWLQJ QHWZRUNf DQG f WKH HIIHFW RI DWPRVSKHULF DWWHQXDWLRQ LV LQFOXGHG LQ WKH DUFKLWHFWXUDO VWUXFWXUH 9*1f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

PAGE 33

LQWHUVHFWLRQ RI WZR RU PRUH VXUIDFHV 7KLV ZRXOG UHTXLUH D ODUJH DPRXQW RI FDOFXODWLRQV 7KH SL[HO OHYHO DSSURDFK RI WKLV QHZ DUFKLWHFWXUH UHGXFHV WKH JHRPHWU\ WKDW LV W\SLFDOO\ LQYROYHG IRU VROYLQJ LQWHUVHFWLRQ SUREOHPV WR WKH FRPSDULVRQ RI GHSWK YDOXHV 7KH VROXWLRQ LV DQ DSSUR[LPDn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

PAGE 34

7DUJHW $SSOLFDWLRQV 7DUJHW DSSOLFDWLRQV RI WKLV GHYLFH ZLOO QRW EH UHVWULFWHG WR DQ\ VSHFLILF UHDOWLPH VLPXODWLRQ WDVN LH YHKLFOH VLPXODWLRQ $ JRDO RI WKLV UHVHDUFK LV WR H[WHQG WKH DUFKLWHFWXUH IRU LQFOXVLRQ RIRWKHU UHDOWLPH VLPXn ODWLRQ DSSOLFDWLRQV HJ SURFHVV DQG V\VWHP VLPXODWLRQV ,W ZLOO EH D JHQHUDO SXUSRVH IUDPHZRUN WR VLPXODWH PDQ\ WKLQJV LQ UHDOWLPH ZLWK YLVXDO RXWSXW ,Q VKRUW WKH REMHFW JHQHUDWLRQ QRGHV FDQ EH WKRXJKW RI DV SURFHVVLQJ ORJLFDO REMHFWV 2EMHFWV FDQ EH D VLQJOH LWHP RU D FROOHFWLRQ RI LWHPV )RU LQVWDQFH DQ REMHFW LV DEVWUDFW EODGH RI JUDVV WRWDO ILHOG RI JUDVV RU SK\VLFDO REMHFW 7KHUHIRUH VRPH RU DOO RI WKH WDVNV RI VLPXODWLRQ FDQ EH PRYHG WR HDFK REMHFW VR ORQJ DV WKHVH WDVNV DUH VHSDUDEOH +RZHYHU WKH WDVNV GR QRW KDYH WR EH FOHDQO\ VHSDUDEOH )RU LQVWDQFH RYHUODSV FRXOG H[LVW ZKLFK ZRXOG EH UHVROYHG LQ FRPSRVLWLQJ 7KLV ZRXOG DOORZ VLPSOH VSOLWWLQJ RI VRPH REMHFWV LQWR WZR VRPHZKDW RYHUODSSLQJ RQHV ZLWKRXW WKH QHHG RI FDOFXODWLQJ QHZ LQWHUVHFWLRQV GXH WR DQ DUWLILFLDO GLYLVLRQ FXW $OVR WUXHFRORU SVHXGRn FRORU RU ERWK FDQ EH DSSOLHG IRU WKH YLVXDO VLPXODWLRQ ZLWK UHVSHFW WR WKH SUREOHP GRPDLQ

PAGE 35

&+$37(5 ,9 &20326,7,1* 1(7:25. 7KH FRPSRVLWLQJ QHWZRUN &1f LV D KDUGZDUH FRPSRVLWRU WKDW SURGXFHV D FRPSXWHU JUDSKLFV SLFWXUH WKURXJK EOHQGLQJ KHWHURJHQRXVO\ UHQGHUHG REMHFWV LQWR D IXOO LPDJH 7KHVH VHSDUDWHO\ UHQGHUHG REMHFWV DUH UHGXFWLRQV RI D WRWDO PRGHOHG HQYLURQPHQW LQWR SLHFHV WKDW UHO\ RQ FRPSRVLWLQJ WHFKQLTXHV IRU DFFXPXODWLRQ (DFK REMHFW LV SURGXFHG E\ DQ LQGLYLGXDO REMHFW JHQHUDWLRQ QRGH 2*1f ZKLFK LV LQ LWVHOI D FRPSXWHU LPDJH JHQHUDWLRQ GHYLFH 7KH QHWZRUN FRQILJXUDn WLRQ LV LQ WKH IRUP RI D V\QFKURQRXV IHHGIRUZDUG WUHH WKDW LV FRQQHFWHG WR D PXOWLSOLFLW\ RI REMHFW JHQHUDWLRQ QRGHV 2*1Vf IRU LQSXW DQG WR D VLQJOH YLGHR JHQHUDWLRQ QRGH 9*1f IRU RXWSXW 7KHUHIRUH PDQ\ REMHFW LPDJHV DUH FRPn SRVLWHG VLPXOWDQHRXVO\ 7KH FRPSRVLWH RI DGGLWLRQDO REMHFW LPDJHV LV GRQH WKURXJK HQODUJLQJ WKH FRPSRVLWLQJ QHWZRUN DQG WKURXJK LQFOXGLQJ DGGLWLRQDO REMHFW JHQHUDWLRQ QRGHV 7KHUH LV QR IL[HG FRQILJXUDWLRQ EXW UDWKHU D JHQHUDO IUDPHZRUN WR FRQILJXUH D FRPSRVLWLQJ QHWZRUN XWLOL]LQJ D FROOHFWLRQ RI EDVLF EXLOGLQJ EORFNV FDOOHG FRPSRVLWLQJ SURFHVVLQJ QRGHV &31Vf 7KH FRPSRVLWLQJ QHWZRUN RSHUDWLRQ UHTXLUHV WKH VLPXOn WDQHRXV LQSXW RI DOO LQVWDQFHV RI SL[HOV ZLWK WKH VDPH ;

PAGE 36

DQG < FDUWHVLDQ FRRUGLQDWH SHU XQLW WLPH (DFK LQVWDQFH RI D SL[HO LV SDUW RI DQ LQGLYLGXDO REMHFW UHQGHUHG E\ DQ REMHFW JHQHUDWLRQ QRGH 7KHVH SL[HO YDOXHV IORZ LQ D V\QFKURQRXV IHHGIRUZDUG PDQQHU WKURXJK WKH FRPSRVLWLQJ QHWZRUN ZKLOH EHLQJ PHUJHG SL[HOE\SL[HO DW SDUWLFXODU VWDJHV 7KH ODVW VWDJH RI WKH QHWZRUN SURYLGHV D VLQJOH VXUYLYLQJ SL[HO DV RXWSXW ZKLFK KDV DQ LPSOLHG ; FRRUGLn QDWH DQG < FRRUGLQDWH 7R VXPPDUL]H WKH FRPSRVLWLQJ SURFHVV LV FDUULHGRXW SL[HOE\SL[HO WKURXJK WKUHH VWHSV f HYHU\ SL[HO YDOXH LV VLPXOWDQHRXVO\ UHDG IURP HDFK LPDJH DUUD\ RI WKH REMHFW JHQHUDWLRQ QRGHV DW D VSHFLILHG ; FRRUGLQDWH DQG < FRRUGLn QDWH f WKH FRPSRVLWLQJ SURFHVV RSHUDWHV RQ WKH FROOHFWLRQ RI SL[HO YDOXHV UHDG IURP WKH 2*1V WR SURGXFH D VLQJOH FRPSRVLWH SL[HO UHVXOWDQW DQG f WKH VLQJOH FRPSRVLWH SL[HO UHVXOWDQW LV ZULWWHQ WR WKH UHVLGHQW LPDJH DUUD\ RI WKH YLGHR JHQHUDWLRQ QRGH DW WKH VDPH ; FRRUGLQDWH DQG < FRRUGLQDWH XVHG IRU WKH UHDG RSHUDWLRQ 7KLV SURFHVV LV UHSHDWHG DW HYHU\ ; FRRUGLQDWH DQG < FRRUGLQDWH RI WKH LPDJH DUUD\ WR SURGXFH HYHU\ FRPSRVLWH SL[HO YDOXH RI WKH LPDJH DUUD\ ZLWKLQ WKH YLGHR JHQHUDWLRQ QRGH 7KH HQWLUH FRPSRVLWLQJ QHWZRUN DFWLRQ IRU HDFK FROOHFWLRQ RI SL[HOV FDQ EH JHQHUDOO\ FKDUDFWHUL]HG E\ 3F RSHUW3/ 3 33MBf f DW HYHU\ SL[HO ZLWK LGHQWLFDO ; < FDUWHVLDQ FRRUGLQDWHV LQ

PAGE 37

WKH L LPDJH DUUD\V 7KH YDOXH 3F UHSUHVHQW D VLQJOH VXUn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n EOHV 5(' *5((1 %/8( DQG $/3+$ 7KXV WKH LQWHUSOD\ RI DOSKD YDOXHV PXVW EH FRQVLGHUHG IRU FRPSRVLWLQJ REMHFWV WR DFFXPXODWH D ILQDO LPDJH >325@ 7KH $/3+$ SRUWLRQ RI DQ REMHFW UHSUHVHQWDWLRQ SURYLGHV WZR SLHFHV RI LQIRUPDWLRQ IRU FRPSRVLWLQJ f WKH VLQJOH $/3+$ YDOXH UHSUHVHQWV WKH H[WHQW RI FRYHUDJH RI DQ REMHFW ZLWKLQ D SL[HO DQG f WKH FROOHFWLRQ RI $/3+$ YDOXHV UHSUHn VHQWLQJ DQ REMHFW SURYLGHV FRYHUDJH LQIRUPDWLRQ WKDW GHVLJn QDWHV WKH VKDSH RI DQ REMHFW ZLWKLQ WKH LPDJH VSDFH 7KH

PAGE 38

SL[HO FRYHUDJH LQIRUPDWLRQ SURYLGHV D PL[LQJ IDFWRU WR FRQWURO OLQHDU LQWHUSRODWLRQ RI IRUHJURXQG DQG EDFNJURXQG FRORUV DW HYHU\ SL[HO 7KH REMHFW VKDSH LQIRUPDWLRQ ZKLFK LV WHUPHG D PDWWH LGHQWLILHV WKH REMHFW IURP ZKDW LV QRW WKH REMHFW ZLWKLQ DQ LVRODWHG LPDJH DUUD\ 7KH $/3+$ YDOXH UHSUHVHQWV WKH RSDFLW\ RI D SL[HO ZKLFK LV D IUDFWLRQDO YDOXH WKDW UDQJHV IURP ]HUR WR RQH 7KH DQWLWKHVLV RI $/3+$ ZKLFK LV WKH WUDQVSDUHQF\ RI D SL[HO LV GHILQHG DV $/3+$f 7KHUHIRUH WKH WUDQVSDUn HQF\ YDOXH DOVR UDQJHV IURP ]HUR WR RQH )LJXUH LOOXVn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n MHFWV DQG SHUIRUPLQJ QRQFRPPXWDWLYH REMHFW HGJH DQWLn DOLDVLQJ IRU UHQGHULQJ RSDTXH VHPLWUDQVSDUHQW RU WUDQVn SDUHQW REMHFWV $OVR VLQFH WKH $/3+$ YDOXH UHSUHVHQWV

PAGE 39

$/3+$ 2 Df 1R &RYHUDJH $/3+$ Ef )XOO &RYHUDJH $/3+$ Ff3DUWLDO &RYHUDJH DUELWUDU\ GHSLFWLRQf )LJXUH 7KUHH GLVWLQFW W\SHV RI SL[HO FRYHUDJH ZLWK UHVSHFW WR WKH $/3+$ YDOXH Df QR FRYHUDJH Ef IXOO FRYHUDJH DQG Ff SDUWLDO FRYHUDJH 7KH VXESL[HO VKDSH RI WKH SL[HO ZLWK SDUWLDO FRYHUDJH LV DUELWUDU\ DQG LV RQO\ VKRZQ LQ WKLV PDQQHU IRU FRQFHSWXDO FODULW\

PAGE 40

WKH DYHUDJH FRYHUDJH RI DQ REMHFW ZLWKLQ D SL[HO WKH SL[HO FRORU LV GHWHUPLQHG E\ WKH SURGXFW RI $/3+$ DQG WKH REMHFWnV WUXH FRORU 3RUWHU DQG 'XII >325@ GLVFXVVHG PDQ\ RSHUDWRUV IRU WKH FRPSRVLWLQJ RI WZRGLPHQVLRQDO LPDJHV 7KH RSHUDWRU RI LQWHUHVW WR WKLV UHVHDUFK LV WKH RYHU RSHUDWRU 7KLV RSHUDWRU FRPSXWHV D FRPSRVLWH SL[HO FRORU GXH WR RQH SL[HO LQ IURQW RI DQRWKHU 7KH FRPSRVLWH SL[HO FRORU LV JLYHQ E\ FF FI $IfFE f DQG WKH FRPSRVLWH RSDFLW\ $F $I $If$E f ZKHUH F GHQRWHV RQH RI WKUHH WULVWLPXOXV FRORU YDOXHV $ GHQRWHV WKH RSDFLW\ YDOXH $/3+$ WKH VXEVFULSW F GHQRWHV WKH FRPSRVLWH VXEVFULSW I GHQRWHV WKH IRUHJURXQG DQG VXEVFULSW E GHQRWHV WKH EDFNJURXQG $OVR WKH WUXH IRUHn JURXQG FRORU &I LV PXOWLSOLHG E\ WKH IRUHJURXQG RSDFLW\ $I WR SURGXFH FI DQG WKH WUXH EDFNJURXQG FRORU &E LV PXOWLn SOLHG E\ WKH EDFNJURXQG RSDFLW\ $E WR SURGXFH FE 7KLV LV GRQH WR NHHS WKH FRPSXWDWLRQ RI FF VLPLODU WR WKH FRPSXWDn WLRQ RI $F 7KH GHULYDWLRQ RI WKH RYHU RSHUDWRU LV SUHVHQWHG E\ 3RUWHU DQG 'XII >35@ $ VLPLODU GHYHORSn PHQW RI RYHU DGMXVWHG IRU WKLV UHVHDUFK LV SUHVHQWHG LQ WKH IROORZLQJ VHFWLRQ RI WKLV FKDSWHU

PAGE 41

3RUWHU DQG 'XIInV DSSURDFK KDV D GUDZEDFN RI UHTXLULQJ WKH SULRULW\ RI LPDJHV WR EH PDQXDOO\ HQWHUHG 7KHUHIRUH 'XII >'8)@ LQWURGXFHG WKH GHSWK YDULDEOH = DV DQ H[n WHQVLRQ WR WKH HDUOLHU LPDJH FRPSRVLWLRQ DOJRULWKP WR FRUUHFW WKLV GUDZEDFN 7KH DSSURDFK H[WHQGHG HDFK SL[HO LQ WKH LPDJH VSDFH WR FRQWDLQ ILYH LQGHSHQGHQW YDULDEOHV 5(' *5((1 %/8( $/3+$ DQG = )URP WKLV UHSUHVHQWDWLRQ DQ 5*%$= DOJRULWKP ZDV GHYHORSHG WKDW FRPELQHG WKH RYHU RSHUDWRU RI 3RUWHU DQG 'XII >35@ ZLWK D =EXIIHU DOJRn ULWKP %HIRUH GLVFXVVLQJ 'XIInV >'8)@ DSSURDFK WKH = EXIIHU DOJRULWKP LV SUHVHQWHG DQG GLVFXVVHG $ =EXIIHU LV D GHSWK EXIIHU WKDW VWRUHV WKH = FDUn WHVLDQ FRRUGLQDWH ZKLFK LV DOVR WHUPHG WKH GHSWK FRRUGLn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nV LQWHQVLW\ YDOXH LV ZULWWHQ LQWR WKH IUDPH

PAGE 42

EXIIHU DQG LWV GHSWK YDOXH LV ZULWWHQ LQWR WKH =EXIIHU >5*@ ,I WKH FRPSDULVRQ GRHV QRW LQGLFDWH WKH QHZ SL[HO LV FORVHU WR WKH YLHZSRLQW WKDQ WKH FXUUHQW SL[HO WKHQ WKH FXUUHQW SL[HO YDOXHV UHPDLQ LQ WKH IUDPH EXIIHU DQG LQ WKH =EXIIHU 7R UHFDSLWXODWH WKH =EXIIHU DOJRULWKP LV D VHDUFK RYHU ; < LQ VSDFH IRU WKH YDOXH RI =;'8)@ LV PRUH FRPn SDFWO\ FKDUDFWHUL]HG DV =F ]PLQ=/ =MMf f 5*%& 5*%O LI =/ ]PLQ HOVH 5*%MA f DW HYHU\ SL[HO LQ WKH WZR LPDJH DUUD\V 7KH VXEVFULSW F GHQRWHV WKH FRPSRVLWH 7ZR SURSHUWLHV RI WKH ]PLQ RSHUn DWRU LV WKDW LW LV ERWK FRPPXWDWLYH DQG DVVRFLDWLYH 7KH =EXIIHU DOJRULWKP DOORZV SL[HOV WR EH ZULWWHQ LQWR WKH IUDPH EXIIHU LQ DUELWUDU\ RUGHU 7KHUHIRUH WKH FRPSXWDWLRQ WLPH DVVRFLDWHG ZLWK D GHSWK VRUW RSHUDWLRQ LV HOLPLQDWHG >52*@ 8QIRUWXQDWHO\ WKH DOJRULWKP KDV LQKHUHQW DOLDVLQJ SUREOHPV GXH WR LWV SRLQW VDPSOLQJ QDWXUH

PAGE 43

>'8)@ ,W DOVR IDLOV IRU UHQGHULQJ WUDQVSDUHQW REMHFWV EXW LW LV IDVW DQG VLPSOH >&$5@ 'XIInV DSSURDFK XWLOL]HG WKH GHSWK YDOXH DW HDFK RI WKH IRXU FRUQHUV RI D SL[HO WR FRPSXWH D IUDFWLRQ FDOOHG %(7$ 7KLV YDOXH LV FRPSXWHG WKURXJK OLQHDUO\ LQWHUSRODWn LQJ WKH IRXU GHSWK FRUQHU YDOXHV 7KH FRPSRVLWH FRORU LV FRPSXWHG E\ FF %FI RYHU FEf %fFE RYHU FIf f DQG =F PLQ=I =Ef f ZKHUH F GHQRWHV RQH RI WKUHH WULVWLPXOXV FRORU YDOXHV PXOWLSOLHG E\ LWV UHVSHFWLYH RSDFLW\ YDOXH = GHQRWHV WKH GHSWK YDOXH % GHQRWHV 'XIInV %(7$ YDOXH WKH VXEVFULSW F GHQRWHV WKH FRPSRVLWH VXEVFULSW I GHQRWHV WKH IRUHJURXQG DQG VXEVFULSW E GHQRWHV WKH EDFNJURXQG 7KLV DSSURDFK FRPELQHV WKH SL[HOV E\ DUHD VDPSOLQJ $ GUDZEDFN RI WKLV FRPSRVLWLQJ DSSURDFK DQG RI WKH SUHYLRXVO\ GLVFXVVHG FRPSRVLWLQJ DSSURDFK LV WKDW WKH\ GR QRW DSSO\ ZKHQ WKH HGJHV RI PRUH WKDQ RQH REMHFW DUH SURMHFWHG RQWR D VLQJOH SL[HO 7KH FRPSRVLWLQJ DOJRULWKP GHYHORSHG LQ WKLV UHn VHDUFK ZKLFK LV GLVFXVVHG LQ WKH IROORZLQJ VHFWLRQ RI WKLV FKDSWHU DGGUHVVHV WKLV SUREOHP $QRWKHU LQWHUHVWLQJ DSSURDFK WR FRPSRVLWLQJ ZDV GLVn FXVVHG E\ &DUSHQWHU >&$5@ ZLWK WKH LQWURGXFWLRQ RI WKH $EXIIHU $Q $EXIIHU LV DQ DQWLDOLDVHG KLGGHQ VXUIDFH

PAGE 44

PHFKDQLVP WKDW LV DQ HQKDQFHPHQW WR WKH =EXIIHU WKURXJK LQFOXVLRQ RI D PDVN WKDW FRQWDLQV VXESL[HO FRYHUDJH LQIRUn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

PAGE 45

0XVW KDQGOH RSDTXH LQWHUVHFWLQJ VXUIDFHV DQG WUDQVn SDUHQW LQWHUVHFWLQJ VXUIDFHV >&$5@ 0XVW KDQGOH KLGGHQ VXUIDFH UHPRYDO >&$5 '8)@ 7KH SURSRVHG QHZ DUFKLWHFWXUDO DSSURDFK DWWHPSWV WR VDWLVI\ WKHVH FRPSRVLWLQJ WHFKQLTXH REMHFWLYHV 8QIRUWXn QDWHO\ GXH WR WUDGHRIIV WDNHQ WR NHHS WKH DSSURDFK ZLWKLQ KDUGZDUH OLPLWV VRPH RI WKHVH REMHFWLYHV DUH QRW HQWLUHO\ PHW 7KH FRQVWUDLQWV DQG WUDGHRIIV DVVRFLDWHG ZLWK WKH DSSURDFK DGGUHVVHG WKURXJK WKLV UHVHDUFK ZKLFK FRQFHUQ WKH VWDWHG LGHDOLF REMHFWLYHV DUH GLVFXVVHG LQ ODWHU VHFWLRQV DQG FKDSWHUV 5*%$= &RPSRVLWLQJ $OJRULWKP 7KH SURSRVHG FRPSRVLWLQJ PHWKRG LV GHYHORSHG WR DOORZ DQ\ QXPEHU RI LPDJHV WR EH FRPSRVLWHG ZLWK KLGGHQ VXUIDFH UHPRYDO DQG DQWLDOLDVLQJ 7KH FRPSRVLWLQJ DOJRULWKP UHDOn L]HG E\ WKH FRPSRVLWLQJ QHWZRUN LV EDVHG RQ 3RUWHU DQG 'XIInV >325@ RYHU RSHUDWRU EXW LV PRGLILHG WKURXJK WKH LQWURGXFWLRQ RI WKH GHSWK YDOXH 7KLV UHQGLWLRQ PRGLILHV WKH RYHU RSHUDWRU WKURXJK LQFRUSRUDWLQJ WKH ]PLQ RSHUn DWRU IRU LGHQWLI\LQJ WKH IRUHJURXQG SL[HO IURP WKH EDFNn JURXQG SL[HO 7KH DOJRULWKP LV ODEHOHG DQ 5*%$= DOJRULWKP DV ZDV 'XIInV >'8)@ EXW GLIIHUV IURP WKDW IRUPXODWLRQ ,W LV GHYHORSHG DQG GHVFULEHG LQ WKH VXEVHTXHQW SDUDJUDSKV &RQVLGHU RSDFLW\ YDOXHV DQG $ EHORQJLQJ WR D SDLU RI VHPLWUDQVSDUHQW SL[HOV 3A DQG 3 WKDW KDYH

PAGE 46

LGHQWLFDO ; DQG < FRRUGLQDWHV EXW GLIIHU LQ WKH = FRRUGLn QDWH ZKHUH WKH YDOXH LV OHVV WKDQ WKDW RI WKH = YDOXH 7KH FRPSRVLWH = YDOXH IRU WKLV VLWXDWLRQ LQ DFn FRUGDQFH ZLWK WKH =EXIIHU DOJRULWKP XWLOL]LQJ (TXDWLRQ LV JLYHQ E\ =F =[ f ZKHUH = GHQRWHV WKH GHSWK YDOXH DQG VXEVFULSW F LGHQWLILHV WKH FRPSRVLWH UHVXOWDQW 7KH GHSWK FRPSDULVRQ LGHQWLILHV SL[HO 3A DV EHLQJ FORVHU WR WKH YLHZSRLQW WKDQ SL[HO 3 7KHUHIRUH SL[HO 3A LV LGHQWLILHG DV WKH IRUHJURXQG SL[HO DQG SL[HO 3 LV LGHQWLILHG DV WKH EDFNJURXQG SL[HO 7KH RSDFLW\ UHSUHVHQn WDWLRQ GHVLJQDWHV WKH RSDTXHQHVV RI SL[HO 3O DV $A DQG LWV FOHDUQHVV DV $Af /LNHZLVH WKH RSDTXHQHVV RI SL[HO 3 LV $ DQG LWV FOHDUQHVV LV $f 7KLV LPSOLHV WKDW WKH FRPSRVLWH RSDFLW\ DFFRUGLQJ WR WKH RYHUf RSHUDWRU RI WKH WZR SL[HOV LV JLYHQ E\ $F $[ $f$ f ZKHUH $ GHQRWHV WKH RSDFLW\ YDOXH $Q H[DPSOH RI WKLV VLWXDWLRQ LV GHSLFWHG LQ )LJXUH 7KH FRPSRVLWH FRORU LV FDOFXODWHG E\ UHDOL]LQJ WKDW SL[HO 3A DOORZV $@Bf RI LWV EDFNJURXQG OLJKW WKURXJK DQG UHIOHFWV $ RI LWV FRORU /LNHZLVH SL[HO 3 DOORZV $f RI LWV EDFNJURXQG OLJKW WKURXJK DQG UHIOHFWV $ RI

PAGE 47

%DFNJURXQG 2EMHFW SDUWLDO SL[HO FRYHUDJHf )RUHJURXQG 2EMHFW SDUWLDO SL[HO FRYHUDJHf $ $ ? f$ ,$22$f )LJXUH 7ZR SL[HO RSDFLW\ YDOXHV DUH FRPSRVLWHG 7KH YDOXHV ZHUH GHULYHG IURP FRYHUDJH LQIRUPDWLRQ IURP WZR GLIIHUHQW REMHFWV 7KH FRYHUDJH GHSLFWLRQV DUH DUELWUDU\ WKH\ DUH JLYHQ VSHFLILF VXESL[HO IRUPV WR FODULI\ WKH FRPSRVLWH RSHUDWLRQ 7KH FRYHUDJH DUHDV DUH DFWXDOO\ DYHUDJHG DFURVV WKH SL[HO

PAGE 48

LWV FRORU 7KHUHIRUH UHIOHFWV $A RI LWV FRORU DQG OHWV $Af RI 3nV UHIOHFWHG FRORU WKURXJK 7KLV LPSOLHV WKDW WKH FRPSRVLWH FRORU DFFRUGLQJ WR WKH RYHU RSHUDWRU RI WKH WZR SL[HOV LV JLYHQ E\ && $& f $f$& f ZKHUH & UHSUHVHQWV WKH WULVWLPXOXV FRORUV 5(' *5((1 DQG %/8( 7KH XSSHU FDVH & LV XVHG WR GHVLJQDWH WKH WUXH FRORU ZKLFK RFFXUV ZKHQ WKH SL[HO LV b RYHUODSSHG E\ WKH REMHFW 7KH ORZHU FDVH FRORU F GHSLFWV WKH WUXH FRORU YDOXH PXOWLSOLHG E\ LWV RSDFLW\ YDOXH ZKLFK LV JLYHQ E\ FF $F&F f $ VLPLODU DUJXPHQW IROORZV DV SUHVHQWHG DERYH ZKHQ = LV OHVV WKHQ =MB )RU WKLV FRQGLWLRQ VXEVWLWXWH SL[HO VXEVFULSW LGHQWLILHUV IRU DQG IRU LQ WKH GHYHORSPHQW SUHVHQWHG DERYH 7KH FRPSRVLWH GHSWK RSDFLW\ DQG FRORU ZRXOG WKHQ EH JLYHQ E\ & = f F $ f $A$ f & $F L f $f$& f UHVSHFWLYHO\ 7KH LQFRUSRUDWLRQ RI WKH ]PLQ RSHUDWRU ZLWK WKH RYHU RSHUDWRU UHTXLUHV DQ DGGLWLRQDO GHYHORSPHQW IRU WKH HIIHFWV RI WZR SL[HOV ZLWK HTXDO GHSWK YDOXHV 7KLV FRQGL

PAGE 49

WLRQ LPSOLHV WKDW WZR REMHFWV DUH RFFXS\LQJ WKH VDPH YR[HO LQ VSDFH 7KHUHIRUH ERWK REMHFWV FRQWULEXWH WR WKH LQn WHQVLW\ RI WKH UHVXOWDQW SL[HO EXW WKH LQWHQVLW\ FRQWULEXn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f LV ZLWKLQ WKH TXDQWL]DWLRQ HUURU 7KH FRPSRVLWH RSDFLW\ ZRXOG WKHQ EH HTXDO WR (TXDWLRQ 1RZ FRQVLGHU WKH FRQGLWLRQ =A = ZKHUH =A =f LV ZLWKLQ WKH TXDQWL]DWLRQ HUURU 7KH FRPSRVLWH RSDFLW\ ZRXOG WKHQ EH HTXDO WR (TXDWLRQ 7KH SUREDELOLW\ RI HLWKHU RI WKHVH FRQGLWLRQV RFFXUULQJ ZLWKLQ WKH VPDOO FXELF YROXPH DUH HTXDO 7KHUHIRUH WKH FRPSRVLWH RSDFLW\ DQG FRORU YDOXHV DUH FRPSXWHG WKURXJK D VLPSOH DYHUDJH RI WKH WZR SRVVLEOH FRQGLWLRQV ZKLFK DUH JLYHQ E\

PAGE 50

$F >$[ $f$f $ $f$f? $A $ f§ $A$ f DQG &F >$& $[f$&f $& $f$&f@ $& $& &[ &f$$ f $OVR WKH FRPSRVLWH GHSWK LV JLYHQ E\ cF ]L = f ,W LV LQWHUHVWLQJ WR QRWH WKDW (TXDWLRQV DQG DUH HTXDO %RXQGDU\ DQDO\VLV RI (TXDWLRQ LV SHUIRUPHG WR FKHFN LWV YDOLGLW\ ZKLFK LV SUHVHQWHG DV IROORZV &F $A LI $ f &F $& LI $ f && & &f} LI $[ $ f 7KH ILUVW WZR ERXQGDU\ H[DPSOHV GHPRQVWUDWH D UHGXFWLRQ WR D VLQJOH SL[HO FDVH ZKLFK LV WR EH H[SHFWHG 7KH ODVW ERXQGDU\ H[DPSOH UHGXFHV WR DQ DYHUDJH FRORU WKDW GRHV QRW EHFRPH DPSOLILHG ZKLFK LV DOVR WR EH H[SHFWHG $ SVXHAR FRGH RXWOLQH RI WKLV 5*%=$ FRPSRVLWLQJ DOJRULWKP ZLWK UHVSHFW WR D SDLU RI LPDJH DUUD\V LV JLYHQ LQ )LJXUH $V VKRZQ HDFK SL[HO RI WKH WZR LPDJH DUUD\V DUH FRPSRVn LWHG WR SURGXFH D FRPSRVLWH LPDJH DUUD\ IRU GLVSOD\ 7KH

PAGE 51

5*%=$ &RPSRVLWLQJ $OJRULWKP JLYHQ $Q DUUD\ 5*%=$A>[\@ $Q DUUD\ 5*%=$>[\@ $Q DUUD\ UJE=$F>[\@ EHJLQ IRU HDFK HOHPHQW[\f RI DUUD\ UJE=$F>[\@ $f $@O $ f n ,I ]O UF EF =4 HQGLI $M5O $L*L $% e $$ WKHQ ,$W-$A5R ,$W-$R* $f$% LI =O UF EF ]F f§ HQGLI DU $* Dp WKHQ O$A$A O$A$A ,$M•$M%O LI =L = WKHQ UF EF fO HQGLI $5 $O"O $% $5 $* D% 5 *L % 5f$$ *f$[$ %f$$ HQGIRU 'LVSOD\ UJEF DUUD\ RI WKH UJE=$F DUUD\ HQG GR )LJXUH 7KH 5*%=$ &RPSRVLWLQJ $OJRULWKP

PAGE 52

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

PAGE 53

$ KDUGZDUH V\QWKHVLV RI WKH K\SRWKHWLFDO KLHUDUFK\ RI FRPSRVLWLQJ RSHUDWLRQV LV ZKDW GHILQHV WKH FRPSRVLWLQJ QHWZRUN ,W LV FUHDWHG WKURXJK LQWHUFRQQHFWLQJ DQ HQVHPEOH RI IXQGDPHQWDO KDUGZDUH FRPSRVLWLQJ XQLWV WKDW UHDOL]H WKH FRPSRVLWLQJ RSHUDWLRQ 7KHVH XQLWV DUH WHUPHG FRPSRVLWLQJ SURFHVVLQJ QRGHV &31Vf 7KH GHILQHG IXQFWLRQ RI D &31 LV WR SURGXFH D VLQJOH FRPSRVLWHG SL[HO YDOXH IURP D SDLU RI LQSXW SL[HO YDOXHV ,W PDLQWDLQV D WRO FRQILJXUDWLRQ ZKHUH WKH RXWSXW RI RQH &31 FDQ VXSSO\ DQ LQSXW WR D VXFn FHHGLQJ &31 7KLV LV DQ LWHUDWLYH SURSHUW\ ZKLFK LV WKH SURSHUW\ UHTXLUHG WR UHDOL]H WKH KLHUDUFK\ RI FRPSRVLWLQJ RSHUDWLRQV LQ KDUGZDUH 7KH VWUXFWXUH RI WKH HQWLUH FRPSRVLWLQJ QHWZRUN LV GULYHQ E\ WKH VWUXFWXUH RI DQ LQGLYLGXDO &31 7KHUHIRUH WKH LQWHUFRQQHFWLRQ RI &31V IRUPV D ELQDU\ WUHH ZKLFK UHDOL]HV WKH FRPSRVLWLQJ QHWn ZRUN $ GHSLFWLRQ RI WKLV VWUXFWXUH LV VKRZQ LQ )LJXUH ZKLFK LOOXVWUDWHV D IXOO\ EDODQFHG OHYHO FRPSRVLWLQJ WUHH WKDW KDV &31V DQG FRQQHFWLRQV IRU GHHSHU &31 OHYHOV RU IRU WHUPLQDO 2*1 FRQQHFWLRQ 7KH JHQHUDO VWUXFn WXUH IRU D IXOO\ EDODQFHG WUHH ZLWK 1 WHUPLQDO FRQQHFWLRQV PDLQWDLQV Q ORJ1 OHYHOV ZLWK 1O &31V IRU WKH QHWZRUN FRQILJXUDWLRQ +RZHYHU WKH FRPSRVLWLQJ QHWZRUN GRHV QRW KDYH WR EH D IXOO\ EDODQFHG WUHH ,W FDQ EH XQEDODQFHG DV ORQJ DV DOO RI WKH 2*1V DUH FRQQHFWHG DW WKH VDPH OHYHO ZLWKLQ WKH V\VWHP WUHH

PAGE 54

7R 9LGHR *HQHUDWLRQ 1RGH 9*1f )URP GHHSHU OHYHOV RI &RPSRVLWLQJ 3URFHVVLQJ 1RGHV &31Vf RU IURP HLJKW 2EMHFW *HQHUDWLRQ 1RGHV 2*1Vf )LJXUH $ IXOO\ EDODQFHG WKUHH OHYHO FRPSRVn LWLQJ WUHH

PAGE 55

7KH FRPSRVLWLQJ QHWZRUN FDQ EH PRGHOHG DV D SLSHOLQHG PDFKLQH ZKHUH HDFK OHYHO LQ WKH V\VWHPnV ELQDU\ WUHH VWUXFWXUH LV D SLSHOLQH VWDJH $W HYHU\ PDFKLQH F\FOH D FROOHFWLRQ RI SL[HOV ZLWK LGHQWLFDO ; < FRRUGLQDWHV DUH URXWHG WR WKH QRGHV ZLWKLQ WKH ORZHVW OHYHO RI WKH V\VWHP WUHH 7KH PDFKLQH RSHUDWLRQ SURFHHGV LQ D V\QFKURQRXV IHHGWKURXJK PDQQHU IRU HYHU\ PDFKLQH F\FOH ZKHUH D FROn OHFWLRQ RI SL[HOV DW D SDUWLFXODU OHYHO LQ WKH V\VWHP WUHH LV FRPSXWHG WR SURGXFH D FROOHFWLRQ RI FRPSRVLWHG SL[HO YDOXHV DV D UHVXOW 7KHVH UHVXOWV DUH URXWHG EHIRUH WKH QH[W PDFKLQH F\FOH WR WKH LQSXWV RI D VXFFHHGLQJ OHYHO LQ WKH V\VWHP WUHH 7KHUHIRUH HDFK VXFFHHGLQJ OHYHO LQ WKH V\VWHP WUHH SURGXFHV KDOI WKH DPRXQW RI SL[HO YDOXHV IXOO\ EDODQFHG WUHHf WKHQ ZHUH SURYLGHG IRU LQSXW 7KH RXWSXW RI WKLV PDFKLQH SURYLGHV D VLQJOH FRPSRVLWHG SL[HO YDOXH DV D UHVXOW ZKLFK LV SURGXFHG IURP WKH KLJKHVW OHYHO RI WKH V\VWHP WUHH 7KLV VWUXFWXUH LV FODVVLILHG DV D V\QFKURQRXV IHHGn IRUZDUG FRQILJXUDWLRQ ZKHUH &31 RSHUDWLRQ LV V\QFKURQRXV ZLWK WKH LPDJH XSGDWH UDWH 7KHUHIRUH WKH PDFKLQH F\FOHn WLPH LV D IXQFWLRQ RI ERWK WKH LPDJH VSDFH UHVROXWLRQ DQG WKH LPDJH XSGDWH UDWH 7KH SLSHOLQH LV FRQVLGHUHG IXOO ZKHQ HYHU\ &31 LQ WKH V\VWHP WUHH KDV D YDOLG LQSXW 'XULQJ D IXOO SLSHOLQH VWDWH HDFK OHYHO RI WKH WUHH LV SURFHVVLQJ D VHW RI SL[HOV WKDW KDYH LGHQWLFDO ; < FRRUGLn QDWHV 7KHUHIRUH WKH VWDUWXS WLPH WKURXJK D WUHH ZLOO EH

PAGE 56

D IXQFWLRQ RI WKH WUHH GHSWK DQG WKH QXPEHU RI SLSHOLQH VWDJHV ZLWKLQ DQ LQGLYLGXDO &31 7KH HIIHFW RI WKH IHHGWKURXJK VWUXFWXUH RI WKH FRPSRVLWLQJ QHWZRUN KDV WR EH FRQVLGHUHG UHJDUGLQJ WKH 5*%=$ DOJRULWKP 7KLV VWUXFWXUH KDV D FXPXODWLYH DIIHFW WKDW GLUHFWO\ LQIOXHQFHV WKH FRPSRVLWLQJ RSHUDWLRQ 7KHUHn IRUH WKH 5*%=$ DOJRULWKP KDV WR EH DGMXVWHG WR DFFRPPRGDWH WKLV IDFW 7KH FRPSRVLWLQJ QHWZRUN LV D VXEWUHH RI WKH V\VWHP WUHH DQG WKH 2*1V DUH WHUPLQDO QRGHV RI WKH V\VWHP WUHH WKDW SURYLGH LQSXW WR WKH FRPSRVLWLQJ QHWZRUN 1RZ FRQn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

PAGE 57

$ $ $ f $$ D $ $V f $$ $ $ $ $$ $L f $L $L f $L$L f ZKHUH WKH VXEVFULSW LGHQWLILHV WKH WUHH QRGH QXPEHU 7KH UHVXOW LV D UHFXUVLYH UHODWLRQ IRU WKH HYDOXDWLRQ RI WKH RSDFLW\ YDOXH 7KH FRPSRVLWH FRORU YDOXH DQG GHSWK YDOXH DUH GHILQHG WKURXJK WKH XVH RI D VLPLODU GHYHORSPHQW IRU HDFK RI WKH WKUHH GHSWK YDOXH FRPSDULVRQV 7KH FRQGLWLRQ ]L ]LO LYHV ]L f ]L FL FL  f $LfrL DQG WKH FRQGLWLRQ = bLO LYHV =L =L FL FLO  f $LOfFL DQG WKH FRQGLWLRQ = ]LL JLYHV ]L ]L ]LO FL FL FLO f L$LFLO $LOFLf f f f f f f ZKHUH WKH ORZHU FDVH FRORU Ff GHSLFWV WKH WUXH FRORU YDOXH PXOWLSOLHG E\ LWV RSDFLW\ YDOXH 7KLV IRUP RI WKH FRPSRVn LWLQJ IXQFWLRQV UHTXLUH HDFK FRORU YDOXH HQWHULQJ WKH

PAGE 58

FRPSRVLWLQJ QHWZRUN WR EH PXOWLSOLHG E\ LWV UHVSHFWLYH RSDFLW\ $OVR HDFK FRPSRVLWH FRORU YDOXH H[LWLQJ WKH QHWZRUN ZLOO EH WKH FRPSRVLWH FRORU PXOWLSOLHG E\ LWV FRPSRVLWH RSDFLW\ 7KH UHFXUVLYH UHODWLRQV DUH KDQGOHG E\ LWHUDWLYH WHFKQLTXHV XWLOL]LQJ &31V 7KH 5*%=$ FRPSRVLWLQJ DOJRULWKP WKDW HDFK &31 VKRXOG H[HFXWH LV GHSLFWHG LQ )LJXUH 7KLV DOJRULWKP ZKLFK LV WHUPHG WKH JHQHUDO 5*%=$ FRPSRVn LWLQJ DOJRULWKP LQFOXGHV WKH LPDJH DUUD\V DQG WKH PXOWLn SOLFDWLRQ RSHUDWLRQ RI WKH 2*1nV ,W DOVR LQFOXGHV WKH LPDJH DUUD\ RI WKH 9*1 DQG D UHIHUHQFH WR WKH ''1 7KH VHFRQG ORRS ZLWKLQ WKH PDLQ ORRS LV WKH DFWXDO QHWZRUN DOJRULWKP 7KLV WDVN LQSXWV D FROOHFWLRQ RI SL[HO YDOXHV IRU SURFHVVLQJ DFFRUGLQJ WR WKHLU UHVSHFWLYH GHSWK UHn ODWLRQVKLS WR SURGXFH D VLQJOH VXUYLYLQJ FRPSRVLWH SL[HO YDOXH IRU RXWSXW 7KH ORRS FRXQWV GRZQ LQ RUGHU WR REYLDWH WKH VWDUWXS WLPH WKDW ZRXOG EH DVVRFLDWHG ZLWK D KDUGZDUH SLSHOLQH 7KH RSHUDWLRQ RI WKH HQWLUH FRPSRVLWLQJ QHWZRUN DFWLRQ LV UHGXFHG WR D VSHFLDO FDVH ZKHQ RQO\ RSDTXH REMHFWV DUH LQYROYHG ZLWKRXW WKH LQFOXVLRQ RI VSHFLDO HIIHFWV HJ GLVVROYHV GDUNHQLQJ DQWLDOLDVLQJ HWFf 7KLV LV JLYHQ DV IROORZV B "Ln + L L ]F f I]LOn ]L ]LO =L LI =L =L f

PAGE 59

*HQHUDO 5*%=$ &RPSRVLWLQJ $OJRULWKP FRQVW Q WRWDO QXPEHU RI &31V LQ WUHH JLYHQ $UUD\ UJE=$ ZKHUH L OQO ^QRGH UHJLVWHUV` $UUD\ 5*%=$L [ \ ZKHUH M O QO ^2*1 0HPRU\` $UUD\ UJEY ^9*1 0HPRU\` EHJLQ n IRU HDFK HOHPHQW[\f RI 5*%=$r [ \ DQG UJE[ \ GR IRU L QO WR QO GR ^ORDG XQnRXWSXW UHJLVWHUV` M BL Q WA[n<";\ JL MM[\GM[\ L B M[\rM[\ WL rM[\ ;\ HQGIRU IRU L Q GRZQWR GR L U $L A ]L UL E ]M HQGLI LI =L UL JL EL ]L HQGLI LI =L UL + =L HQGLI $ ]LL WKHQ L rL =L =L ULO "LO ELO =L OKH[L Oa$fU cLALLO Of$LfEL ^HQG ORDG 2*1 RXWSXW UHJLVWHUV` ^&31 FRPSRVLWLQJ RSHUDWLRQ` $LA$LOf WKHQ $LOfUL ALf§$LO_"L B$LOfEL =L WKHQ ULO n "LO n E UL EL EL =L  $LUL -$LJLO n$LELO $LOULf $LOJLc $LOELA HQGIRU UE[Y HQGIRU UJE 'LVSOD\ UJE< f DUUD\ HQG ;< ^HQG &31 FRPSRVLWLQJ RSHUDWLRQ` ^ZULWH FRPSRVLWH UHVXOW WR 9*1` ^''1` )LJXUH 7KH JHQHUDO 5*%=$ FRPSRVLWLQJ DOJRULWKP IRU D IXOO\ EDODQFHG WUHH 1RWH WKDW ORZHU FDVH OHWWHUV GHVLJQDWH WKH SURGXFW RI LQWHQVLW\ DQG RSDFLW\

PAGE 60

f & F ^&L W&LOn ^ FL &LOfn M"L =L "L =L OI =L f =L DW HYHU\ SL[HO LQ WKH L LPDJH DUUD\V 7KH FRPSRVLWH SL[HO KDV HLWKHU IXOO FRYHUDJH RU QR FRYHUDJH 7KHUHIRUH WKH RSDFLW\ LQIRUPDWLRQ LV QRW QHHGHG $OVR WKH PDWWH LQIRUPDWLRQ LV LPSOLHG E\ D GHSWK YDOXH WKDW LV QRW WKH PD[LPXP 7KH VSHFLDOL]HG 5*%= DOJRULWKP LV SUHVHQWHG LQ )LJXUH $V IRU )LJXUH WKH VHFRQG ORRS ZLWKLQ WKH PDLQ ORRS LV WKH DFWXDO QHWZRUN DOJRULWKP 7KLV WDVN LQSXWV D FROOHFWLRQ RI SL[HO YDOXHV IRU SURFHVVLQJ DFn FRUGLQJ WR WKHLU UHVSHFWLYH GHSWK UHODWLRQVKLS WR SURGXFH D VLQJOH VXUYLYLQJ FRPSRVLWH SL[HO YDOXH IRU RXWSXW $ PL[WXUH RI ERWK WKH VSHFLDOL]HG DQG WKH JHQHUDO IRUPV RI WKH FRPSRVLWLQJ DOJRULWKP IRU &31V FDQ FRPSRVH D FRPSRVLWLQJ QHWZRUN 7KH 2*1V FDQ EH VSHFLDOL]HG IRU RSDTXH REMHFWV ZLWKRXW DQWLDOLDVLQJ DQG VSHFLDO HIIHFWV 7KHVH QRGHV ZRXOG EH DVVLJQHG WR WKH VHFWLRQ RI WKH WUHH WKDW FRQWDLQ WKH VSHFLDOL]HG &31V $OVR 2*1V WKDW SURFHVV REMHFWV ZLWK DQWLDOLDVLQJ DQG VSHFLDO HIIHFWV FDQ EH DVVLJQHG WR WKH VHFWLRQ RI WKH WUHH WKDW FRQWDLQ WKH JHQHUDO &31V &RQILJXUDWLRQV FRXOG LQFOXGH D PL[ RI JHQHUDO DQG VSHFLDOL]HG &31V 7KH SXUSRVH RI PL[LQJ &31V ZRXOG EH WR UHGXFH WKH V\VWHP FRPSOH[LW\ VLQFH WKH VSHFLDOL]HG &31V DUH RI D VLPSOHU IRUP WKDQ WKH JHQHUDO &31V

PAGE 61

6SHFLDOL]HG 5*%= &RPSRVLWLQJ $OJRULWKP FRQVW Q WRWDO QXPEHU RI &31V LQ WUHH JLYHQ $UUD\ 5*%=A ZKHUH L OQO ^QRGH UHJLVWHUV` $UUD\ 5*%=V [ \ ZKHUH M OQO ^2*1 0HPRU\f $UUD\ 5*%[\ \ ^9*1 0HPRU\` EHJLQ n IRU HDFK HOHPHQW[\f RI 5*%= [ \ DQG 5*%; \ GR IRU L QO WR QO GR ^ORDG-•*“\RXWSXW UHJLVWHUV` M L Q AL f FM;< 6L B %O;\ 6L 6LA\ HQGURU n n ^HQG ORDG 2*1 RXWSXW UHJLVWHUV` IRU L Q GRZQWR GR ^&31 FRPSRVLWLQJ RSHUDWLRQ` LI =L =L WKHQ 5L HQGLI LI = L 5L %L =L HQGLI 5L *L %L =L =L WKHQ 5L 6L %L =L LI =L =L WKHQ 5L *L Q HQGLI 5L AL 5LA *LOf %LOf HQGIRU 5*% HQGIRU < 5*% 'LVSOD\ 5*%; \ DUUD\ HQG \ ^HQG &31 FRPSRVLWLQJ RSHUDWLRQ` ^ZULWH FRPSRVLWH UHVXOW WR 9*1` ^''1` )LJXUH 7KH VSHFLDOL]HG 5*%= FRPSRVLWLQJ DOJRULWKP RI D IXOO\ EDODQFHG WUHH

PAGE 62

&RPSRVLWLQJ 3URFHVVLQJ 1RGH 7KH SXUSRVH RI D &31 LV WR SHUIRUP SL[HOE\SL[HO FRPSRVLWLQJ ,W LV D IXQGDPHQWDO LWHUDWLYH KDUGZDUH EXLOGn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 DQG 3,n ZKLFK FDQ EH URXWHG WR WKH &31 E\ HLWKHU WZR SUHFHGLQJ &31V RU E\ WZR SUHFHGLQJ 2*1V 7KH GDWD RXWSXW FRQVLVWV RI D VLQJOH SL[HO YDOXH ZKLFK FDQ EH URXWHG WR WKH LQSXW RI D VXFn FHHGLQJ &31 RU WR WKH LQSXW RI D YLGHR JHQHUDWLRQ QRGH 7KH &31 LQSXW FORFN &/. LV GULYHQ E\ D V\VWHP FORFN WKDW V\QFKURQL]HV WKH LQWHUQDO &31 RSHUDWLRQ ZLWK WKH HQWLUH V\VWHP 7KLV VLJQDO LV SURYLGHG E\ WKH YLGHR JHQHUDWLRQ QRGH 9*1f ZKLFK PDLQWDLQV WKH HQWLUH V\VWHP WLPLQJ DQG FRQWURO $ SL[HO LV UHSUHVHQWHG E\ ILYH LQGHSHQGHQW YDULDEOHV 5(' *5((1 %/8( $/3+$ DQG = 7KH WULVWLPXOXV FRORU RU LQWHQVLW\ LV UHSUHVHQWHG E\ WKH YDOXHV RI 5(' *5((1 DQG %/8( 7KH $/3+$ YDOXH UHSUHVHQWV WKH DYHUDJH RSDTXHQHVV RI

PAGE 63

3L[HO RXWSXW WR QH[W VWDJH RI V\VWHP WUHH ZKHUH 3 ^U c J c Ec $ = M` 3L fLUL f Lf EL f $ L f = LA OLO rUL f L f E L f $ L f = L r &31M LV D &31 ORFDWHG LQ WKH &1 DW QRGH SRVLWLRQ L &/. LV WKH V\VWHP WLPLQJ LQSXW )LJXUH $Q LWHUDWLYH EXLOGLQJ EORFN GHSLFWLRQ RI D FRPSRVLWLQJ SURFHVVLQJ QRGH &31f

PAGE 64

WKH SL[HO RU WKH DYHUDJH OLJKW EORFNLQJ FKDUDFWHULVWLF RI WKH PDWHULDO WKDW WKH SL[HO UHSUHVHQWV 7KH = YDOXH UHSUHn VHQWV WKH = FRRUGLQDWH LQ FDUWHVLDQ VSDFH ZKHUH WKH SL[HO H[LVWV 7KH ; < FDUWHVLDQ FRRUGLQDWHV DUH LPSOLHG DV LGHQWLFDO IRU ERWK LQSXW SL[HOV EXW PD\ EH GLIIHUHQW ZLWKLQ WKH VDPH FORFN F\FOH IRU WKH VLQJOH RXWSXW SL[HO GXH WR WKH KDUGZDUH SLSHOLQH DSSURDFK 6FKHPHV IRU UHDOL]LQJ WKH SUHYLRXVO\ GLVFXVVHG 5*%$= FRPSRVLWLQJ DOJRULWKPV DUH GHYHORSHG WKDW DUH IDVW DQG LQH[SHQVLYH WR LPSOHPHQW LQ KDUGZDUH EXW ZKLFK SURGXFHV UHVXOWV RI QXPHULFDOO\ KLJK TXDOLW\ 7KHVH VFKHPHV KRQRUV WZR FRQVLGHUDWLRQV PDFKLQH DQG QXPHULFDO FRQVLGHUDWLRQV 0DFKLQH FRQVLGHUDWLRQV FRQFHUQ VSHHG DQG FRVW RI WKH SK\VLn FDO GHYLFH 1XPHULFDO FRQVLGHUDWLRQV FRQFHUQ WKH FORVHVW DSSUR[LPDWLRQV WR WKH H[DFW QXPEHUV 7KH VFKHPHV DWWHPSW WR PDLQWDLQ D EDODQFH EHWZHHQ ERWK $OVR WKH HIIHFWV RI URXQGRII HUURU DFFXPXODWLRQ GXH WR WKH IHHGWKURXJK RSHUDn WLRQ RI WKH ELQDU\ WUHH RI &31V DUH WDNHQ LQWR FRQVLGHUn DWLRQ )LQLWH SUHFLVLRQ IL[HGSRLQW QXPEHUV DUH XVHG LQ WKLV PDFKLQH IRU UHSUHVHQWDWLRQ RI WKH SL[HO YDOXHV 7KLV UHSUHVHQWDWLRQ DOORZV VWRUDJH RI SL[HO YDOXHV ZLWKLQ WKH ORFDO LPDJH EXIIHUV RI WKH 2*1V DQG RI WKH 9*1 WR EH LQWHn JHUV ZKLFK VLPSOLILHV WKH LPDJH EXIIHU RUJDQL]DWLRQ $OVR WKH KDUGZDUH FRPSOH[LW\ IRU UHDOL]DWLRQ RI WKH FRPn SRVLWLQJ DOJRULWKPV DQG RI WKH YLGHR JHQHUDWLRQ SURFHVVLQJ

PAGE 65

DOJRULWKPV LV UHGXFHG DORQJ ZLWK DFFRPPRGDWLRQ RI IDVWHU F\FOH WLPHV IRU DQ LPSOHPHQWDWLRQ 7KHUHIRUH WKH FRPSRVn LWLQJ DOJRULWKPV WKDW DUH GHSLFWHG LQ )LJXUHV DQG PXVW EH DGMXVWHG WR DFFRPPRGDWH WKH IL[HGSRLQW UHSUHn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

PAGE 66

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n SDUHQW ,W DOVR KDQGOHV DQWLDOLDVLQJ DQG VSHFLDO HIIHFWV VXFK DV IDGHRXWV DQG IDGHLQV 7KH KDUGZDUH RUJDQL]DWLRQ FRQWDLQV WKUHH GLVWLQFW IXQFWLRQDO XQLWV WKH GHSWK FRPSXn WDWLRQ XQLW WKH RSDFLW\ FRPSXWDWLRQ XQLW DQG WKH FRORU FRPSXWDWLRQ XQLW 7KHVH IXQFWLRQDO XQLWV DUH GLVFXVVHG ZLWK UHVSHFW WR ILQLWH IL[HGSRLQW SL[HO YDOXH UHSUHn VHQWDWLRQ 7KH DOJRULWKP DQG WKH FRQFHSWXDO KDUGZDUH RUJDQL]DWLRQ RI HDFK XQLW LV SUHVHQWHG 'HSWK FRPSXWDWLRQ XQLW 7KH GHSWK FRPSXWDWLRQ XQLW GLVFHUQV WKH IRUHJURXQG SL[HO IURP WKH EDFNJURXQG SL[HO RU LGHQWLILHV ERWK DV IRUHJURXQG SL[HOV 7KLV XQLW IXQFWLRQV DFFRUGLQJ WR WKH

PAGE 67

DOJRULWKP SUHVHQWHG LQ )LJXUH ZKLFK LV D VXEVHW RI WKH JHQHUDO 5*%=$ FRPSRVLWLQJ DOJRULWKP RI )LJXUH 7KH GHSWK YDOXH = LV UHSUHVHQWHG E\ D VLQJOH ]ELW LQWHJHU ZKHUH = =f 7KHUHIRUH WKH IORDWLQJ SRLQW UHSUHn VHQWDWLRQ RI WKLV YDOXH LV LQLWLDOO\ WUXQFDWHG RU URXQGHG 7KH WDVN SHUIRUPHG E\ WKLV XQLW DV WKH DOJRULWKP LQGLn FDWHV FRQVLVWV RI f UHFHLYLQJ D SDLU RI GHSWK YDOXHV f SHUIRUPLQJ D FRPSDULVRQ RI GHSWK YDOXHV f SURYLGLQJ VWDWXV LQIRUPDWLRQ DQG f RXWSXWWLQJ WKH VPDOOHVW GHSWK YDOXH 6WDWXV LQIRUPDWLRQ FRQVLVWV RI WKH /(66 ELW DQG (48$/ ELW ZKLFK DUH XVHG E\ WKH FRORU FRPSXWDWLRQ XQLW 7KH /(66 ELW ZKHQ VHW LQGLFDWHV WKDW WKH = YDOXH LV VPDOOHU WKHQ WKH = YDOXHr 7KH (48$/ ELW ZKHQ VHW LQGLFDWHV WKDW WKH = YDOXH DQG = YDOXH DUH HTXDO LQ PDJQLWXGH $ EORFN GLDJUDP RI WKH &31 GHSWK FRPSXWDWLRQ XQLW LV GHSLFWHG LQ )LJXUH 6WDJH SHUIRUPV DQ LQLWLDO ORDG RI WKH LQFRPLQJ SDLU RI GHSWK YDOXHV IURP WKH &31 LQWHUFRQn QHFW 6WDJH SHUIRUPV D FRPSDULVRQ RI WKH WZR GHSWK YDOXHV IRU VWDWXV LQIRUPDWLRQ DQG SDVVHV WKH WZR GHSWK YDOXHV DORQJ ZLWK WKH VWDWXV LQIRUPDWLRQ 6WDJH URXWHV WKH VXUYLYLQJ GHSWK YDOXH ZKLFK LV WKH FRPSRVLWH GHSWK YDOXH WR VXFFHHGLQJ VWDJHV XWLOL]LQJ D PXOWLSOH[HU ZLWK WKH /(66 VWDWXV ELW DV D VHOHFWRU 7KH VXFFHHGLQJ VWDJHV DUH ZDLWLQJ VWDJHV WKDW DOORZ D ILQDO UHVXOW WR

PAGE 68

&31 'HSWK &RPSXWDWLRQ 8QLW $OJRULWKP JLYHQ OLWHUDO =s OLWHUDO = EHJLQ (48$/ LI =L =L WKHQ /LOVV HOVH 8VV L LI = HT6O93 WKHQ HQGLI HQGLI HQG ^]ELW LQWHJHU` ^]ELW LQWHJHU` ^UHVXOW LV D ]ELW LQWHJHU` )LJXUH 7KH DOJRULWKP SHUIRUPHG E\ D JHQHUDO &31 GHSWK FRPSXWDWLRQ XQLW

PAGE 69

=c )LJXUH %ORFN GLDJUDP RI D JHQHUDO &31 GHSWK FRPSXWDn WLRQ XQLW

PAGE 70

RFFXU VLPXOWDQHRXVO\ ZLWK WKH UHPDLQLQJ &31 FRPSXWDWLRQ XQLW UHVXOWV 2SDFLW\ FRPSXWDWLRQ XQLW 7KH RSDFLW\ FRPSXWDWLRQ XQLW SURGXFHV D VLQJOH FRPn SRVLWH RSDFLW\ YDOXH IURP WZR RSDFLW\ YDOXHV WKDW DUH SURYLGHG DV LQSXW 7KH RSDFLW\ LV GHILQHG DV D SRVLWLYH IUDFWLRQDO YDOXH WKDW UDQJHV IURP ]HUR WR RQH (DFK RSDFn LW\ YDOXH LV VWRUHG LQ WKH LPDJH EXIIHUV RI WKLV PDFKLQH DV IL[HGSRLQW ELQDU\ QXPEHUV 7KHUHIRUH WKH RSDFLW\ YDOXH $ LV UHSUHVHQWHG E\ D SRVLWLYH IL[HGIUDFWLRQDO YDOXH JLYHQ E\ $ f AD[ ZKHUH $ LV D ELQDU\ LQWHJHU VXFK WKDW $ $PD[ DQG LV D FRQVWDQW WKDW GHILQHV WKH UDQJH RI RSDFLW\ 7KH ORFDO LPDJH EXIIHUV VWRUH WKH LQWHJHU YDOXH $ ZKLOH WKH IL[HGIUDFWLRQDO YDOXH LV LQFRUSRUDWHG E\ WKH KDUGZDUH 6XEVWLWXWLQJ WKH RSDFLW\ UHSUHVHQWDWLRQ RI (TXDWLRQ LQWR (TXDWLRQ DQG FROOHFWLQJ WHUPV JLYHV $L $L APD[ f $Lf$LO AD[ f 7KH GLYLVLRQ UHTXLUHG LQ (TXDWLRQ LV HOLPLQDWHG E\ GHILQLQJ $AA DV PB ZKHUH P LV WKH QXPEHU RI ELWV LQ $ 7KLV WUDQVIRUPV WKH GLYLVLRQ RSHUDWLRQ WR D VKLIW RSHUD

PAGE 71

WLRQ $ WUDGHRII RFFXUV ZLWK WKLV WHFKQLTXH VLQFH HDFK LPDJH EXIIHU ZLWKLQ WKH 2*1V ZLOO UHTXLUH DQ H[WUD ELW SODQH DQG DQ H[WUD VLJQDO OLQH WR UHSUHVHQW WKH RSDFLW\ YDOXH IRU D SDUWLFXODU UDQJH 6XEVWLWXWLQJ WKH YDOXH RI $MMMD[ LQWR (TXDWLRQ JLYHV $L $L Q $Lf$ ROWOO f ,Q RUGHU WR KDYH D PRUH DFFXUDWH UHVXOW WKH KDUGZDUH XQLW UHSUHVHQWV HDFK RSDFLW\ YDOXH DV D KLJKHU SUHFLVLRQ QXPEHU ZKLFK UHGXFHV WKH URXQGRII HUURU DFFXPXODWLRQ WKURXJK WKH FRPSRVLWLQJ QHWZRUN 7KLV LV VKRZQ E\ PXOWLSO\LQJ ERWK VLGHV RI (TXDWLRQ ZLWK P DQG DGMXVWLQJ WKH SURGXFW WHUP ZKLFK JLYHV P$ P$L $Lf}$ !PO f (TXDWLRQ VKRZV WKDW WKH RSDFLW\ YDOXH FDQ EH KDQGOHG DV D GRXEOH SUHFLVLRQ QXPEHU LI WKH RSDFLW\ YDOXH LV VKLIWHG OHIW E\ P ELWV DQG LI WKH OHDVWVLJQLILFDQWKDOI RI WKH ZRUG LV SDGGHG ZLWK ]HURHV EHIRUH HQWHULQJ WKH &1 WUHH 7KHUHIRUH WKH RSDFLW\ FRPSXWDWLRQ ZLWK WKH RSDFLW\ YDOXHV GHILQHG DV GRXEOH SUHFLVLRQ QXPEHUV LV JLYHQ E\ $L $L } $Lf$L PO f

PAGE 72

ZKHUH WKH RSDFLW\ YDOXH $ LV D ELQDU\ LQWHJHU VXFK WKDW $s p 7KH RSDFLW\ FRPSXWDWLRQ XQLW IXQFWLRQV DFFRUGLQJ WR WKH DOJRULWKP SUHVHQWHG LQ )LJXUH ZKLFK IROORZV WKH GHYHORSHG UHODWLRQV 7KH WDVN SHUIRUPHG E\ WKLV XQLW FRQVLVWV RI f UHFHLYLQJ D SDLU RI RSDFLW\ YDOXHV f SHUIRUPLQJ DQ RSDFLW\ FRPSRVLWLQJ RSHUDWLRQ DQG f RXWSXWn WLQJ WKH FRPSRVLWH RSDFLW\ UHVXOW $ EORFN GLDJUDP RI WKH FRPSRVLWLQJ FRPSXWDWLRQ XQLW LV GHSLFWHG LQ )LJXUH 6WDJH SHUIRUPV DQ LQLWLDO ORDG RI WKH SDLU RI RSDFLW\ YDOXHV IURP WKH &31 LQWHUFRQn QHFW 6WDJH SHUIRUPV D VXEWUDFWLRQ RSHUDWLRQ DQG SDVVHV WKH WZR RSDFLW\ YDOXHV DORQJ ZLWK WKH VXEWUDFWLRQ UHVXOW 6WDJH SHUIRUPV D PXOWLSOLFDWLRQ RI WKH VXEWUDFWLRQ UHVXOW ZLWK WKH $A RSDFLW\ YDOXH DQG VKLIWV WKH PXOWLn SOLFDWLRQ UHVXOW ULJKW E\ P ELWV GLYLVLRQf ,W DOVR SDVVHV WKH $ RSDFLW\ YDOXH DORQJ ZLWK WKH VKLIWHG PXOWLn SOLFDWLRQ UHVXOW 6WDJH VXPV WKH $ YDOXH ZLWK WKH VKLIWHG PXOWLSOLFDWLRQ UHVXOW DQG SHUIRUPV URXQGLQJ ZKLFK SURGXFHV WKH FRPSRVLWH RSDFLW\ 1RWH WKDW HOLPLQDWLQJ WKH VLJQDO LQSXW WR WKH FDUU\ ELW DQG VHWWLQJ WKH FDUU\ ELW WR ZLOO FDXVH FKRSSLQJ RI WKH PXOWLSOLFDWLRQ UHVXOW LQVWHDG RI URXQGLQJ 7KH VXFFHHGLQJ VWDJHV DUH ZDLWLQJ VWDJHV WKDW DOORZ D ILQDO UHVXOW WR RFFXU VLPXOWDQHRXVO\ ZLWK WKH UHPDLQLQJ &31 FRPSXWDWLRQ XQLW UHVXOWV

PAGE 73

&31 2SDFLW\ &RPSXWDWLRQ 8QLW $OJRULWKP FRQVW P QXPEHU RI ELWV RI LQLWLDOO\ VWRUHG RSDFLW\ YDOXH JLYHQ OLWHUDO $ ^PELW LQWHJHU` OLWHUDO $A ^PELW LQWHJHU` EHJLQ $L $L >PB $Lf$LO VKU Pf LI > PB $Lf$L $1' PB@ Pf WKHQ $M KL ^URXQGRII HUURU` HQGLI HQG ^UHVXOW LV D PELW LQWHJHU` )LJXUH 7KH DOJRULWKP SHUIRUPHG E\ D JHQHUDO &31 RSDFLW\ FRPSXWDWLRQ XQLW

PAGE 74

$L )LJXUH %ORFN GLDJUDP RI D JHQHUDO &31 RSDFLW\ FRPSX WDWLRQ XQLW

PAGE 75

&RORU FRPSXWDWLRQ XQLW 7KH FRORU FRPSXWDWLRQ XQLW SURGXFHV D FRPSRVLWH FRORU YDOXH IURP WZR FRORU YDOXHV WKDW DUH SURYLGHG DV LQSXW 7KH FRORU YDOXHV DUH GHILQHG DV WKH WUXH WULVWLPXOXV FRORU YDOXHV PXOWLSOLHG E\ WKHLU UHVSHFWLYH RSDFLW\ YDOXH (DFK SULPDU\ FRORU LQWHQVLW\f YDOXH F LV VWRUHG LQ WKH PDFKLQHnV LPDJH EXIIHUV DV DQ QELW LQWHJHU ZKHUH F QO %XW WKLV KDUGZDUH XQLW KDQGOHV WKH RSDFLW\ DQG WKH FRORU YDOXHV DV KLJKHU SUHFLVLRQ QXPEHUV P DQG PQ ELWV UHVSHFWIXOO\f LQ RUGHU WR UHGXFH WKH URXQGRII HUURU DFFXPXODWLRQ WKURXJK WKH FRPSRVLWLQJ QHWZRUN 7KH FRPSRVLWH FRORU RSHUDWLRQ IRU WKH =s ]LL FRQGLWLRQ LV GYHORSHG E\ VXEVWLWXWLQJ WKH KLJKHU SUHFLn VLRQ UHSUHVHQWDWLRQV RI ERWK WKH LQWHQVLW\ DQG WKH RSDFLW\ YDOXHV LQWR (TXDWLRQ ZKLFK JLYHV FL f $Lf&L L PO f ZKHUH HDFK SULPDU\ FRORU YDOXH F LV GHILQHG DV DQ QP ELW YDOXH ZLWKLQ WKH &1 WUHH 7KHUHIRUH HDFK QELW SULPDn U\ FRORU YDOXH UHTXLUHV PXOWLSOLFDWLRQ E\ WKH PELW RSDFLW\ YDOXH EHIRUH HQWHULQJ WKH &1 WUHH :KHQ H[LWLQJ WKH &1 WUHH HDFK FRORU YDOXH UHTXLUHV VKLIWLQJ ULJKW E\ P ELWV ZLWK URXQGLQJ RU FKRSSLQJ WR SURYLGH DQ QELW UHVXOW 7KH =L ]LL FRQGLWLRQ LV REWDLQHG WKURXJK D VLPLn ODU GHYHORSPHQW DV DERYH EXW ZLWK WKH XVH RI (TXDWLRQ

PAGE 76

,W LV JLYHQ LQ ILQDO IRUP E\ FLO PO f 7KH = bLO FRQGLWLRQ LV DOVR REWDLQHG WKURXJK D VLPLODU GHYHORSPHQW DV DERYH EXW ZLWK WKH XVH RI (TXDWLRQ ,W LV JLYHQ LQ ILQDO IRUP E\ PO FL FLO f $LOAFL $LAFLO !PO !PO f 1RWH WKDW WKH ILUVW WZR WHUPV RI (TXDWLRQ DUH VLPLODU WR (TXDWLRQ 7KLV UHGXFHV WKH KDUGZDUH UHTXLUPHQW IRU D UHDOL]DWLRQ 7KH FRORU FRPSXWDWLRQ XQLW IXQFWLRQV DFFRUGLQJ WR WKH DOJRULWKP SUHVHQWHG LQ )LJXUH ZKLFK IROORZV WKH GHYHORSHG UHODWLRQV ZKHUH WKH FRORU WULDG LV UHSUHVHQWHG E\ F 7KH WDVN SHUIRUPHG E\ WKLV XQLW FRQVLVWV RI f UHFHLYLQJ D SDLU RI FRORU WULDGV D SDLU RI RSDFLW\ YDOXHV DQG VWDWXV LQIRUPDWLRQ f SHUIRUPLQJ D FRPSRVLWLQJ RSHUDn WLRQ DFFRUGLQJ WR WKH GHSWK FRPSDULVRQ DQG f RXWSXWWLQJ WKH UHVXOW $ EORFN GLDJUDP RI WKH FRORU FRPSXWDWLRQ XQLW LV GHSLFWHG LQ )LJXUH 6WDJH SHUIRUPV DQ LQLWLDO ORDG RI WKH LQFRPLQJ SDLU RI FRORU YDOXHV IURP WKH &31 LQWHUFRQn QHFW 6WDJH LV D ZDLWLQJ VWDJH IRU WKH VWDWXV UHVXOW RI WKH GHSWK FRPSXWDWLRQ XQLW 6WDJH URXWHV WKH FRORU DQG

PAGE 77

&31 &RORU &RPSXWDWLRQ 8QLW $OJRULWKP FRQVW Q QXPEHU RI ELWV RI LQLWLDOO\ VWRUHG LQWHQVLW\ YDOXH P QXPEHU RI ELWV RI LQLWLDOO\ VWRUHG RSDFLW\ YDOXH JLYHQ OLWHUDO F OLWHUDO F OLWHUDO $ OLWAL tJLLO O[WHUDO /(66 OLWHUDO (48$/ ^PQ ELW LQWHJHU ^PQ ELW LQWHJHU ^UD ELW LQWHJHU` ^P ELW LQWHJHU` ^ ELW` ^ ELW` UHG JUHHQ RU EOXH` UHG JUHHQ RU EOXH` EHJLQ LI /(66 WKHQ [M;L22 f§ M XQHQ ^=e Y ArLOA F Fs > PB $fFM@ VKU PO PM B P ^URXQGRII HUURU` = ` LI >PB $LfFL $1' P@ WKHQ FL HQGLI HOVH LI (48$/ WKHQ L=_L QR ‘ m ] ` F FLO >OWOB DR VKU OfF@ VKU PO L@ VQU PO ^8 VKU OfFLf >PO B $ VKU Of&R $ f§ FA ^URXQGRII $1' Pf@ Pf WKHQ HUURU` LI FL HQGLI LI >$L VKU OfFL $1' Pf@ Pf WKHQ FW & ^URXQGRII HUURU` HQGLI HOVH FL FLO >Pff[ $LLfrL VKU PB O="L =  ` LI >PB $LfF $1' P@ Pf WKHQ & &M ^URXQGRII HUURU` HQGLI HQGLI HQGLI HQG ^UHVXOW LV DQ PQ ELW LQWHJHU` )LJXUH 7KH DOJRULWKP SHUIRUPHG E\ D JHQHUDO &31 FRORU FRPSXWDWLRQ XQLW

PAGE 78

$ L $L /(66 (48$/ 7UDQVSDUHQF\ )LJXUH %ORFN GLDJUDP RI D JHQHUDO &31 FRORU FRPSXn WDWLRQ XQLW

PAGE 79

)LJXUH f§&RQWLQXHG

PAGE 80

7 )LJXUH f§&RQWLQXHG

PAGE 81

)LJXUH f§&RQWLQXHG

PAGE 82

RSDFLW\ YDOXHV DFFRUGLQJ WR WKHLU GHSWK SULRULW\ ,W DOVR VKLIWV WKH URXWHG RSDFLW\ YDOXH ULJKW E\ LI WKH WZR GHSWK YDOXHV DUH HTXDO ,QFOXGHG LV WKH PXOWLSOLFDWLRQ RI WKH FLL FRORU YDOXH ZLWK WKH KDOYHG $ RSDFLW\ YDOXH $OVR WKH PXOWLSOLFDWLRQ UHVXOW LV VKLIWHG ULJKW E\ P ELWV GLYLVLRQf 6WDJH SHUIRUPV WKH RSDFLW\ VXEWUDFWLRQ RSHUDWLRQ DQG URXQGV WKH VKLIWHG PXOWLSOLFDWLRQ UHVXOW RI VWDJH ,W DOVR SDVVHV WKH URXWHG FRORU YDOXHV WKH (48$/ VWDWXV ELW DQG WKH VXEWUDFWLRQ UHVXOW WUDQVSDUn HQF\f 6WDJH SHUIRUPV D PXOWLSOLFDWLRQ RI WKH VXEWUDFn WLRQ UHVXOW WUDQVSDUHQF\f ZLWK D URXWHG FRORU YDOXH DORQJ DQG SDVVHV D URXWHG FRORU YDOXH ,QFOXGHG LV VKLIWLQJ WKH PXOWLSOLFDWLRQ UHVXOW E\ P ELWV GLYLVLRQf ,W DOVR URXWHV WKH URXQGHG YDOXH RI VWDJH LI WKH WZR GHSWK YDOXHV DUH HTXDO EXW URXWHV DOO ]HURHV LI WKH WZR GHSWK YDOXHV DUH QRW HTXDO 6WDJH VXPV WKH VKLIWHG PXOWLSOLn FDWLRQ UHVXOW ZLWK WKH SDVVHG FRORU YDOXH DORQJ ZLWK URXQGLQJ DQG SDVVHV WKH PXOWLSOH[HU UHVXOW RI VWDJH 6WDJH VXEWUDFWV WKH PXOWLSOH[HU UHVXOW IURP WKH DGGLWLRQ UHVXOW RI VWDJH ZKLFK SURGXFHV WKH FRPSRVLWH FRORU YDOXH 6SHFLDOL]HG &RPSRVLWLQJ 3URFHVVLQJ 1RGH $ VSHFLDOL]HG &31 SHUIRUPV SL[HOE\SL[HO FRPSRVLWLQJ RI RSDTXH REMHFWV ZLWKRXW DQWLDOLDVLQJ RU VSHFLDO HIIHFWV 7KH KDUGZDUH RUJDQL]DWLRQ FRQWDLQV WZR GLVWLQFW IXQFWLRQDO

PAGE 83

XQLWV WKH GHSWK FRPSXWDWLRQ XQLW DQG WKH FRORU FRPSXWDWLRQ XQLW $Q RSDFLW\ FRPSXWDWLRQ XQLW LV XQQHFHVVDU\ VLQFH WKLV VSHFLDOL]HG &31 GRHV QRW LQFRUSRUDWH DQWLDOLDVLQJ VHPLWUDQVSDUHQF\ WUDQVSDUHQF\ DQG VSHFLDO HIIHFWV 7KHVH WZR FRPSXWDWLRQ XQLWV DUH GLVFXVVHG ZLWK UHVSHFW WR ILQLWH IL[HGSRLQW SL[HO YDOXH UHSUHVHQWDWLRQ 7KH DOJRn ULWKP DQG WKH FRQFHSWXDO KDUGZDUH RUJDQL]DWLRQ RI HDFK XQLW LV SUHVHQWHG 'HSWK FRPSXWDWLRQ XQLW 7KH GHSWK FRPSXWDWLRQ XQLW GLVFHUQV WKH IRUHJURXQG SL[HO IURP WKH EDFNJURXQG SL[HO RU LGHQWLILHV ERWK DV IRUHJURXQG SL[HOV 7KLV XQLW FRQFHSWXDOO\ IXQFWLRQV LGHQn WLFDOO\ WR WKH GHSWK FRPSXWDWLRQ XQLW RI WKH JHQHUDO &31 7KHUHIRUH LW IXQFWLRQV DFFRUGLQJ WR WKH DOJRULWKP SUHn VHQWHG LQ )LJXUH $V IRU WKH JHQHUDO &31 WKH GHSWK YDOXH = LV UHSUHVHQWHG E\ D VLQJOH ]ELW LQWHJHU ZKHUH = =f 7KHUHIRUH WKH IORDWLQJ SRLQW UHSUHn VHQWDWLRQ RI WKLV YDOXH LV LQLWLDOO\ WUXQFDWHG RU URXQGHG 7KH DOJRULWKP GLVFXVVLRQ FDQ EH IRXQG LQ WKH JHQHUDO &31 VHFWLRQ 7KH EORFN GLDJUDP RI WKH GHSWK FRPSXWDWLRQ XQLW LV LGHQWLFDO WR WKH XQLW RI WKH JHQHUDO &31 7KHUHIRUH LWV GHSLFWLRQ LV VKRZQ LQ )LJXUH 7KH KDUGZDUH GLVFXVVLRQ FDQ EH IRXQG LQ WKH JHQHUDO &31 VHFWLRQ

PAGE 84

&RORU FRPSXWDWLRQ XQLW 7KH FRORU FRPSXWDWLRQ XQLW SURGXFHV D VLQJOH FRPSRVLWH FRORU YDOXH IURP WKH SL[HO YDOXHV WKDW DUH SURYLGHG DV LQSXW 7KH FRORU YDOXH & LV GHILQHG DV WKH WUXH WULn VWLPXOXV FRORU YDOXHV 7KLV PDFKLQH VWRUHV HDFK SULPDU\ FRORU LQWHQVLW\f YDOXH LQ LWV LPDJH EXIIHUV DV DQ QELW LQWHJHU ZKHUH & QO 7KH FRORU YDOXH LV SDVVHG DV DQ QELW LQWHJHU LQ WKH KDUGZDUH WKHUHIRUH QR VKLIWLQJ LV QHFHVVDU\ EHIRUH HQWHULQJ D VSHFLDOL]HG &31 7KH XQLW IXQFWLRQV DFFRUGLQJ WR WKH DOJRULWKP SUHVHQWHG LQ )LJXUH ZKLFK IROORZV WKH UHODWLRQV GHYHORSHG LQ (TXDWLRQ ZKHUH WKH FRORU WULDG LV UHSUHVHQWHG E\ & DQG HDFK FRORU LV DQ QELW LQWHJHU 7KH WDVN SHUIRUPHG E\ WKLV XQLW FRQVLVWV RI f UHFHLYLQJ D SDLU RI FRORU WULDG YDOXHV DQG VWDWXV LQIRUPDWLRQ f SHUIRUPLQJ D FRPSRVLWH RSHUDWLRQ RI WKH FRORU WULDG DFFRUGLQJ WR WKH GHSWK FRPSDULVRQ DQG f RXWSXWWLQJ WKH UHVXOW $ EORFN GLDJUDP RI WKH FRORU FRPSXWDWLRQ XQLW LV GHSLFWHG LQ )LJXUH 6WDJH SHUIRUPV DQ LQLWLDO ORDG RI WKH LQFRPLQJ SDLU RI FRORU YDOXHV IURP WKH &31 LQWHUFRQn QHFW 6WDJH VXPV ERWK FRORU YDOXHV DORQJ ZLWK VKLIWLQJ WKH UHVXOW ULJKW E\ RQH ,W LV DOVR D ZDLWLQJ VWDJH IRU WKH VWDWXV UHVXOW RI WKH GHSWK FRPSXWDWLRQ XQLW 6WDJH URXWHV D FRORU WULDG DFFRUGLQJ WR LWV GHSWK SULRULW\ XWLOL]LQJ D PXOWLSOH[HU ZLWK ERWK WKH /(66 DQG (48$/ VWDWXV ELWV DV VHOHFWRUV 7KH VXFFHHGLQJ VWDJHV DUH

PAGE 85

&31 &RORU &RPSXWDWLRQ 8QLW $OJRULWKP JLYHQ OLWHUDO & OLWHUDO & EHJLQ LI /(66 WKHQ &L &L HOVH LI (48$/ WKHQ FL FL FL HOVH FL FLO HQGLI ^QELW LQWHJHU` ^QELW LQWHJHU` ^=L ]LO! ]L ]LO! VKU =L ]LOHQG ^UHVXOW LV DQ QELW LQWHJHU` )LJXUH 7KH DOJRULWKP SHUIRUPHG E\ D VSHFLDOL]HG &31 FRORU FRPSXWDWLRQ XQLW

PAGE 86

5L )LJXUH %ORFN GLDJUDP RI D VSHFLDOL]HG &31 FRPSXWDWLRQ XQLW FRORU

PAGE 87

*c )LJXUH f§&RQWLQXHG

PAGE 88

%c )LJXUH f§&RQWLQXHG

PAGE 89

ZDLWLQJ VWDJHV WKDW DOORZ D ILQDO UHVXOW WR RFFXU VLPXOWDn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n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

PAGE 90

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n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n PDWHG E\ FRQVLGHULQJ LW WR EH D IXOO DGGHU WUHH ZLWKRXW LQSXW DQG RXWSXW UHJLVWHUV >.8&@ 7KLV ZDV GRQH VLQFH WKH LQSXW DQG RXWSXW UHJLVWHUV DUH WDNHQ LQWR DFFRXQW ZKHQ HVWLPDWLQJ JDWH HTXLYDOHQFHV RI WKH VWDJLQJ UHJLVWHUV 7KHVH JDWH FRXQWV DUH H[SHFWHG WR EH FORVH WR DQ XSSHU

PAGE 91

7DEOH )XQFWLRQDO ORJLF EORFN HTXLYDOHQW RI WKH JHQHUDO &31 DQG WKH VSHFLDOL]HG &31 /RJLF )XQFWLRQ *HQHUDO &31 '&8 2&8 &&8 6SHFLDOL]HG &31 '&8 &&8 &RPSDUDWRU ]ELWf $GGHU PELWf $GGHU QELWf 0XOWLSOH[HU ] PQf§ ] 0XOWLSOH[HU PQf§ Q )OLS)ORS = PO PQ = 2Q 0XOWLSOLHU P;Pf 0XOWLSOLHU PQf;Pf 1RWH ,QYHUWHUV DUH QRW LQFOXGHG VLQFH LQYHUVLRQ FDQ EH SURGXFHG WKURXJK IOLSIORS RXWSXW VHOHFWLRQ

PAGE 92

7DEOH 3LQ UHTXLUHPHQW IRU WKH JHQHUDO &31 WKH VSHFLDOL]HG &31 DQG HDFK &31 FRPSXWDWLRQ XQLW 6LJQDO 1DPH '&8 *HQHUDO &31 2&8 &&8 *&31 6SHFLDOL]HG '&8 &&8 &31 6&31 5('L PQ PQ Q Q *5((1L PQ PQ Q Q %/8(L PQ PQ Q Q =L ] ] ] ] $/3+$L P P P 5('LO PQ PQ Q Q *5((1 PQ PQ Q Q %/8(LL PQ PQ Q Q =L ] ] ] ] $/3+$L P P P 5('L PQ PQ Q Q *5((1L PQ PQ Q Q %/8(L PQ PQ Q Q =L ] ] ] ] $/3+$L P P &/. /(66 (48$/ 32:(5 *5281' WRWDO SLQV = P Q Q ] Q Q P P ] ]

PAGE 93

7DEOH *DWH HTXLYDOHQW DQG SDFNDJH SLQ FRXQW RI YDULRXV IXQFWLRQDO ORJLF EORFNV /RJLF )XQFWLRQ 3DFNDJH 3LQV *DWH (TXLYDOHQW ELW 0DJQLWXGH &RPSDUDWRU )f ELW %LQDU\ )XOO $GGHU )f 4XDG 0XOWLSOH[HU )f 'XDO 0XOWLSOH[HU )f 2FWDO '7\SH )OLS)ORS )f ; %LW 0XOWLSOLHU $f r r 7KLV DSSUR[LPDWH QXPEHU H[FOXGHV WKH LQSXW DQG RXWSXW UHJLVWHUV ZKLFK ZRXOG DFFRXQW IRU DERXW DGGLWLRQDO JDWH HTXLYDOHQW XQLWV

PAGE 94

ERXQG 7KH SURFHGXUH IRU HVWLPDWLQJ WKH WRWDO JDWH FRXQW IRU D VSHFLILF GHVLJQ LV IRXQG XWLOL]LQJ WKH WDEOHV VXEVHTXHQW WR GHWHUPLQLQJ WKH &31 SDUDPHWHU YDOXHV P Q DQG ] 7KH WRWDO &31 JDWH FRXQW FDQ EH HVWLPDWHG IRU D GLIIHUHQW VHW RI IXQFWLRQDO EORFNV E\ FKDQJLQJ 7DEOH IROORZHG E\ SHUIRUPLQJ WKH VXJJHVWHG SURFHGXUH $ JUDSKLFV V\VWHP LV GHILQHG WR H[HPSOLI\ WKH VXJn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f 7KH YDOXH RI ] LV VHOHFWHG DV VLQFH WKH GHSWK UHVROXWLRQ RI ELWV LV VDWLVIDFWRU\ IRU KLJKHQG JUDSKLFV GHYLFHV 5HODWLQJ WKHVH VHOHFWHG SDUDPHWHU YDOXHV RI P Q DQG ] ZLWK 7DEOHV WKURXJK 7DEOH SURGXFHV WKH VSHFLILHG V\VWHP HVWLPDWHG FRPSOH[LW\ ZKLFK LV SUHVHQWHG LQ 7DEOH 7KH JHQHUDO &31 KDV D FRPSOH[LW\ RI DERXW WLPHV WKDW RI WKH VSHFLDOL]HG &31 7KHUHIRUH D FRPSRVLWLQJ

PAGE 95

7DEOH (VWLPDWHG FRPSOH[LW\ RI WKH JHQHUDO &31 WKH VSHFLDOL]HG &31 DQG HDFK &31 FRPSXWDWLRQ XQLW 7\SH RI &RXQW '&8 *HQHUDO &31 RFX HFX *&31 6SHFLDOL]HG &31 '&8 &&8 6&31 3LQV *DWHV 3DFNDJHV 3LQ 3LQ 3LQ 1RWH 7KH &31 SDUDPHWHUV IRU P Q DQG ] DUH DQG

PAGE 96

QHWZRUN WKDW FDQ XWLOL]H D PL[WXUH RI ERWK WKH JHQHUDO DQG WKH VSHFLDOL]HG &31V ZRXOG EH WKH PRVW HIILFLHQW FRQILJXUDn WLRQ 7DEOH LQGLFDWHV WKDW D ERDUG OHYHO &31 LPSOHn PHQWDWLRQ ZRXOG KDYH D UHDVRQDEOH SDFNDJH FRXQW IRU WKH JHQHUDO &31 DQG D YHU\ UHDVRQDEOH SDFNDJH FRXQW IRU WKH VSHFLDOL]HG &31 7KLV LQGLFDWHV WKDW D &31 LPSOHPHQWHG XVLQJ RIIWKHVKHOI SDUWV LV ZLWKLQ ERXQGV $W WKH WLPH RI WKLV ZULWLQJ D JDWH ELSRODU (&/77/ DUUD\ ZLWK ORRn SV GHOD\V DQG LQSXWRXWSXW FHOOV ZDV DYDLODEOH >&2/@ &KLS GHQVLWLHV RI +&026 DUUD\V DUH DV KLJK DV JDWHV ZLWK SV VZLWFKLQJ GHOD\V >%85@ 7KHUHIRUH WKH &31 JDWH FRXQWV DQG SLQ FRXQWV DUH ZLWKLQ ERXQGV IRU D VLQJOH FKLS 9/6, LPSOHPHQWDWLRQ RU D VLQJOHFKLS JDWHDUUD\ LPSOHPHQWDWLRQ 3HUIRUPDQFH 7KH &31 SHUIRUPV SL[HOE\SL[HO SURFHVVLQJ WKDW LV LQGHSHQGHQW RI VFHQH FRPSOH[LW\ 7KHUHIRUH LWV SURn FHVVLQJWLPH LV D IXQFWLRQ RI ERWK WKH LPDJH VSDFH UHVRn OXWLRQ DQG WKH LPDJH XSGDWH UDWH ZKLFK LV JLYHQ E\ 3URFHVVLQJ7LPH f ,PDJH 8SGDWH 5DWHf5HVROXWLRQf 7KH LPDJH XSGDWH UDWH LV FRQVLGHUHG UHDOWLPH DW IUDPHV SHU VHFRQG VLQFH LPDJHV VHTXHQFHG DW WKLV UDWH DSSHDU WR KDYH D VPRRWK YLVXDO IORZ 7KH LPDJH VSDFH UHVROXWLRQ LV GHILQHG DV WKH WRWDO QXPEHU RI YLVLEOH SL[HOV 7KH &31

PAGE 97

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n FHVVLQJWLPH WR VXFFHVVIXOO\ FRPSRVLWH D FROOHFWLRQ RI SL[HOV 7KHUHIRUH WKH VORZHVW VWDJH LQ WKH SLSHOLQH LV ZKDW GHWHUPLQHV WKH SHDN SHUIRUPDQFH RI WKH FRPSRVLWLQJ QHWZRUN 7KLV LV WKH PXOWLSOLFDWLRQ VWDJH IRU WKH JHQHUDO &31 ZKLFK LPSOLHV WKDW WKH PXOWLSOLHU SDUWV DUH ZKDW GHWHUPLQH WKH FRPSRVLWLQJ QHWZRUN SHUIRUPDQFH LI DQ\ &31 LV RI WKH JHQHUDO W\SH ,Q FRQWUDVW WKH FRPSDUDWRU VWDJH GHWHUPLQHV WKH FRPSRVLWLQJ QHWZRUN SHUIRUPDQFH LI DOO &31nV DUH RI WKH VSHFLDOL]HG W\SH &RQVLGHU WKH H[DPSOH RI WKH FRQVWUDLQWV VHFWLRQ ZKHUH DOO RI WKH &31nV DUH RI WKH JHQHUDO W\SH 7KH ELW PXOWLSOLHU ZKLFK KDG EHHQ VSHFLILHG PDLQWDLQV D QV PXOWLSO\ WLPH LQFOXGLQJ VHWXS WLPHf >$'9@ 7KLV SDUW KDV LQWHUQDO LQSXW DQG RXWSXW UHJLVWHUV WKHUHIRUH WKH PXOWLSO\ WLPH FDQ EH FRQVLGHUHG WKH WRWDO SLSHOLQH VWDJH

PAGE 98

7DEOH &31 SURFHVVLQJWLPH IRU YDULRXV LPDJH VSDFH UHVROXWLRQV 7KH LPDJH XSGDWH UDWH LV IUDPHV SHU VHFRQG ,PDJH 6SDFH 5HVROXWLRQ SL[HOVf &31 3URFHVVLQJ7LPH QVf ; ; ; ; ;

PAGE 99

WLPH 7KHUHIRUH WKH FRPSRVLWLQJ QHWZRUN ZRXOG KDYH D PD[LPXP EDQGZLGWK RI PLOOLRQ UHVXOWV SHU VHFRQG )URP 7DEOH DOO EXW WKH ODVW HQWU\ FRXOG EH VXSSRUWHG ZLWK D VLQJOH FRPSRVLWLQJ QHWZRUN 7KH ODVW HQWU\ FRXOG EH VXSn SRUWHG LI WZR &1nV ZHUH XVHG ZKHUH HDFK &1 ZRXOG EH GHGLFDWHG WR D VHSDUDWH KDOI RI WKH LPDJH DUUD\ ZKLOH RSHUDWLQJ DW KDOI WKH LPDJH XSGDWH UDWH 7KH FRPSXWDWLRQDO SHUIRUPDQFH RI D FRPSRVLWLQJ QHWZRUN WKDW LV FRQILJXUHG ZLWK DOO JHQHUDO &31V LV PHDVXUHG WKURXJK FDOFXODWLQJ WKH WRWDO QXPEHU RI DGGLWLRQV DQG PXOWLSOLFDWLRQV WKDW HYHU\ JHQHUDO &31 SHUIRUPV SHU XQLW WLPH $ JHQHUDO &31 SHUIRUPV DV D ORZHU ERXQG DOO =nV QRW HTXDOf HLJKW DGGLWLRQV DQG IRXU PXOWLSOLFDWLRQV $V DQ XSSHU ERXQG DOO =nV HTXDOf D JHQHUDO &31 SHUIRUPV HOHYHQ DGGLWLRQV DQG VHYHQ PXOWLSOLFDWLRQV 7KHUHIRUH WKH UDQJH RI FRPSXWDWLRQDO SHUIRUPDQFH IRU D FRPSRVLWLQJ QHWn ZRUN FRQILJXUHG ZLWK DOO JHQHUDO &31V LV JLYHQ E\ &31Vf%:f DGGLWLRQVV &31Vf%:f f &31Vf%:f PXOWLSOLFDWLRQVV &31Vf%:f f &31Vf%:f RSHUDWLRQVV &31Vf%:f f ZKHUH %: UHIHUV WR WKH JHQHUDO &31 EDQGZLGWK RU JHQHUDO &31 UHVXOWV SHU VHFRQG 7KH &31V UHIHU WR WKH WRWDO QXPEHU RI FRPSRVLWLQJ SURFHVVLQJ QRGHV WKDW FRPSULVH D FRPSRVLWLQJ QHWZRUN

PAGE 100

)RU H[DPSOH FRQVLGHU DQ DXJPHQWDEOH V\VWHP DUFKLn WHFWXUH FRQILJXUHG ZLWK D WKUHH OHYHO &1 WUHH ZLWK DOO JHQHUDO &31V DQG D ; UHVROXWLRQ GLVSOD\ GHYLFH QRGH ,W ZLOO PDLQWDLQ D &1 SURFHVVLQJ SHUIRUPDQFH RI EHWZHHQ 0236 DQG 0236 PLOOLRQ RSHUDWLRQV SHU VHFRQGf 7KLV WKURXJKSXW LV ZKDW VXSHUFRPSXWHUV SURYLGH ZKLFK GHPRQVWUDWHV WKH SRWHQWLDO RI GLVWULEXWHG VLPXOWDn QHRXV FDOFXODWLRQV 7KH SHUIRUPDQFH RI D &1 FRQILJXUHG ZLWK DOO VSHFLDOn L]HG &31V LV PHDVXUHG WKURXJK WKH WRWDO EDQGZLGWK RI WKH &1 ZKLFK LV HTXDO WR WKH EDQGZLGWK RI D XQLWDU\ VSHFLDOn L]HG &31 7KLV PHWULF LV XVHG VLQFH VSHFLDOL]HG &31V SULPDULO\ URXWH GDWD DV DSSRVHG WR SHUIRUPLQJ D FRPSXWDn WLRQ ZLWK UHJDUGV WR WKH GDWD ,I DOO GHSWK YDOXHV DUH HTXDO HDFK VSHFLDOL]HG &31 ZLOO SHUIRUP RQH DGGLWLRQ 7KLV ZLOO SURYLGH DQ DGGLWLRQV SHU VHFRQG UDWH WKDW LV FRPSXWHG WKURXJK WKH SURGXFW RI WKH QXPEHU RI &31V FRQILJXUHG DQG WKH &31 EDQGZLGWK 7KH SHUIRUPDQFH OLPLWLQJ VWDJH RI D VSHFLDOL]HG &31 LV LWV FRPSDULVRQ VWDJH EXW GHSHQGLQJ RQ ZRUG VL]H LW FRXOG EH WKH DGGLWLRQ VWDJH LQVWHDG &RQVLGHUWKH H[DPSOH SUHVHQWHG LQ WKH FRQVWUDLQWV VHFWLRQ EXW ZKHUH DOO RI WKH &31nV DUH RI WKH VSHFLDOL]HG W\SH 7KH FRPSDULVRQ VWDJH XWLOL]LQJ WKH FRPSRQHQWV VSHFLILHG LQ 7DEOH PDLQWDLQV D QV SURSDJDWLRQ GHOD\ IURP FORFN WR RXWSXW 7KHUHIRUH WKH V\VWHP ZRXOG KDYH D

PAGE 101

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n IRUPDQFH 7KHUHIRUH DOO RI WKH HQWULHV RI 7DEOH FRXOG EH DFFRPPRGDWHG 7KXV &31V ZHUH VKRZQ LQ WKLV PDQQHU WR EH SUDFWLFDO

PAGE 102

&+$37(5 9 9,'(2 *(1(5$7,21 12'( 7KH YLGHR JHQHUDWLRQ QRGH 9*1f SURYLGHV V\VWHP FRQWURO SURFHVVHV GLJLWDO GDWD IURP WKH FRPSRVLWLQJ QHWZRUN DQG FRQYHUWV WKH SURFHVVHG GLJLWDO GDWD WR DQDORJ YLGHR IRU LQSXW WR WKH GLVSOD\ GHYLFH QRGH 3URFHVVLQJ IXQFWLRQV LQFOXGH GLVSOD\ GHYLFH GHSHQGHQW SURFHVVLQJ DQG JOREDO VFHQH GHSHQGHQW SURFHVVLQJ 7KH GLVSOD\ GHYLFH GHSHQGHQW SURFHVVLQJ IXQFWLRQ SHUIRUPV FRUUHFWLRQ IRU QRQOLQHDU FRORU UHSUHVHQWDWLRQ RI WKH GLVSOD\ GHYLFH ZKLFK LV FDOOHG JDPPD FRUUHFWLRQ 7KH JOREDO VFHQH GHSHQGHQW SURFHVVLQJ IXQFWLRQ FRPSXWHV WKH HIIHFW RI DWPRVSKHULF DWWHQXDWLRQ IRU LQFOXVLRQ WR WKH VFHQH &RQILDXUDWLRQ 7KH 9*1 KDV D SK\VLFDO VWUXFWXUH FRQVLVWLQJ RI VHYHQ PRGXOHV DQ DWPRVSKHULF DWWHQXDWLRQ XQLW D SL[HOFDFKH D GRXEOHEXIIHUHG IUDPH EXIIHU YLGHR VKLIW UHJLVWHUV D FRORU SDOHWWH GLJLWDOWRDQDORJ FRQYHUWHUV DQG D V\VWHP FRQWUROOHU 7KH EORFN GLDJUDP RI D 9*1 ZLWK UHVSHFW WR LWV VHYHQ PRGXOHV LV LOOXVWUDWHG LQ )LJXUH 7KH GLVFXVVLRQ RI HDFK PRGXOH LV SUHVHQWHG EHORZ

PAGE 103

3L[HO 9DOXHV 9LGHR )LJXUH %ORFN GLDJUDP RI D YLGHR JHQHUDWLRQ QRGH UHVSHFW WR LWV VHYHQ PRGXOHV ZLWK

PAGE 104

$WPRVSKHULF $WWHQXDWLRQ 8QLW 7KH DWPRVSKHULF DWWHQXDWLRQ XQLW $$8f FRPSXWHV WKH HIIHFW RI DWPRVSKHULF SDUWLFOHV DORQJ WKH SDWK EHWZHHQ WKH REVHUYHU DQG WKH REMHFWV IRU LQFOXVLRQ LQ WKH VFHQH YLHZ LPDJH VSDFHf :KHQ OLJKW WUDYHOV WKURXJK DQ DEVRUELQJ PHGLXP VXFK DV DWPRVSKHUH ZLWK LWV GXVW DQG PRLVWXUH WKH LQWHQVLW\ RI OLJKW GHFUHDVHV DORQJ WKH SDWK PDNLQJ REMHFWV DSSHDU JUD\HU DQG PLVWLHU WKH IDUWKHU DZD\ WKH\ DUH >6&+D@ 7KH LQWHQVLW\ RI OLJKW LV GHILQHG DV WKH UDGLDQW HQHUJ\ FURVVLQJ DQ DUHD SHU XQLW WLPH SHU XQLW DUHD DQG SHU XQLW VROLG DQJOH 7KHUHIRUH WKH DWPRVSKHULF DWWHQXDn WLRQ PHWKRG PHUHO\ FDOFXODWHV DWWHQXDWLRQ DV D IXQFWLRQ RI GHSWK IURP WKH YLHZSRLQW ZLWK UHVSHFW WR D IDGLQJ FRQVWDQW JLYHQ DV & F4 H[SI=4f &K>O H[SI=4f@ f ZKHUH & LV WKH WULVWLPXOXV SL[HO FRORU DIWHU DWWHQXDWLRQ F4 LV WKH WUXH WULVWLPXOXV SL[HO FRORU DIWHU EHLQJ PXOWLn SOLHG E\ WKH SL[HO RSDFLW\ &K LV WKH WULVWLPXOXV SL[HO FRORU RI WKH KRUL]RQ I LV WKH IDGLQJ FRQVWDQW DQG =4 LV WKH GLVWDQFH IURP WKH REVHUYHU WR WKH REMHFW VXUIDFH HOHPHQW WKDW WKH SL[HO YDOXH UHSUHVHQWV >6&+D@ 7KH IDGLQJ FRQVWDQW LV DGMXVWHG IRU YDU\LQJ DWPRVSKHULF FRQGLn WLRQV VXFK DV IRJJ\ KD]\ DQG PXUN\ DWPRVSKHUHV 7KH VXEVFULSW LV WKH QRGH QXPEHU WKDW LQGLFDWHV D 9*1

PAGE 105

(TXDWLRQ DVVXPHV D XQLIRUP KRPRJHQHRXVf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n SOH[HU 7KLV VWDJH DOVR URXQGV HDFK RI WKH WKUHH FRORU YDOXHV WKURXJK WKH XVH RI WKH DGGHUV 6WDJH LQGH[HV WKH ORRNXS WDEOHV IRU WKH DWWHQXDWHG FRORU YDOXHV DQG IRU WKH PRGLILHG KRUL]RQ FRORU YDOXH ,W DOVR FRQWDLQV GLDJQRVWLFV SLSHOLQH UHJLVWHUV ZLWK D GXDO SXUSRVH f GXULQJ LQLWLDOn L]DWLRQ WKH\ SURYLGH D SDWK IURP WKH 001 IRU ZULWLQJ GDWD WR WKH ORRNXS WDEOHV DQG IRU UHDGLQJ GDWD IURP WKH ORRNXS WDEOHV DQG f GXULQJ QRUPDO RSHUDWLRQ WKH\ IXQFWLRQ DV SLSHOLQH VWDJLQJf UHJLVWHUV 6WDJH PXOWLSOLHV HDFK

PAGE 106

%ORFN GLDJUDP RI WKH DWPRVSKHULF DWWHQXDWLRQ XQLW XVHG WR LQFOXGH DWPRVSKHULF HIIHFWV LQ D VFHQH )LJXUH

PAGE 107

FRORU YDOXH ZLWK WKH DWWHQXDWLRQ YDOXH DQG SHUIRUPV D VKLIW RSHUDWLRQ IRU HDFK PXOWLSOLFDWLRQ UHVXOW ,W DOVR SDVVHV WKH PRGLILHG KRUL]RQ FRORU 6WDJH VXPV HDFK DWWHQXDWHG FRORU YDOXH UHVXOW RI VWDJH ZLWK WKH PRGLILHG KRUL]RQ FRORU DORQJ ZLWK URXQGLQJ WKH DWWHQXDWHG FRORU YDOXH WR SURGXFH WKH DWPRVSKHUH DWWHQXDWHG WULVWLPXOXV FRORU LQ ELWVf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f WKH GDWD UHJLVWHU DQG f WKH PHPRU\ VRXUFH UHJLVWHU >*5@ 7KH GDWD UHJLVWHU KROGV D URZ RI LQWHQVLW\ YDOXHV WKDW DUH UHFHLYHG IURP WKH $$8 7KH PHPRU\ VRXUFH UHJLVWHU KROGV

PAGE 108

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n VSHHG IUDPH EXIIHU 5$0V 7KH GHWDLOV RI D SL[HO FDFKH FDQ EH IRXQG LQ *RULV >*5@ )RU GLDJQRVWLFV WKH 001 ZLOO KDYH DFFHVV WR WKH IUDPH EXIIHU PHPRU\ 7KHUHIRUH LQWHQVLW\ YDOXHV ZLOO EH SURn YLGHG E\ WKH 001 ,W ZLOO ORDG WKH IUDPH EXIIHU PHPRU\ WKURXJK WKH SL[HO FDFKH DQG LW ZLOO UHDG WKH YDOXHV IRU YHULILFDWLRQ IURP WKH YLGHR RXWSXW UHJLVWHU 'RXEOH%XIIHUHG )UDPH %XIIHU $ IUDPH EXIIHU LV D FRQWLJXRXV SLHFH RI FRPSXWHU PHPRU\ WKDW VWRUHV WKH LQWHQVLW\ DWWULEXWHV RI DQ LPDJH LQ DFFRUGDQFH ZLWK HDFK SL[HOnV SRVLWLRQ RQ WKH GLVSOD\ $V D

PAGE 109

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nV RYHUDOO KXH DQG LQWHQVLW\ )RU H[DPSOH D IXOO FRORU IUDPH EXIIHU PD\ KDYH HLJKW ELW SODQHV DVVLJQHG IRU HDFK SULPDU\ FRORU IRU DQ DJJUHJDWH RI ELW SODQHV WKDW FRPELQH LQWR SRVn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

PAGE 110

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nV VHULDO LQSXW RU WKH 5$0nV GDWD LQSXW ZRXOG EH XVHG IRU LPDJH XSGDWH DQG WKH LQWHUQDO VKLIW UHJLVWHUn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f RI QV >:+,@ 7KLV KLJKSHUIRUPDQFH LV DFKLHYHG WKURXJK DF

PAGE 111

FHVVLQJ PXOWLSOH SL[HO YDOXHV VLPXOWDQHRXVO\ IURP WKH IUDPH EXIIHU DQG WKHQ ZULWLQJ WKHP LQ SDUDOOHO WR WKH YLGHR VKLIW UHJLVWHUV RQH IRU HDFK FRORU FKDQQHOf >)/(@ 7KHQ WKH GDWD ZLWKLQ WKH YLGHR VKLIW UHJLVWHUV DUH VHULDOO\ VKLIWHG RXW DW WKH GRW FORFN UDWH UHFLSURFDO RI WKH SL[HO WLPHf WR SURYLGH WKH DSSURSULDWH SL[HO YDOXHV DW WKH UHTXLUHG EDQGZLGWK &RORU 3DOHWWH 7KH FRORU SDOHWWH LV XVHG WR H[SDQG WKH IUDPH EXIIHUnV SRVVLEOH FRORUV ,W LV D ORRNXS WDEOH PHPRU\ WKDW LV LQGH[HG E\ WKH IUDPH EXIIHU RXWSXW YLD WKH YLGHR VKLIW UHJLVWHUV &RQVHTXHQWO\ LQVWHDG RI VWRULQJ FRORU LQWHQVLn WLHV YDOXHV GLUHFWO\ WKH IUDPH EXIIHU VWRUHV WKHLU ORFDWLRQV ZLWKLQ WKH FRORU ORRNXS WDEOH PHPRU\ (DFK DGGUHVV SRLQWV WR WKH VHW RI WKUHH SULPDU\ FRORUV WKDW GHILQHV WKH GHVLUHG SL[HO FRORU IRU GLVSOD\ )RU H[DPSOH D V\VWHP WKDW FRQWDLQV D IXOOFRORU IUDPH EXIIHU ZLWK WKUHH ELW ZLGH FRORU ORRNXS WDEOHV FDQ SURGXFH VLPXOn WDQHRXV FRORUV RXW RI D SRVVLEOH FRORUV >5*@ 7KXV UHTXLULQJ D ELW DGGUHVV WR DFFHVV RYHU PLOOLRQ ORFDWLRQV DW ELWV HDFK $ FRORU SDOHWWH DOOHYLDWHV WKH RYHUKHDG RI FKDQJLQJ FRORUV VLQFH HDFK FRORU FKDQJH LV WR RQO\ RQH HQWU\ RI WKH SDOHWWH KRZHYHU LW UHVWULFWV WKH QXPEHU RI VLPXOWDQHRXV FRORUV WKDW DUH DYDLODEOH WR WKH GLVSOD\

PAGE 112

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n YHUWHU '$&f >52*@ 7KH LQSXW WR WKH '$&V DUH FRQQHFWHG WR WKH RXWSXW RI WKH FRORU SDOHWWH DQG WKH RXWSXW RI WKH '$&V DUH FRQQHFWHG WR WKH LQSXW RI WKH ''1 6RPH PRQLWRUV LQFOXGH WKLV DQDORJ VHFWLRQ WKXV IRU WKHVH PRQLWRUV WKH DQDORJ VHFWLRQ LV E\SDVVHG 6\VWHP &RQWUROOHU 7KH V\VWHP FRQWUROOHU SURYLGHV WKH WLPLQJ DQG FRQWURO RI WKH HQWLUH V\VWHP ,W SURYLGHV IRXU SULPDU\ IXQFWLRQV f VWDUW RI LPDJH UHDG F\FOH LQIRUPDWLRQ IRU WKH 2*1 LPDJH PHPRU\ FRQWURO DQG DGGUHVVLQJ f 9*1 LPDJH PHPRU\ FRQWURO

PAGE 113

DQG DGGUHVVLQJ f ''1 YLGHR FRQWURO DQG f V\VWHP FORFN JHQHUDWLRQ ,W FDQ EH LPSOHPHQWHG E\ D JHQHULF RIIWKH VKHOI YLGHR V\VWHP FRQWUROOHU LQWHJUDWHG FLUFXLW DORQJ ZLWK DGGLWLRQDO KDUGZDUH ORJLF WR JHQHUDWH WKH V\VWHP VSHFLILF VLJQDOV >)/(@ 7KH VWDUW RI D 9*1 LPDJH PHPRU\ XSGDWH RFFXUV DIWHU WKH 2*1 LPDJH PHPRU\ UHDG VWDUWV 7KLV WLPH GLIIHUHQFH LV HTXDO WR WKH GHOD\ WKURXJK WKH 2*1 RXWSXW UHJLVWHU WKURXJK WKH FRPSRVLWLQJ QHWZRUN DQG WKURXJK WKH DWPRVSKHUH DWn WHQXDWLRQ XQLW 7KH GHOD\ WLPH ZLOO EH PHDVXUHG E\ D FRXQWHUWLPHU FLUFXLW WKDW LV LQLWLDOO\ ORDGHG ZLWK D WLPH FRQVWDQW E\ WKH 001 $QDO\VLV 7KH YLGHR JHQHUDWLRQ QRGH DQDO\VLV H[DPLQHV WZR DUHDV FRPSOH[LW\ DQG SHUIRUPDQFH &RPSOH[LW\ LV HVWLPDWHG E\ DSSUR[LPDWLQJ WKH TXDQWLW\ RI UDQGRP DFFHVV PHPRU\ WKDW ZRXOG EH QHFHVVDU\ IRU DQ LPSOHPHQWDWLRQ 3HUIRUPDQFH LV H[DPLQHG ZLWK UHVSHFW WR LPDJH VSDFH UHVROXWLRQ LPDJH UHIUHVK UDWH LPDJH XSGDWH UDWH DQG PRQLWRU UHWUDFH FKDUDFWHULVWLFV &RPSOH[LW\ 7KH YLGHR JHQHUDWLRQ QRGH PHPRU\ UHTXLUHPHQW LV SULPDn ULO\ D IXQFWLRQ RI WKH LPDJH VSDFH UHVROXWLRQ DQG WKH ZRUG VL]H XVHG IRU HDFK LQWHQVLW\ YDOXH )RU H[DPSOH D IXOO FRORU ; V\VWHP ZLWK D ELW ZLGH FRORU SDOHWWH

PAGE 114

PHPRU\ ZRXOG UHTXLUH ; ELWV RI PHPRU\ IRU LWV GRXEOHEXIIHUHG IUDPH EXIIHU ELWV RI PHPRU\ IRU LWV FRORU SDOHWWH DQG ; ELWV RI PHPRU\ IRU LWV $$8 DVVXPLQJ RQO\ XSSHU ELWV RI = XVHG IRU $$8f 7KLV EULQJV WKH DJJUHJDWH WRWDO IRU PHPRU\ WR RYHU PLOOLRQ ELWV 3HUIRUPDQFH 7KH 9*1 UHFHLYHV SL[HO YDOXHV DW WKH LPDJHXSGDWH UDWH DQG WUDQVPLWV SL[HO YDOXHV DW WKH LPDJHUHIUHVK UDWH 7KHUHIRUH LWV SHUIRUPDQFH LV D IXQFWLRQ RI WKH LPDJH VSDFH UHVROXWLRQ RI WKH PRQLWRU VHOHFWHG IRU WKH ''1 7KH SHUn IRUPDQFH DQDO\VLV FRQVLGHUV WKH HOHPHQWV RI WKH 9*1 DW WKH LQSXW VHFWLRQ DV VHSDUDWH IURP WKH HOHPHQWV RI WKH 9*1 DW WKH RXWSXW VHFWLRQ 7KH UHFHLYLQJ RI SL[HO YDOXHV E\ WKH 9*1 LQYROYHV WKH $$8 WKH SL[HO FDFKH WKH IUDPH EXIIHU KDOI WKDW LV WHPSRn UDULO\ GHGLFDWHG IRU LPDJH XSGDWH DQG WKH V\VWHP FRQn WUROOHU 6LQFH WKH $$8 SHUIRUPV SL[HOE\SL[HO SURFHVVLQJ LWV SHUIRUPDQFH LV GHWHUPLQHG LQ WKH VDPH PDQQHU DV ZDV GRQH IRU D &31 RI WKH FRPSRVLWLQJ QHWZRUN 7KHUHIRUH (TXDWLRQ DQG 7DEOH GHVFULEH WKH $$8 SURFHVVLQJWLPH UHTXLUHPHQW 7KH LQSXW HQG RI WKH SL[HO FDFKH GDWD UHJLVWHUf KDV WR SHUIRUP GDWD ORDGLQJ DW WKH VDPH UDWH DV WKH $$8 7KHUHIRUH LWV SHUIRUPDQFH UHTXLUHPHQW IRU ORDGLQJ DOVR IROORZV (TXDWLRQ DQG 7DEOH 7KH RXWSXW HQG RI WKH SL[HO FDFKH PHPRU\ VRXUFH UHJLVWHUf KDV WR

PAGE 115

PDWFK WKH PHPRU\ ZULWH F\FOH WLPH RI WKH VHOHFWHG PHPRULHV IRU WKH IUDPH EXIIHU UHDOL]DWLRQ 7KH IUDPH EXIIHU SHUn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f 95@9/) +5 37 f 93/ ZKHUH 37 LV WKH SL[HO WLPH 55 LV WKH UHIUHVK UDWH 95 LV WKH YHUWLFDO UHWUDFH XVH WZR WLPHV 95 IRU LQWHUODFHG V\VWHPVf 9/) LV WKH YLVLEOH OLQHV SHU IUDPH +5 LV WKH

PAGE 116

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

PAGE 117

&+$37(5 9, ',63/$< '(9,&( 12'( 7KH GLVSOD\ GHYLFH QRGH ''1f FRQVLVWV RI D GLVSOD\ GHYLFH DV VSHFLILHG LQ WKH W\SLFDO UHDOWLPH &*, DUFKLn WHFWXUH SUHVHQWDWLRQ RI &KDSWHU ,, KRZHYHU LW LV UHn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n WLRQ VLQFH WKH YLVXDO UHVROXWLRQ RI WKH H\H QHDU FHQWHU RI YLVLRQ LV DUF PLQXWH SHU OLQH SDLU ZLWK YLVLRQ >6&+D@ 5HFUHDWLRQ RI D ZLGHILHOG RI YLHZ FDQ EH GRQH E\ PRYLQJ WKH SURMHFWLRQ VFUHHQ FORVHU WR WKH REVHUYHU EXW UHVROXWLRQ GHJUDGDWLRQ ZLOO DOORZ WKH REVHUYHU WR VHH

PAGE 118

UDVWHU OLQHV RU SL[HOV 7KXV ZLGH ILHOGRIYLHZ HJ GHJUHHV KRUL]RQWDO E\ GHJUHHV YHUWLFDOf GLVSOD\V DUH VDWLVILHG E\ WKUHH WHFKQLTXHV PRVDLF RI PRQLWRUV ><$1 6&+E@ GRPH ZLWK SURMHFWHG LPDJHU\ >),6 6&+E@ DQG KHOPHW ZLWK LQWHUQDO LPDJHU\ >),6 6&+E@ 7KH PRVDLF RI PRQLWRUV DSSURDFK XWLOL]H PDQ\ PRQLWRUV WR VDWLVI\ WKH HQWLUH ILHOGRIYLHZ ZKLFK UHTXLUHV LQGLYLGXDO FRPSXWHUJHQHUDWHG LPDJHU\ KDUGZDUH WR GULYH HDFK PRQLWRU 7KH GRPH DQG KHOPHW GLVSOD\V XWLOL]H DQ DUHDRILQWHUHVW $2,f GLVSOD\ WHFKQLTXH ZKLFK SURYLGHV KLJKUHVROXWLRQ LPDJHU\ ZLWKLQ D VPDOO ILHOGRIYLHZ DW WKH FHQWHU RI YLVLRQ ZLWK ORZUHVROXWLRQ LPDJHU\ ZLWKLQ WKH SHULSKHU\ 7KLV DSSURDFK UHTXLUHV LQGLYLGXDO FRPSXWHUJHQHUDWHG LPDJn HU\ KDUGZDUH IRU HDFK YLHZ 5DVWHU 6FDQ &RQYHUVLRQ 5DVWHU VFDQ FRQYHUVLRQ LV WKH SURFHVV RI FRQYHUWLQJ D UDVWHUL]HG SLFWXUH VWRUHG LQ D IUDPH EXIIHU WR WKH ULJLG GLVSOD\ SDWWHUQ RI YLGHR >5*@ 7KH VFDQQLQJ SDWWHUQ IRU D QRQLQWHUODFHG GLVSOD\ EHJLQV DW WKH XSSHU OHIW FRUQHU RI WKH VFUHHQ 7KH HOHFWURQ EHDP PRYHV RQ WKH VFUHHQ KRUL]RQn WDOO\ IURP OHIW WR ULJKW DQG PRYHV YHUWLFDOO\ GRZQZDUG DIWHU HDFK VFDQ OLQH LV WUDFHG 7KH EHDP LV PDGH YLVLEOH DV LW PRYHV KRUL]RQWDOO\ DFURVV WKH VFUHHQ WR GLVSOD\ D VOLFH RI WKH LPDJH FDOOHG DFWLYH OLQH WLPHf :KHQ WKH EHDP UHDFKHV WKH ULJKW HGJH RI WKH VFUHHQ LW LV PDGH LQYLVLEOH EODQNLQJf DQG UDSLGO\ UHWXUQV WR WKH OHIW HGJH

PAGE 119

WR VWDUW WKH QH[W VFDQ OLQH FDOOHG KRUL]RQWDO UHWUDFHf 7KLV SURFHVV LV UHSHDWHG IRU HYHU\ VFDQ OLQH RI WKH &57 :KHQ WKH EHDP ILQLVKHV WKH ODVW VFDQ OLQH RI WKH VFUHHQ LW LV PDGH LQYLVLEOH DQG UDSLGO\ UHWXUQV WR WKH XSSHU OHIW HGJH WR VWDUW WKH QH[W VFUHHQ UHIUHVK FDOOHG YHUWLFDO UHWUDFHf 7KLV HQWLUH DFWLRQ GLVSOD\V D VLQJOH IUDPH $Q LQWHUODFHG GLVSOD\ KDV D IUDPH WKDW FRQWDLQV WZR ILHOGV FRQVLVWLQJ RI RGG DQG HYHQ VFDQ OLQHV RI WKH LPDJH 7KH VFDQ FRQYHUVLRQ LV GRQH LQ D PDQQHU VLPLODU WR WKH QRQn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

PAGE 120

IRUPDQFH RI WKH V\VWHP RXWSXW VHFWLRQ LV D IXQFWLRQ RI WKH YLGHR WLPLQJ DQG WKH IUDPH EXIIHU RUJDQL]DWLRQ LV D IXQFWLRQ RI ERWK WKH DVSHFW UDWLR DQG WKH GLVSOD\ UHVRn OXWLRQ 7KH ''1 EDQGZLGWK LV GHILQHG E\ WKH QRPLQDO KRULn ]RQWDO UHWUDFH WLPH WKH QRPLQDO YHUWLFDO UHWUDFH WLPH DQG WKH GLVSOD\ UHVROXWLRQ RI WKH PRQLWRU 7KHVH VSHFLILFDn WLRQV SURYLGH WKH LQIRUPDWLRQ QHFHVVDU\ WR FRPSXWH WKH SL[HOWLPH ZKLFK LV GLVFXVVHG LQ &KDSWHU 9 DQG JLYHQ E\ (TXDWLRQ $ V\VWHP LPSOHPHQWDWLRQ ZRXOG EHJLQ E\ VHOHFWLQJ D PRQLWRU WKDW PHHWV WKH GHVLJQDWHG DVSHFW UDWLR GLVSOD\ UHVROXWLRQ UHIUHVK UDWH DQG LQWHUODFH W\SH 7KHQ WKH V\VWHP GHVLJQHU ZRXOG XWLOL]H WKRVH PRQLWRU VSHFLILFDWLRQV DV IXQGDPHQWDO GHVLJQ FULWHULD

PAGE 121

&+$37(5 9,, 2%-(&7 *(1(5$7,21 12'( 7KH REMHFW JHQHUDWLRQ QRGH 2*1f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nV HQWLUH VXUIDFH DV D IXQFWLRQ RI LWV UHODWLRQVKLS WR WKH YLHZLQJ VFUHHQ DORQJ ZLWK UHIOHFWHG OLJKW DQG SHUVSHFWLYH DWWULEXWHV 7KLV SURFHVV DQG WKH JUDSKLFDO GHVFULSWLRQ WHFKQLTXHV DUH

PAGE 122

GHVFULEHG LQ YDULRXV FRPSXWHU JUDSKLFV WH[WV VXFK DV 5RJHUV >5*@ 7KH REMHFW JHQHUDWLRQ QRGH XWLOL]HV RQO\ D SRUWLRQ RI WKH ZRUOG PRGHO DV LQSXW ZKLFK FRQVLVWV RI DQ REMHFW WR EH UHQGHUHG ,Q HVVHQFH WKH WRWDO ZRUOG PRGHO LV GLVWULEXWHG DFURVV HYHU\ REMHFW JHQHUDWLRQ QRGH RI WKH V\VWHP WUHH &RQILJXUDWLRQ $Q 2*1 DELGHV E\ VSHFLILF SHUIRUPDQFH DQG RUJDQL]Dn WLRQDO JXLGHOLQHV LQ RUGHU WR DFFRPPRGDWH FRPSDWLELOLW\ ZLWK WKH HQWLUH V\VWHP ,W KDV D SK\VLFDO VWUXFWXUH ZKLFK LV GHSLFWHG LQ )LJXUH WKDW FRQVLVWV RI WKUHH PRGXOHV DQ REMHFW JHQHUDWLRQ QRGH QXFOHXV 2*11f DQ REMHFW JHQHUDn WLRQ XQLW 2*8f DQG D VHFRQGDU\ PHPRU\ XQLW 608f 7KH 608 KROGV D PDWKHPDWLFDO PRGHO RI WKH VFHQH WKH 2*8 UHQGHUV D YLHZ RI WKH VFHQH PRGHO LQWR LPDJH VSDFH DQG WKH 2*11 KROGV WKH LPDJH VSDFH YLHZ RI WKH VFHQH PRGHO 7KH GLVFXVn VLRQ RI HDFK PRGXOH LV SUHVHQWHG EHORZ 2EMHFW *HQHUDWLRQ 1RGH 1XFOHXV 7KH REMHFW JHQHUDWLRQ QRGH QXFOHXV SURYLGHV DQ LQWHUn IDFH RI WKH 2*8 DQG WKH 608 WR WKH FRPSRVLWLQJ QHWZRUN ,W DOORZV GLIIHUHQW W\SHV RI SURFHVVRU RUJDQL]DWLRQV WR EH WDUJHWHG IRU 2*8 XVDJH DQG PDLQWDLQV D VWDQGDUG LQWHUIDFH IRU DXJPHQWDWLRQ WR WKH FRPSRVLWLQJ QHWZRUN 7KH 2*1 QXFOHXV DV VKRZQ LQ )LJXUH FRQVLVWV RI WKUHH

PAGE 123

,OO 3L[HO 9DOXHV WR &1 2EMHFW *HQHUDWLRQ 1RGH 1XFOHXV 2EMHFW *HQHUDWLRQ 8QLW 6HFRQGDU\ 0HPRU\ 8QLW )LJXUH %ORFN GLDJUDP RI DQ REMHFW JHQHUDWLRQ QRGH ZLWK UHVSHFW WR LWV WKUHH PRGXOHV

PAGE 124

VHFWLRQV D GRXEOHEXIIHUHG LPDJH EXIIHU DQ LQWHQVLW\ PXOWLSOLFDWLRQ XQLW DQG D QXFOHXV FRQWUROOHU 'RXEOHEXIIHUHG LPDJH EXIIHU 7KH GRXEOHEXIIHUHG LPDJH EXIIHU FRQVLVWV RI WZR IUDPH EXIIHUV WZR =EXIIHUV DQG WZR RSDFLW\ EXIIHUV ,WV SXUSRVH LV WR PDWFK WKH FRPSRVLWLQJ QHWZRUN EDQGZLGWK WR WKH 2*8 EDQGZLGWK WR KROG DQ LPDJH VSDFH YLHZ RI WKH VFHQH DQG WR SURYLGH VPRRWK WUDQVLWLRQV EHWZHHQ LPDJH XSGDWHV 2QH LPDJH PHPRU\ DUHD LV DFFHVVHG E\ WKH FRPSRVn LWLQJ QHWZRUN ZKLOH WKH RWKHU LPDJH PHPRU\ DUHD LV DFFHVVHG E\ WKH 2*8 IRU UHQGHULQJ D QHZ LPDJH 7KH WDVNV RI WKH WZR LPDJH PHPRU\ DUHDV DUH VZLWFKHG ZKHQ D QHZ LPDJH LV DYDLODEOH DQG WKH SUHYLRXV LPDJH KDV EHHQ UHDG 'XULQJ LPDJH PHPRU\ VZLWFKLQJ WKH LPDJH PHPRU\ WKDW EHFRPHV GHVLJQDWHG IRU LPDJH XSGDWH E\ WKH 2*8 LV DXWRPDWLFDOO\ LQLWLDOL]HG HQDEOHGGLVDEOHG YLD 2*8f WR D GHIDXOW VWDWH 7KLV LQLWLDOL]DWLRQ VHWV HYHU\ PHPRU\ ORFDWLRQ LQ WKH GHSWK EXIIHU WR WKH PD[LPXP GHSWK YDOXH DQG VHWV HYHU\ PHPRU\ ORFDWLRQ LQ WKH RSDFLW\ EXIIHU WR WKH PLQLPXP RSDFLW\ YDOXH 7KH LQLWLDOL]DWLRQ LV GRQH E\ VSHFLDO KDUGZDUH ORJLF ZKLFK LV DQ HOHPHQW RI WKH QXFOHXV FRQWURO VHFWLRQ ,QLWLDOL]DWLRQ LV GRQH WR VLPSOLI\ WKH LPDJH XSGDWH SURn FHGXUH WKDW WKH 2*8 SHUIRUPV 'XULQJ DQ LPDJH XSGDWH SULRU KDUGZDUH LQLWLDOL]DWLRQ DOORZV WKH 2*8 WR LJQRUH DOO EXW WKRVH SL[HOV RI WKH LPDJH EXIIHU ZLWKLQ WKH GRPDLQ RI

PAGE 125

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nV VHULDO GDWD RXWSXW ZRXOG EH XVHG IRU LPDJH XSGDWH WR WKH FRPSRVLWLQJ QHWZRUN DQG LWV '5$0 H[WHUQDO GDWD ,2 ZRXOG EH XVHG IRU LPDJH XSGDWH E\ WKH 2*8 7KH DGGUHVVLQJ WLPLQJ DQG FRQWURO RI WKH YLGHR 5$0V IRU WKH &1 VLGH ZRXOG EH GRQH E\ WKH QXFOHXV FRQWUROOHU ZKLOH WKH 2*8 ZRXOG KDYH XQUHVWULFWHG DFFHVV RI WKH LPDJH PHPRU\ KDOI WKDW LV WHPSRUDULO\ GHGLFDWHG WR LWV VLGH 'DWD DFFHVV RI

PAGE 126

WKH LPDJH PHPRU\ WKDW LV WHPSRUDULO\ GHGLFDWHG WR WKH &1 VLGH ZLOO EH VHTXHQWLDO RQ D URZE\URZ EDVLV VWDUWLQJ DW WKH XSSHU OHIW SL[HO ORFDWLRQ 'DWD DFFHVV RI WKH LPDJH PHPRU\ WKDW LV WHPSRUDULO\ GHGLFDWHG WR WKH 2*8 VLGH ZLOO EH RQ D UDQGRP EDVLV ,QWHQVLW\ PXOWLSOLFDWLRQ XQLW 7KH LQWHQVLW\ PXOWLSOLFDWLRQ XQLW UHFHLYHV DW WKH LPDJH XSGDWH UDWH ILYH SL[HO YDOXHV IURP WKH GRXEOHEXIn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

PAGE 127

+RZHYHU IRU D VSHFLDOL]HG &31 QR RSDFLW\ YDOXH LV URXWHG IRU LQSXW 7KH GHSWK YDOXH LV URXWHG WR ERWK W\SHV RI &31V LQ WKH VDPH PDQQHU 7KH EORFN GLDJUDP RI DQ LQWHQVLW\ PXOWLSOLFDWLRQ XQLW LV GHSLFWHG LQ )LJXUH 6WDJH UHFHLYHV SL[HO YDOXHV IURP WKH LPDJH EXIIHU 6WDJH PXOWLSOLHV HDFK QELW FRORU FRPSRQHQW E\ WKH PELW RSDFLW\ YDOXH DQG URXWHV WKH PELW RSDFLW\ YDOXH $ WR WKH PRVW VLJQLILFDQW KDOI RI WKH P ELW RSDFLW\ YDOXH $ 7KH RXWSXW RI VWDJH SURYLGHV LQSXW WR D JHQHUDO &31 DQG SURYLGHV WKH OHDVW VLJQLILFDQW KDOI RI $ ZLWK ]HURHV 1RWH WKDW WKH PXOWLSOLHUV RI VWDJH DQG WKH UA J E DQG $ UHJLVWHUV RI VWDJH FDQ EH RPLWWHG LI WKH FRQQHFWLRQ LV WR D VSHFLDOL]HG &31 $OVR WKH UHJLVWHUV RI VWDJH IRU WKH VSHFLDOL]HG &31 LQSXW DUH LQFOXGHG WR NHHS WKH GHOD\ FRQVLVWHQW WR DOORZ D PL[ RI &31 W\SHV 1XFOHXV FRQWUROOHU 7KH QXFOHXV FRQWUROOHU JRYHUQV WKH LPDJH EXIIHU WKDW LV WHPSRUDULO\ GHVLJQDWHG IRU LQSXW WR WKH FRPSRVLWLQJ QHWZRUN WKH VZLWFKLQJ RI LPDJH PHPRU\ WDVNV WKH LQLWLDOn L]LQJ RI PHPRU\ ORFDWLRQV RI WKH GHSWK EXIIHU GHVLJQDWHG IRU 2*8 DFFHVV DQG WKH LQLWLDOL]LQJ RI PHPRU\ ORFDWLRQV RI WKH RSDFLW\ EXIIHU WKDW LV WHPSRUDULO\ GHVLJQDWHG IRU 2*8 DFFHVV 'DWD DUH DFFHVVHG IURP WKH LPDJH EXIIHU ZKLFK LV FXUUHQWO\ GHVLJQDWHG IRU LQSXW WR WKH FRPSRVLWLQJ QHWZRUN

PAGE 128

% UJc J J! EEc = 6 f6 n6 7R *HQHUDO &31 7R 6SHFLDOL]HG &31 )LJXUH %ORFN GLDJUDP RI WKH LQWHQVLW\ PXOWLSOLFDWLRQ XQLW XVHG WR FRQGLWLRQ WKH FRORU DQG RSDFLW\ YDOXHV IRU LQSXW WR WKH FRPSRVLWLQJ QHWZRUN

PAGE 129

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n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

PAGE 130

SURSHU YDOXHV ZLOO EH LQSXW WR WKH LQWHUQDO VKLIW UHJLVWHU IRU D TXLFN PHPRU\ ORDG RSHUDWLRQ 7KLV PHWKRG ZRXOG H[SHGLWH WKH LQLWLDOL]DWLRQ SURFHVV VLQFH FORFNLQJ GDWXP LQWR WKH LQWHUQDO VKLIW UHJLVWHU RI D YLGHR 5$0 LV IDVW DERXW QV IRU WKH 706f DQG VLQFH WKH LQWHUQDO VKLIW UHJLVWHU RI D YLGHR 5$0 DOORZV PRUH GDWD WR EH ZULWWHQ WR LWV 5$0 LQWHUQDOO\ ELWV IRU WKH 706f ZLWK D VLQJOH ZULWH F\FOH >7(;@ 7KHVH VSHHGV DUH RI FRXUVH H[SHFWHG WR LQFUHDVH ZLWK FRQWLQXLQJ GHYHORSPHQWV LQ VHPLFRQGXFWRU WHFKQRORJ\ 2EMHFW *HQHUDWLRQ 8QLW $Q REMHFW JHQHUDWLRQ XQLW 2*8f LV D VSHFLDOL]HG SURFHVVRU ZLWK ORFDO RQOLQH PHPRU\ WKDW H[HFXWHV DOJRn ULWKPLF IXQFWLRQV WR SHUIRUP VSHFLILF REMHFW JHQHUDWLRQ WDVNV ,W LV D 9/6,RULHQWHG LPDJH V\QWKHVLV SURFHVVRU WKDW PD\ UHTXLUH WKH XVH RI D VSHFLDOSXUSRVH DUFKLWHFWXUH WR DFFRPPRGDWH WKH UHDOWLPH SHUIRUPDQFH UHTXLUHPHQWV 2*8 SHUIRUPDQFH LV D IXQFWLRQ RI ERWK WKH QXPEHU RI RSHUDWLRQV LH IORDWLQJSRLQW DGGLWLRQV DQG PXOWLSOLFDWLRQVf UHn TXLUHG WR UHQGHU DQ DVVLJQHG REMHFW DQG WKH LPDJH XSGDWH UDWH 7KXV WKH UHTXLUHG WKURXJKSXW ZKLFK LV GLVFXVVHG LQ WKH SHUIRUPDQFH VHFWLRQ LV LQ GLUHFW SURSRUWLRQ WR WKH FRPSOH[LW\ RI WKH DVVLJQHG LPDJH JHQHUDWLRQ WDVN *HQHUDWLQJ HYHQ WKH VLPSOHVW LPDJH RI D WKUHHGLPHQn VLRQDO VROLG FDQ UHTXLUH D ODUJH DPRXQW RI IORDWLQJSRLQW RSHUDWLRQV 7KXV WKH 2*8 SURFHVVRU DUFKLWHFWXUH SULPDULO\

PAGE 131

UHTXLUHV DQ HIILFLHQW IORDWLQJSRLQW SURFHVVLQJ FDSDELOLW\ 9DULRXV 2*8 DUFKLWHFWXUDO RUJDQL]DWLRQV FDQ EH DFKLHYHG WR PHHW WKH LPDJH JHQHUDWLRQ WDVN %DVLFDOO\ WKHUH DUH WZR YDULDWLRQV DSSO\ D VLQJOH SURFHVVRU WDVNHG ZLWK WKH HQWLUH LPDJH JHQHUDWLRQ SUREOHP RU SDUWLWLRQ WKH LPDJH JHQHUDWLRQ SUREOHP DPRQJ PDQ\ SURFHVVRUV WKDW RSHUDWH FRQFXUUHQWO\ 7KH VLQJOH SURFHVVRU VROXWLRQ KDV RQH EDVLF DSSURDFK LW QHHGV DQ H[WUHPHO\ KLJKSHUIRUPDQFH VSHFLDOSXUSRVH SURn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f FRQWDLQV D SDUWLWLRQ RI WKH HQWLUH GDWDEDVH DQG SURJUDPV UHODWLQJ WR WKH LPDJH JHQHUDWLRQ SUREOHP 7KLV GDWDEDVH SDUWLWLRQ LV D VHJPHQW RI D GLVWULEXWHG GDWDEDVH DQG LQFOXGHV SDUWLFXODU REMHFW GHVFULSWLRQ GDWD 3URJUDPV ZLOO FRQVLVW RI UHDOL]DWLRQV RI LPDJH JHQHUDWLRQ DOJRULWKPV IRU WKH REMHFW JHQHUDWLRQ XQLW

PAGE 132

WR XVH LQ SURFHVVLQJ WKH GDWDEDVH SDUWLWLRQ 7KLV GDWDEDVH PD\ DOVR EH WDJJHG IRU D G\QDPLFDOO\ DOORFDWDEOH SURFHVVRU DV SDUW RI WKH REMHFW JHQHUDWLRQ XQLW 'DWDEDVH GHVLJQ LV D PDMRU SDUW RI WKH YLVXDO VLPXn ODWLRQ SUREOHP )RU H[DPSOH WKH GDWDEDVH IRU IOLJKW VLPXODWLRQ LV RUGHUHG LQ D PDQQHU WKDW HQKDQFHV PRGHOHG HQYLURQPHQW GDWD DFFHVV 7KH XVH RI D UHODWLRQDO GDWDEDVH IRU WKLV DSSOLFDWLRQ ZRXOG EH FRQYHQLHQW EXW LW ZRXOG EH WRR VORZ ZLWK FXUUHQWO\ DYDLODEOH PDFKLQHU\ 7KH 608 PD\ FRQVLVW RI LQGLYLGXDO RU PXOWLSOH GLVN GULYHV HLWKHU RSWLFDO RU PDJQHWLFf DQG WKH GLVN FRQWUROOHU PHFKDQLVP IRU WKHLU DFFHVV 7KH FRQWUROOHU PD\ EH VLPLODU WR WKH YLUWXDO PHPRU\ PHFKDQLVP RI JHQHUDO SXUSRVH FRPn SXWHUV EXW WDUJHWHG IRU YLVXDO UHSUHVHQWDWLRQ 7KH HPHUJHQFH RI 9/6, GLVN FRQWUROOHUV VPDOO IRUPIDFWRU KLJK FDSDFLW\ PDJQHWLF PHGLD GLVN GULYHV DQG RSWLFDO GLVNGULYHV PDNH WKH 608 WUDFWDEOH $Q H[DPSOH VROXWLRQ WR DFFRPPRGDWH WKH YHKLFOH VLPXn ODWLRQ SUREOHP LV WR RUJDQL]H WZR GULYHV VXFK WKDW WKH GDWDEDVH ZLOO H[LVW LQ WZR IRUPDWV RUJDQL]HG IRU HDV\ 1RUWK6RXWK WUDYHUVDO DQG RUJDQL]HG IRU HDV\ (DVW:HVW WUDYHUVDO ,I WKH WUDYHUVDO LV DW DQ DQJOH WKHQ WKH PRUH HIILFLHQW GULYH IRU GDWD DFFHVV VKRXOG EH XVHG ZKLOH SRVLWLRQLQJ WKH KHDGV RI WKH OHVV HIILFLHQW RQH

PAGE 133

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n WHQVLW\ YDOXH RSDFLW\ YDOXH DQG GHSWK YDOXH RI WKH GRXEOHEXIIHUHG LPDJH EXIIHU )RU H[DPSOH FRQVLGHU D IXOOFRORU ; V\VWHP ZLWK DQ ELW ZLGH RSDFLW\ EXIIHU DQG D ELW ZLGH GHSWK EXIIHU 7KH WRWDO PHPRU\ UHTXLUHPHQW IRU WKH GRXEOHEXIIHUHG LPDJH EXIIHU ZRXOG EH ; ELWV 1RZ FRQVLGHU WKDW WKH ORFDO PHPRU\ UHTXLUHPHQW RI WKH 2*8 ZKLFK KDV DQ DUELWUDU\ RUJDQL]Dn WLRQ ZRXOG PRVW OLNHO\ GHPDQG DW OHDVW PHJDZRUG RI ELW ZLGH PHPRU\ RU ; ELWV 7KLV EULQJV WKH DJJUHJDWH WRWDO IRU PHPRU\ WR RYHU PLOOLRQ ELWV SHU 2*1 2EYLRXVO\ WKLV DSSURDFK LV PHPRU\ LQWHQVLYH KRZHYHU KLJK FDSDFLW\ PHPRU\ GHYLFHV PDNH D PXOWLSOH 2*1 V\VWHP LPSOHPHQWDWLRQ UHDOLVWLF

PAGE 134

3HUIRUPDQFH 7KH 2*1 PXVW SHUIRUP LWV REMHFW JHQHUDWLRQ WDVN DW WKH LPDJH XSGDWH UDWH 7KHUHIRUH WKH SHUIRUPDQFH FULWHULRQ RI WKH VLQJOH SURFHVVRU RU PDQ\ SURFHVVRUV DSSURDFK RI WKH 2*8 LV D IXQFWLRQ RI WKH REMHFW JHQHUDWLRQ WDVN FRPSOH[LW\ 7KLV FRPSOH[LW\ LV D PHDVXUH RI WKH WRWDO QXPEHU RI RSHUDn WLRQV LH IORDWLQJ SRLQW DGGLWLRQV DQG PXOWLSOLFDWLRQVf WKDW DUH UHTXLUHG WR SURGXFH WKH GHVLUHG REMHFW 7KH UHTXLUHG 2*8 SHUIRUPDQFH WR VDWLVI\ WKH LPDJH JHQHUDWLRQ WDVN LV JLYHQ E\ 3HUIRUPDQFH ,PDJH 8SGDWH 5DWHf7DVN 2SHUDWLRQVf f 6LQFH WKH LPDJH XSGDWH UDWH LV IL[HG DW IUDPHV SHU VHFRQG (TXDWLRQ LV UHGXFHG WR 3HUIRUPDQFH f7DVN 2SHUDWLRQVfVHFRQG f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

PAGE 135

DSSURDFK ZRXOG EH WR VXUYH\ VSHFLDOL]HG SURFHVVRU DSn SURDFKHV VXFK DV RUJDQL]DWLRQV EDVHG RQ ELWVOLFH PLFURn SURFHVVRU HOHPHQWV 7KH UHVXOW RI WKLV DQDO\VLV ZRXOG SURGXFH D RUJDQL]DWLRQDO FKRLFH IRU WKH REMHFW JHQHUDWLRQ XQLW RI WKH 2*1 7KH VHFRQGDU\ PHPRU\ XQLW ZRXOG EH VHOHFWHG DV HLWKHU PDJQHWLF PHGLD RU RSWLFDO PHGLD 7KH ILQDO VWHS ZRXOG EH WR VHOHFW WKH REMHFWJHQHUDWLRQ QRGH QXFOHXV IRU JHQHUDO &31 FRQQHFWLRQ RU IRU VSHFLDOL]HG FRQQHFWLRQ &31

PAGE 136

&+$37(5 9,,, 0$,17(1$1&( 0$1$*(0(17 12'( 7KH PDLQWHQDQFH PDQDJHPHQW QRGH 001f LV D GHGLFDWHG SURFHVVRU WKDW PRQLWRUV FRQWUROV DQG PDLQWDLQV WKH RSHUDWLRQ RI WKH V\VWHP WUHH FRPSOH[ ,W LV DQ DXWRQRPRXV SURFHVVRU WKDW SURYLGHV VHOIPDLQWHQDQFH RSHUDWLRQV DQG SURYLGHV V\VWHP VXSSRUW IXQFWLRQV 7KH VHOIPDLQWHQDQFH RSHUDWLRQV LQFOXGH LQWHUIDFH FKHFNLQJ WR HQVXUH LWV RZQ FRUUHFW RSHUDWLRQ 7KH V\VWHP VXSSRUW IXQFWLRQV LQFOXGH V\VWHP LQLWLDOL]DWLRQ FRQFXUUHQW PRQLWRULQJ RSHUDWLRQ IDXOW GLDJQRVLV IDXOW UHFRYHU\ FRQVROH IXQFWLRQ GHYHORSn PHQW WHVWLQJ DQG SURGXFWLRQ WHVWLQJ >/,8@ &RQILJXUDWLRQ 7KH PDLQWHQDQFH PDQDJHPHQW QRGH KDV D SK\VLFDO VWUXFWXUH FRQVLVWLQJ RI WKUHH PRGXOHV D PDLQWHQDQFH PDQDJHPHQW XQLW 008f D VHFRQGDU\ PHPRU\ XQLW 608f DQG D FRQVROH 7KH PDLQWHQDQFH PDQDJHPHQW XQLW LV D PHGLXPVSHHG 9/6,RULHQWHG JHQHUDO SXUSRVH FRPSXWDWLRQDO SURFHVVRU ZLWK RQOLQH PHPRU\ 7KH VHFRQGDU\ PHPRU\ XQLW LV WKH 008nV ORFDO VWRUDJH GHYLFH ,W FRQVLVWV RI VLQJOH RU PXOWLSOH KLJKGHQVLW\ GLVNGULYHV XWLOL]LQJ HLWKHU PDJQHWLF PHGLD RSWLFDO PHGLD RU ERWK 7KH GLVNGULYHV VWRUH LWHPV VXFK DV WKH WRWDO ZRUOG PRGHO REMHFW JHQHUDWLRQ QRGH SURJUDPV

PAGE 137

GLDJQRVWLF SURJUDPV GHYHORSPHQW SURJUDPV DQG SURJUDPV IRU LWV RZQ RSHUDWLRQ 7KH FRQVROH LV D VWDQGDUG DOSKDQXPHULF W\SH ZLWK D NH\ERDUG DQG D PHGLXP UHVROXWLRQ JUDSKLFV GLVSOD\ ,W PD\ DOVR FRQWDLQ D GLDO ER[ DQG D PRXVH 7KH 001 LV LQWHUIDFHG WR DOO 2*1V DQG WR WKH 9*1 WKURXJK D KLJKVSHHG JHQHUDO FRPPXQLFDWLRQV OLQN EDQGZLGWK RQ WKH RUGHU RI PHJDELWV SHU VHFRQGf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

PAGE 138

ORDGLQJ WKH 9*1 FRORU SDOHWWH LQLWLDOL]LQJ WKH DWPRVSKHULF DWWHQXDWLRQ XQLW VHWWLQJ WKH V\VWHP KDUGZDUH WR D SUHn GHWHUPLQHG FRQILJXUDWLRQ DQG VWDUWLQJ WKH H[HFXWLRQ RI WKH GLVWULEXWHG LPDJH JHQHUDWLRQ SURJUDPV 6\VWHP 1RUPDO 2SHUDWLRQ 7KH 001 SURYLGHV LQWHUQDO VXEV\VWHPV ZLWK H[WHUQDO V\VWHP GDWD DQG PRQLWRUV IRU V\VWHP PDOIXQFWLRQV ,W LV FRQWLQXRXVO\ FKHFNLQJ IRU V\VWHP PDOIXQFWLRQV E\ VFDQQLQJ QRGH KDUGZDUH ORJLF DFFHVVLQJ QRGH PHPRU\ PRQLWRULQJ SRZHU DQG PRQLWRULQJ WKHUPDO FRQGLWLRQV 7KH PRQLWRULQJ LV LQWHUOHDYHG ZLWK QRUPDO V\VWHP RSHUDWLRQV RU LV LQLWLn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f RU GLVWULEXWLQJ WKH WDVN

PAGE 139

DFURVV PDQ\ 2*1V 2WKHU IXQFWLRQV LQYROYH SODQQLQJ WKH VLPXODWLRQ GRPDLQ UHSRUWLQJ WKH QRQYLVXDO GDWD UHVXOWV RI D VLPXODWLRQ ORDGLQJ WKH FRORU SDOHWWH ORDGLQJ WKH DWPRVSKHULF DWWHQXDWLRQ XQLW DQG VHWWLQJ WKH V\VWHP KDUGZDUH WR DQ RSHUDWRU GHWHUPLQHG FRQILJXUDWLRQ 6LPXODWLRQ 'HEXJJLQJ 7KH 001 DOORZV D VSHFLDO GHEXJJLQJ PHFKDQLVP RI WKH VLPXODWLRQ HQYLURQPHQW ZKLFK LV D SDUW RI WKH V\VWHP QRUPDO RSHUDWLRQ GLVFXVVHG HDUOLHU 7KH GHEXJJLQJ WHFKn QLTXH UHVXOWV IURP WKH REVHUYDWLRQ WKDW WKH LPDJH JHQHUDn WLRQ SURFHVV LV VHSDUDEOH 7R H[HPSOLI\ WKH GHEXJJLQJ PHFKDQLVP VXSSRVH WKHUH LV DQ REMHFW GLVSOD\HG RQ WKH ''1 WKDW DSSHDUV IDXOW\ 7KHQ DOO 2*1V WKDW GR QRW JHQHUDWH WKDW SDUWLFXODU IDXOW\ REMHFW ZRXOG EH LVVXHG D VHOHFWLYH VKXWGRZQ FRPPDQG 7KLV FRPPDQG LQVWUXFWV DQ 2*1 WR ORDG LWV LPDJH EXIIHU ZLWK WUDQVOXFHQW SL[HOV DW PD[LPXP GHSWK DQG WR VKXWGRZQ LWV 2*8 LGOH SURFHVVRU VWDWHf 7KH UHPDLQLQJ 2*1 RU 2*1Vf ZLOO FRQWLQXH H[HFXWLRQ RI LWV WKHLUf REMHFW JHQHUDWLRQ SURJUDPV $IWHU DQDO\VLV DQG FRUUHFWLRQ RI WKH IDXOW WKH GRUPDQW 2*1V ZRXOG EH UHDFWLn YDWHG E\ PHDQV RI D PDVWHU VWDUW FRPPDQG RU IURP D VHOHFn WLYH UHVHW VLJQDO $QDO\VLV 6LQFH WKH V\VWHP PDLQWHQDQFH UHVSRQVLELOLW\ LV UHOn HJDWHG WR WKH 001 WKH FRPSOH[LW\ RI WKH V\VWHP WUHH LV

PAGE 140

UHGXFHG 7KLV FRPSOH[LW\ LV HTXDO WR ZKDW ZRXOG EH UHn TXLUHG LI WKH V\VWHP WUHH KDG WR PDLQWDLQ LWVHOI $OVR WKH VHSDUDWLRQ RI WDVNV EHWZHHQ WKH 001 DQG WKH V\VWHP WUHH LV D KHOS GXULQJ SURGXFW GHYHORSPHQW DQG DOORZV IRU DQ LQn FUHDVH LQ V\VWHP SHUIRUPDQFH GXH WR WKH DGGHG SURFHVVRU 6LQFH WKHUH LV D VLPXODWLRQ GHEXJJLQJ PRGH JHWWLQJ LQWR WKLV PRGH E\ D KDUGZDUH HUURU LQ WKH 001 PXVW EH GHWHFWDEOH DQG VKRXOG EH SUHYHQWDEOH 7KLV ZRXOG GHPDQG WKH QHHG IRU UHGXQGDQW KDUGZDUH IRU SDUW RI WKH 001 7KH UHGXQGDQW KDUGZDUH ZRXOG HQKDQFH 001 UHOLDELOLW\ E\ PRQLn WRULQJ SDUWLFXODU ORJLF HJ SDULW\ FKHFNHUVf

PAGE 141

&+$37(5 ,; &21&/86,21 7R YHULI\ WKH RSHUDWLRQ RI WKH V\VWHP GHVFULEHG LQ WKH HDUOLHU FKDSWHUV D VLPXODWRU SDFNDJH ZDV GHYHORSHG 7KLV VLPXODWRU ZDV XVHG WR YHULI\ WKH DXJPHQWDEOH &*, DUFKLn WHFWXUDO DSSURDFK +HUH WKH VLPXODWRU LV GHVFULEHG IROn ORZHG E\ D GLVFXVVLRQ RI WZR V\VWHP VLPXODWLRQV )LQDOO\ D VXPPDU\ RI WKH V\VWHP LV SUHVHQWHG 6\VWHP 6LPXODWRU $ V\VWHP VLPXODWRU ZDV GHYHORSHG WR YHULI\ WKH DUFKLn WHFWXUDO DSSURDFK RI WKLV UHVHDUFK >)/(@ 7KH & SURJUDPn PLQJ ODQJXDJH ZDV XVHG IRU LWV LPSOHPHQWDWLRQ 7KH V\VWHP VLPXODWLRQ FRQVWLWXWHV D KLJK OHYHO DOJRULWKPLF DQG VWUXFn WXUDO VLPXODWLRQ RI WKH GHVFULEHG KDUGZDUH WKDW PDLQWDLQV WKH VDPH QXPHULFDO SUHFLVLRQ DV UHDO KDUGZDUH ,W ZDV XVHG WR YHULI\ WKH DOJRULWKPV DQG WKH IXQFWLRQDO EHKDYLRU RI WKH V\VWHP DUFKLWHFWXUH )HDWXUHV RI WKH VLPXODWRU LQFOXGH f DXWRPDWLF VLPXODWHG V\VWHP FRQILJXUDWLRQ WKURXJK WKH GHVLJQDWLRQ RI WKH ''1 UHVROXWLRQ WKH QXPEHU RI 2*1V DORQJ ZLWK WKH QXPEHU RI ELWV IRU FRORU RSDFLW\ DQG GHSWK f LQLWLDOL]DWLRQ RI WKH $$8 WKURXJK VSHFLI\LQJ D IDGLQJ FRQVWDQW DQG D KRUL]RQ FRORU f GHDFWLYDWLRQ DQG DFWLYDWLRQ RI LQGLYLGXDO 2*1V f V\VWHP VLPXODWLRQ WKURXJK

PAGE 142

VSHFLI\LQJ WKH QXPEHU RI FORFN F\FOHV f YLHZ DQG PRGLI\ RI 2*1 &31 DQG 9*1 VLPXODWHG RXWSXW UHJLVWHU FRQWHQWV f YLHZ DQG PRGLI\ RI LQGLYLGXDO SL[HO YDOXHV RI DQ\ VLPXODWHG 2*1 LPDJH EXIIHU f YLHZ RI LQGLYLGXDO SL[HO YDOXHV RI WKH VLPXODWHG 9*1 IUDPH EXIIHU f YLGHR GLVSOD\ RI WKH VLPXODWHG 9*1 IUDPH EXIIHU DQG RI DQ\ VLPXODWHG 2*1 IUDPH EXIIHU DQG f VLPXODWLRQ RI WKH 001 WKURXJK WKH VLPXODWLRQ FRQWURO DQG WDVN VHOHFWRU 6\VWHP 6LPXODWLRQ 7ZR V\VWHP VLPXODWLRQV DUH GLVFXVVHG WKDW H[HPSOLI\ WKH V\VWHP RSHUDWLRQ 7KH UHVXOWV RI WKHVH VLPXODWLRQV LOOXVWUDWH KLGGHQ VXUIDFH UHPRYDO WUDQVSDUHQF\ LQWHUn VHFWLRQ DWPRVSKHULF DWWHQXDWLRQ DQG 2*1 GHDFWLYDWLRQ %RWK V\VWHP VLPXODWLRQV FRQVLGHU WZR FRQVWDQW VKDGHG UHFWn DQJOHV WKDW LQWHUVHFW $ YLHZ RI WKH WZR UHFWDQJOHV LQ REMHFW VSDFH LV LOOXVWUDWHG LQ )LJXUH 5HFWDQJOH $ KDV FRQVWDQW GHSWK ZLWK FRUQHU FRRUGLQDWHV 3$f 3$f 3$f DQG 3$f 7KH XSSHU KDOI RI WKLV UHFWDQJOH LV SHUFHQW RSDTXH DQG WKH ORZHU KDOI LV SHUFHQW RSDTXH 5HFWDQJOH % KDV LQFUHDVLQJ GHSWK ZLWK FRUQHU FRRUGLQDWHV 3%f 3%f 3%f DQG 3%f 7KH HQWLUH UHFWDQJOH LV SHUFHQW RSDTXH 7KH XSSHU OHIW FRUQHU RI WKH ;< SODQH LV GHVLJQDWHG WKH RULJLQ ZLWK SRVLWLYH GHSWK JRLQJ IURP IURQW

PAGE 143

5HFWDQJOH $ )LJXUH 9LHZ RI UHFWDQJOH $ DQG UHFWDQJOH % VSDFH LQ REMHFW

PAGE 144

WR EDFN SRVLWLYH RUGLQDWH JRLQJ IURP WRS WR ERWWRP DQG SRVLWLYH DEVFLVVD JRLQJ IURP OHIW WR ULJKW (DFK UHFWDQJOH ZDV FRQVLGHUHG DQ LQGLYLGXDO REMHFW WKHUHIRUH HDFK UHFWDQJOH ZDV DVVLJQHG DQ LQGLYLGXDO VLPXn ODWHG 2*1 LPDJH EXIIHU 7KH WZR REMHFWV DQG WKHLU DVVLJQn PHQW WR VLPXODWHG 2*1 LPDJH EXIIHUV GHILQH WKH VLPXODWHG V\VWHP FRQILJXUDWLRQ WZR 2*1V RQH &31 RQH 9*1 RQH ''1 DQG RQH 001 %RWK VLPXODWLRQV VSHFLILHG ELWV HDFK IRU UHSUHVHQWLQJ WKH FRORU WKH RSDFLW\ DQG WKH GHSWK YDOXHV $OVR WKH ''1 ZDV GHFODUHG ZLWK D SL[HO UHVROXWLRQ RI URZV E\ FROXPQV $OO WKHVH QXPEHUV ZHUH FKRVHQ VR WKDW SULQWHG SL[HO YDOXHV FRXOG FRQYHQLHQWO\ EH UHSUHVHQWHG RQ D SULQWHG SDSHU 7KH V\VWHP VLPXODWLRQV FRQVLGHU WKH VFHQH YLHZSRLQW DW LQILQLW\ RQ WKH QHJDWLYH ] D[LV $OVR WKH GHSLFWLRQV RI LPDJH EXIIHU DQG IUDPH EXIIHU FRQWHQWV LQFOXGH RQO\ D VLQJOH FRORU YDOXH WKHUHIRUH DOO FRORU FKDQQHOV DUH FRQVLGHUHG HTXDO WR WKH FRORU YDOXH VKRZQ 7KH FRQWHQWV RI HDFK VLPXODWHG 2*1 LPDJH EXIIHU ZDV SURGXFHG E\ D WZR VWHS SURFHVV )LUVW HDFK VLPXODWHG LPDJH EXIIHU ZDV LQLWLDOn L]HG ZLWK GHIDXOW GDWD ]HUR FRORU ]HUR RSDFLW\ DQG PD[LPXP GHSWK 7KHQ HDFK UHFWDQJOH ZDV VFDQ FRQYHUWHG WR SURGXFH LPDJH VSDFH GDWD IRU VWRUDJH LQ LWV DVVLJQHG VLPXODWHG LPDJH EXIIHU 7KH LPDJH VSDFH YLHZV RI UHFWn DQJOHV $ DQG % DUH VWRUHG LQ WKH VLPXODWHG 2*A DQG 2*1 LPDJH EXIIHUV 7KH FRQWHQWV RI WKH VLPXODWHG 2*1MA LPDJH

PAGE 145

EXIIHU LV VKRZQ LQ )LJXUH DQG WKH FRQWHQWV RI WKH VLPXODWHG 2*1 LPDJH EXIIHU LV VKRZQ LQ )LJXUH 7KH 2*1 LPDJH EXIIHU HQWULHV DUH UHSUHVHQWHG DV JURXSV RI WKUHH QXPEHUV 7KH ILUVW QXPEHU VWDUWLQJ IURP WKH WRS RI D JURXS LV WKH FRORU YDOXH WKH VHFRQG QXPEHU LV WKH RSDFLW\ YDOXH DQG WKH WKLUG QXPEHU LV WKH GHSWK YDOXH 1RWH WKDW SHUFHQW RSDFLW\ LV UHSUHVHQWHG E\ DQG SHUFHQW RSDFLW\ LV UHSUHVHQWHG E\ ZKLFK IROORZV (TXDWLRQ IRU P HTXDO WR 7KH WZR V\VWHP VLPXODWLRQV ZHUH UXQ XVLQJ WKH FRQWHQWV RI WKH WZR VLPXODWHG 2*1 LPDJH EXIIHUV DV LQSXW 7KH ILUVW V\VWHP VLPXODWLRQ KDG ERWK 2*1V HQDEOHG DQG FRQVLGHUHG WKH VFHQH DWPRVSKHUH DV FOHDU 7KH FRQWHQWV RI WKH VLPXODWHG 9*1 IUDPH EXIIHU ZKLFK KROGV WKH SRVWVLPXODWLRQ LPDJH VSDFH YLHZ RI WKH FRPSRVLWHG REMHFWV IRU WKLV H[DPSOH LV VKRZQ LQ )LJXUH 7KH VHFRQG V\VWHP VLPXODWLRQ KDG 2*1A GLVDEOHG DQG FRQVLGHUHG WKH VFHQH DWPRVSKHUH DV IRJJ\ 7KH IDGLQJ IDFWRU ZDV VHW WR DQG WKH KRUL]RQ FRORU ZDV VHW WR 7KH FRQWHQWV RI WKH VLPXODWHG 9*1 IUDPH EXIIHU ZKLFK KROGV WKH SRVWVLPXODWLRQ LPDJH VSDFH YLHZ RI WKH FRPSRVLWHG REMHFWV IRU WKLV H[DPSOH LV VKRZQ LQ )LJXUH 7KH UHVXOWV RI WKH ILUVW V\VWHP VLPXODWLRQ GHSLFWHG LQ )LJXUH GHPRQVWUDWHV LQWHUVHFWLRQ KLGGHQ VXUIDFH UHPRYDO DQG WUDQVSDUHQF\ 7KH WZR UHFWDQJOHV LQWHUVHFW DW GHSWK SRVLWLRQ $V VKRZQ WKH FRORU YDOXHV DW WKH

PAGE 146

&RQWHQWV RI WKH VLPXODWHG IUDPH EXIIHU DIWHU VFDQ FRQYHUWLQJ UHFWDQJOH $ 2*1O )LJXUH RI

PAGE 147

&RQWHQWV RI WKH VLPXODWHG IUDPH EXIIHU DIWHU VFDQ FRQYHUWLQJ UHFWDQJOH % RJQ )LJXUH RI

PAGE 148

&RQWHQWV RI WKH VLPXODWHG IUDPH EXIIHU RI WKH 9*1 IRU WKH ILUVW V\VWHP VLPXODWLRQ )LJXUH

PAGE 149

&RQWHQWV RI WKH VLPXODWHG IUDPH EXIIHU RI WKH 9*1 IRU WKH VHFRQG V\VWHP VLPXODWLRQ )LJXUH

PAGE 150

LQWHUVHFWLRQ ZHUH FRPSXWHG VXFFHVVIXOO\ DFFRUGLQJ WR (TXDWLRQ 6LQFH WKH H[DFW SRLQWV RI LQWHUVHFWLRQ DUH QRW FRPSXWHG IRU LQSXW WR WKH FRPSRVLWLQJ QHWZRUN WKHVH YDOXHV UHVXOW LQ DQ DSSUR[LPDWLRQ RI WKH FRORU DW WKH SRLQWV RI LQWHUVHFWLRQ 7KH YLVLELOLW\ RI UHFWDQJOH % RFFXUV DFFRUGLQJ WR WKUHH FDVHV f ZKHUH UHFWDQJOH %nV GHSWK YDOXHV DUH OHVV WKDQ WKDW RI UHFWDQJOH $nV f ZKHUH UHFWDQJOH $ LV QRW RYHUODSSLQJ UHFWDQJOH % DQG f ZKHUH SDUWV RI UHFWDQJOH % LV EHKLQG WKH VHPLWUDQVSDUHQW SRUWLRQ RI UHFWDQJOH $ 7KH ILUVW FDVH GHPRQVWUDWHV KLGGHQ VXUIDFH UHPRYDO IROORZV (TXDWLRQ f DQG WKH WKLUG FDVH GHPRQn VWUDWHV WUDQVSDUHQF\ IROORZV (TXDWLRQ f 7KH UHJLRQ FRQFHUQLQJ WKH WKLUG FDVH LV ORFDWHG E\ WKH DUHD ZKHUH UHFWDQJOH % LV GLUHFWO\ EHKLQG WKH VHPLWUDQVSDUHQW XSSHU SRUWLRQ RI UHFWDQJOH $ 7KH XSSHU SRUWLRQ RI UHFWDQJOH $ LV SHUFHQW RSDTXH WKHUHIRUH SHUFHQW RI UHFWDQJOH %nV FRORU LV VKRZQ DORQJ ZLWK SHUFHQW RI UHFWDQJOH $nV FRORU $OVR QRWLFH WKDW WKH EDFNJURXQG FRORU LV VKRZQ ZKHUH QR REMHFWV H[LVW LQ GLUHFW YLHZ DQG WKDW WKH XSSHU SRUWLRQ RI UHFWDQJOH $ LV VKRZQ DV D TXDUWHU RI LWV RULJLQDO FRORU YDOXH SHUFHQW RSDTXHf LQ WKH UHJLRQV QRW RYHUODSSHG E\ UHFWDQJOH % VLQFH WKH EDFNJURXQG FRORU LV ]HURf 7KH UHVXOWV RI WKLV V\VWHP VLPXODWLRQ ZDV DV H[SHFWHG DQG WKH YDULRXV HIIHFWV IXQFWLRQHG FRUUHFWO\ 7KH UHVXOWV RI WKH VHFRQG V\VWHP VLPXODWLRQ GHSLFWHG LQ )LJXUH GHPRQVWUDWHV WKH HIIHFW RI DWPRVSKHULF

PAGE 151

DWWHQXDWLRQ KLGGHQ VXUIDFH UHPRYDO DQG 2*1 GHDFWLYDWLRQ 5HFWDQJOH $ ZDV QRW JHQHUDWHG VLQFH 2*1MA ZDV GLVDEOHG $V VKRZQ UHFWDQJOH % LV LPPHUVHG LQ D IRJJ\ PHGLXP WKDW LV LOOXPLQDWHG E\ WKH KRUL]RQ ZKLFK KDV D FRORU YDOXH RI 7KH IXUWKHU EDFN D SL[HO RI UHFWDQJOH % LV IURP WKH REVHUYHU WKH PRUH LWV VXUIDFH FRORU LV DWWHQXDWHG DQG EHJLQV WR UHVHPEOH WKDW RI WKH KRUL]RQ FRORU IROORZV (TXDWLRQ f ,Q FRQWUDVW WKH FORVHU LQ GHSWK SRUWLRQV RI UHFWDQJOH % LV WR WKH REVHUYHU WKH FOHDUHU LWV VXUIDFH FRORU DSSHDUV $OVR ZKHUH UHFWDQJOH % GRHV QRW FRYHU WKH LPDJH VSDFH WKH RQO\ FRORU WKDW LV VHHQ LV WKDW RI WKH KRUL]RQ FRORU 7KH UHVXOWV RI WKLV V\VWHP VLPXODWLRQ ZDV DOVR DV H[SHFWHG DQG WKH YDULRXV HIIHFWV IXQFWLRQHG FRUn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n WUDQVSDUHQW SL[HO DQG D GLVWDQW UHG RSDTXH SL[HO DQG OHW &31 FRPSRVLWH D SDLU RI PHGLXP GLVWDQW EOXH RSDTXH SL[HOV

PAGE 152

&31 ZLOO SURGXFH D UHVXOWDQW \HOORZ SL[HO ZLWK D GHILQHG GHSWK DW WKH VHPLWUDQVSDUHQW JUHHQ SL[HOnV GHSWK FRRUGLn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

PAGE 153

FRUUHFWO\ EXW ZLOO LQFOXGH VRIWZDUH FRQVLGHUDWLRQV RU JXLGHOLQHV IRU SURSHU EHKDYLRU $OVR LI WKHVH YLVXDO DUWLIDFWV ZHUH SURGXFHG WKH\ ZRXOG QRW GHWUDFW IURP WKH VLPXODWHG VFHQH TXDOLW\ EHFDXVH RI WKH UHDOWLPH YLVXDO IORZ +RZHYHU LI WKH LPDJH VHTXHQFH ZRXOG VWRS WKHUH ZRXOG EH WURXEOH 7KH SUREOHP RI SURSHUO\ DVVLJQLQJ YDULRXV REMHFWV WR REMHFW JHQHUDWLRQ QRGHV IRU YLVXDO DFFXUDF\ DV ZHOO DV SURFHVVLQJ HIILFLHQF\ LV D VHSDUDWH UHVHDUFK SURMHFW EHLQJ SXUVXHG 3UREOHPV RFFXU ZLWK FRPSRVLWLQJ SL[HOV ZLWK HTXDO GHSWK YDOXHV 7KLV LV GRQH WKURXJK DQ DSSUR[LPDWLRQ WKDW PD\ UHVXOW LQ DQ DOLDVHG OLQH DW WKH LQWHUVHFWLRQ RI VXUIDFHV ZLWK GLIIHUHQW FRORU YDOXHV 7R KDQGOH LQWHUn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

PAGE 154

7KH UHVXOW LV QRW H[DFW KRZHYHU LW LV YLVXDOO\ FORVH HQRXJK )RUWXQDWHO\ WKH LQWHUVHFWLRQ FDVH GRHV QRW RIWHQ RFFXU IRU UHDOWLPH &*, $Q HQKDQFHPHQW WR WKH LQWHUn VHFWLRQ FDVH FRXOG EH WR LQFRUSRUDWH D IHHGEDFN PHFKDQLVP WKDW ZRXOG VLJQDO WKH REMHFW JHQHUDWLRQ QRGHV ZKHQ WKH HTXDO GHSWK FRQGLWLRQ RFFXUV 7KLV ZRXOG LQGLFDWH DQ LQWHUVHFWLRQ SUREOHP IRU WKH REMHFW JHQHUDWLRQ QRGHV WR KDQGOH +DUGZDUH IHDWXUHV ZLWK WKLV VFKHPH DUH WZRIROG WKH FRPSXWDWLRQ ORJLF UHTXLUHG WR SHUIRUP SL[HOE\SL[HO FRPn SRVLWLQJ LV GXSOLFDWHG ZLWKLQ HDFK &31 DQG WKH DPRXQW RI SK\VLFDO ZLUHV WR LQWHUFRQQHFW WKH &31V LV IRUPLGDEOH 7KH KDUGZDUH UHTXLUHPHQW IRU UHDOL]DWLRQ RI WKH FRPSRVLWLQJ DOJRULWKP UHTXLUHV D PRGHVW DPRXQW RI KDUGZDUH ZKLFK LV VXLWDEOH IRU 9/6, LPSOHPHQWDWLRQ 7KHUHIRUH WKLV GXSOLFDn WLRQ GRHV QRW SUHVHQW D PDMRU SUREOHP ZKHQ FRQVLGHULQJ WKH SHUIRUPDQFH JDLQ DQG WKDW RQH 9/6, FKLS FDQ UHDOL]H D &31 7KH QXPEHU RI SK\VLFDO ZLUHV WKDW DUH QHFHVVDU\ WR UHDOL]H D FRPSRVLWLQJ QHWZRUN LV DQ RXWJURZWK RI WKH SDUDOOHO SURFHVVLQJ QDWXUH RI WKLV VFKHPH %XW VLQFH D &31 FDQ EH D VLQJOH 9/6, FKLS PDQ\ &31V FDQ H[LVW RQ D VLQJOH SULQWHG FLUFXLW ERDUG ZKLFK UHGXFHV WKH RIIERDUG LQWHUFRQQHFW SUREOHP +RZHYHU SDUDOOHO GDWD VWLOO QHHGV WR JHW WR WKH ERDUGV WKDW FRQILJXUH D V\VWHP ZKLFK PD\ GLFWDWH D GLVn WULEXWHG EDFNSODQH DSSURDFK IRU D SK\VLFDO FRQILJXUDWLRQ

PAGE 155

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f L f

PAGE 156

Df )XOO\ %DODQFHG 6\VWHP 7UHH 8QEDODQFHG 6\VWHP 7UHH )LJXUH 7ZR V\VWHP WUHH FRQILJXUDWLRQV Df IXOO\ EDODQFHG V\VWHP WUHH DQG Ef XQEDODQFHG V\VWHP WUHH

PAGE 157

ZKHUH 1F LV DQ LQWHJHU QXPEHU RI &31V 14 LV DQ LQWHJHU QXPEHU RI 2*1V DQG WKH FHLO RSHUDWRU SURGXFHV WKH VPDOOHVW LQWHJHU WKDW LV QRW OHVV WKDQ LWV DUJXPHQW $QRWKHU LVVXH ZLWK UHJDUGV WR H[SDQVLRQ FRQFHUQV FORFN GLVWULEXWLRQ &ORFNLQJ WKH REMHFW JHQHUDWLRQ QRGHV DQG FRPSRVLWLQJ SURFHVVLQJ QRGHV ZLOO KDYH WR EH GRQH LQ D PDQQHU WKDW GRHV QRW LQGXFH DQ H[FHVVLYH DPRXQW RI VLJQDO VNHZ DV FRPSDUHG IURP RQH QRGH GHVWLQDWLRQ WR DQRWKHU QRGH GHVWLQDWLRQ 7KH XVH RI D ILEHU RSWLF FDEOH IRU GLVWULEXWn LQJ WKH FORFN VLJQDO ZRXOG HOLPLQDWH WKH VWUD\ FDSDFLWDQFH SUREOHP DVVRFLDWHG ZLWK FRQYHQWLRQDO ZLULQJ 7KHUHIRUH WKH FORFN GLVWULEXWLRQ SUREOHP ZKLFK WKLV V\VWHP SUHVHQWV ZRXOG EH PRUH SUHGLFWDEOH 7KH GDWD SDWK VLJQDO OLQHV IRU FRQQHFWLQJ QRGHV WRJHWKHU LQ WKH VWUXFWXUH UHPDLQ SK\VLn FDOO\ VKRUW DQG WKXV FDQ UHPDLQ VWDQGDUG FRSSHU ZLUH $QWLDOLDVLQJ LV FXUUHQWO\ SHUIRUPHG WKURXJK WKH XWLn OL]DWLRQ RI WKH RSDFLW\ YDOXH WKDW LV SURYLGHG IRU VXESL[HO FRQWURO +RZHYHU WKH MDJJLHV FDQ EH QHJOHFWHG GXULQJ UHDOWLPH YLVXDO IORZ VLQFH WKH MDJJ\ ORRN LV DYHUDJHG WKHUHIRUH DQWLDOLDVLQJ FRXOG EH LJQRUHG IRU PRYLQJ REMHFWV $OVR IRU PRYLQJ REMHFWV D ORZHU OHYHORIGHWDLO UHSUHn VHQWDWLRQ RI WKH REMHFW FRXOG EH XVHG >%(5@ 7KLV ZRXOG UHGXFH WKH FRPSOH[LW\ RI WKH REMHFW JHQHUDWLRQ SUREOHP ZKLFK ZRXOG HQKDQFH 2*1 SHUIRUPDQFH +RZHYHU ZKHQ WKH LPDJH LV VWDWLF WKHQ DQWLDOLDVLQJ ZRXOG EH LQYRNHG DQG D KLJKHU OHYHORIGHWDLO UHSUHVHQWDWLRQ RI WKH REMHFW ZRXOG

PAGE 158

EH XVHG 7KXV D WUDGHRII FDQ EH ZHLJKHG IRU GHGLFDWLQJ 2*1 SURFHVVLQJ WLPH f WR SURGXFH D ILQHU REMHFW LPDJH f WR SURGXFH D GLIIHUHQW YLHZ RI WKH REMHFW LI LW LV PRYLQJf RU f D PL[WXUH RI ERWK DQG $QRWKHU DSSURDFK WR DQWLDOLDVLQJ FRXOG EH UHDOL]HG E\ JHQHUDWLQJ DQ LPDJH WKDW KDV D KLJKHU UHVROXWLRQ WKDQ WKH ILQDO LPDJH VXSHUn VDPSOLQJf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n DOLDVLQJ ZKLFK LQFUHDVHV WKH FRPSXWDWLRQDO GHPDQG +RZn HYHU LW PD\ SURYLGH D EHWWHU DSSUR[LPDWLRQ IRU WKH VXUIDFH LQWHUVHFWLRQ FDVH 7KH GHQVLW\ RI '5$0 KDV EHHQ LQFUHDVLQJ E\ DERXW D IDFWRU RI IRXU HYHU\ \HDUV 7KXV D PHPRU\ LQWHQVLYH DUFKLWHFWXUH WKDW HQKDQFHV RYHUDOO V\VWHP SHUIRUPDQFH LV WUDFWDEOH $OVR WKH VSHHGXS RI QHZO\ LQWURGXFHG PLFURn SURFHVVRUV XVXDOO\ UHTXLUH DQ LQFUHDVHG EDQGZLGWK FRPSDUHG WR WKHLU SUHGHFHVVRUV 7KH SDUDOOHO QDWXUH RI WKLV DUFKLn WHFWXUDO DSSURDFK HIIHFWLYHO\ LQFUHDVHV EDQGZLGWK ZLWK

PAGE 159

H[SDQVLRQ DQG WKXV SURYLGHV D VDWLVIDFWRU\ VWUXFWXUH IRU WKH DGGLWLRQ RI KLJK SHUIRUPDQFH SURFHVVRUV (QKDQFHPHQWV WR WKH DSSURDFK PD\ LQFOXGH VXEVWLWXWLQJ WKH GLVWULEXWHG GLVN GULYHV RI WKH 2*1V ZLWK D YHU\ KLJK EDQGZLGWK ILEHU RSWLF FRPPXQLFDWLRQV QHWZRUN 0Ef 7KLV ZRXOG SURGXFH D V\VWHP ZLWK WKH GLVN GULYHV ORFDWHG DW WKH 001 $QRWKHU FRQFHUQ LV WKH PRQLWRU UHVROXWLRQ 7KH UHVROXWLRQ ZLOO PRVW OLNHO\ LQFUHDVH LQ WKH IXWXUH EXW SUREDEO\ HFRQRPLFDO GHYLFHV ZLWK PXFK PRUH WKDQ OLQHV RI UHVROXWLRQ ZLOO QRW EH DYDLODEOH VRRQ 6XPPDU\ $Q H[SDQGDEOH 9/6, RULHQWHG UHDOWLPH &*, DUFKLn WHFWXUDO DSSURDFK KDV EHHQ SUHVHQWHG DQG YHULILHG WKURXJK WKLV UHVHDUFK WKDW DOORZV D IXOO UDQJH RI &*, V\VWHPV ZKLFK GHPDQG GLIIHUHQW SHUIRUPDQFH UHTXLUHPHQWV WR EH DFFRPPRGDWHG WKURXJK RQH EDVLF VHW RI PRGXOHV 7KLV DUFKLn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

PAGE 160

H[DPSOH WKH VHFRQG SO\ PD\ SDUWLWLRQ WKH REMHFW VSDFH LQWR LPDJH VSDFH ZKLOH WKH WKLUG SO\ PD\ SDUWLWLRQ WKH LPDJH VSDFH LQWR WHPSRUDO VSDFH 7KH FRPSXWHUJHQHUDWHG LPDJHU\ SURFHVV EDVLFDOO\ FRQWDLQV ILYH FRPSRQHQWV LQSXW PRGHOLQJ UHQGHULQJ FRPSRVLWLQJ DQG RXWSXW :KHQ JUDSKLFV DOJRULWKPV DUH ZHOO XQGHUVWRRG WKH\ DUH XVXDOO\ UHDOL]HG LQ KDUGZDUH WR HQKDQFH SHUIRUPDQFH 6SHFLDO KDUGZDUH SUHVHQWO\ UHDOL]H WKH UHQGHULQJ DQG RXWSXW FRPSRQHQWV +HUH WR LPSURYH SHUn IRUPDQFH WKH KDUGZDUH LV H[WHQGHG LQWR WKH FRPSRVLWLQJ FRPSRQHQW 7KLV DOORZV D JHQHULF IUDPHZRUN IRU EXLOGLQJ V\VWHPV DSSURSULDWH IRU PDQ\ VLPXODWLRQV 2EMHFWV DUH UHQGHUHG LQGHSHQGHQWO\ IURP HDFK RWKHU DQG ZKHQ FRPSOHWH WKH\ DUH DXWRPDWLFDOO\ FRPSRVLWHG E\ WKH KDUGZDUH 7KH IUDPHZRUN PDLQWDLQV DQ REMHFWRULHQWHG VWUXFWXUH WKDW DOORZV HQODUJHPHQW E\ DGGLWLRQV HLWKHU G\QDPLFDOO\ RU VWDWLFDOO\f ,I G\QDPLFDOO\ VSDZQHG SURFHVVHV RFFXU LQ LGOH REMHFW JHQHUDWLRQ QRGHV ,I VWDWLFDOO\ DGGLWLRQDO V\VWHP QRGHV DUH SK\VLFDOO\ DGGHG WR WKH VWUXFWXUH 7KH KDUGZDUH FRPSRVLWRU DFFHOHUDWHV UHQGHULQJ RI FRPSOH[ VFHQHV ,W SURYLGHV D KDUGZDUH WRRO WR FRPSRVH PXOWLSOH VW\OHV DQG DOORZV D VWUXFWXUH IRU VLPSOLILHG V\VWHP H[SDQn VLRQ ,Q UHWURVSHFW WKH DUFKLWHFWXUDO DSSURDFK PDNHV D SUDFWLFDO XVH RI WKH NQRZOHGJH WKDW HDFK HOHPHQW RI D SLFWXUH LV D SDUDPHWHU LQ D PXOWLGLPHQVLRQDO FRQWLQXXP

PAGE 161

%,%/,2*5$3+< $'9 $GYDQFHG 0LFUR 'HYLFHV %LSRODU 0LFURSURFHVVRU /RJLF DQG ,QWHUIDFH $GYDQFHG 0LFUR 'HYLFHV 6XQQ\YDOH &DOLIRUQLD %(1 %HQQHWW : 6 $ 5HYLHZ RI 6RPH RI WKH %HWWHU .QRZQ 7HFKQLTXHV $SSOLFDEOH WR 6LPXODWLRQ &RPSXWHU ,PDJH *HQHUDWLRQ % 6FKDFKWHU HGf :LOH\ ,QWHUVFLHQFH -RKQ :LOH\ t 6RQV 1HZ
PAGE 162

&2/ &ROH % & 5HFRUG6HWWLQJ &38V '5$0V DQG 65$0V 6WDU DW ,66&& (OHFWURQLFV 9RO 1R 0DUFK SS &2/ &ROH % & &RPLQJ 6RRQ LV DQ (&/ $UUD\ WKDWnV WKH %LJJHVW
PAGE 163

*5, .8& /(9 /,8 0($ 02. 1(: 3$1 325 5* 6&+ *ULPHV DQG 'LOO JXHVW HGLWRUV IRU VSHFLDO LVVXH 9/6, IRU *UDSKLFV ,((( &RPSXWHU *UDSKLFV DQG $SSOLFDWLRQV 9RO 1R 2FWREHU .XFN 7KH 6WUXFWXUH RI &RPSXWHUV DQG &RPSXWDWLRQV 9ROXPH -RKQ :LOH\ t 6RQV 1HZ
PAGE 164

6&+E 6&+ 6,* 67$ 68* 6:$ 7(; 7+ 781D 781E :(, :+, 6FKDFKWHU % &RPSXWHU ,PDJH *HQHUDWLRQ 6\VWHPV &RPSXWHU ,PDJH *HQHUDWLRQ % 6FKDFKWHU HGf :LOH\ ,QWHUVFLHQFH -RKQ :LOH\ t 6RQV 1HZ
PAGE 165

<$1
PAGE 166

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n JHQHUDWHG LPDJHU\ DQG SDUDOOHO FRPSXWLQJ )OHLVFKPDQ LV D PHPEHU RI WKH ,((( 7DX %HWD 3L (QJLQHHULQJ +RQRU 6RFLHW\ DQG (WD .DSSD 1X (OHFWULFDO (QJLQHHULQJ +RQRU 6RFLHW\ +H LV DOVR D UHJLVWHUHG SURIHVVLRQDO HQJLQHHU LQ WKH 6WDWH RI )ORULGD

PAGE 167

, FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ -t9DD A37;M8/R,QOL &[ K D f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r 3URIHVVRU RI 0HFKDQLFDO (QJLQHHULQJ

PAGE 168

)URP 8)'LVVHUWDWLRQV KWWSZHEPDLODWWQHWZPFYZP&$%$)& 09L 56, e ,QWHUQHW 'LVWULEXWLRQ &RQVHQW $JUHHPHQW ,Q UHIHUHQFH WR WKH IROORZLQJ GLVVHUWDWLRQ $87+25 )OHLVFKPDQ 5RVV 7,7/( $XJPHQWDEOH 2EMHFW2ULHQWHG 3DUDOOHO 3URFHVVRU $UFKLWHFWXUHV IRU 5HDO7LPH 38%/,&$7,21 '$7( 1266
PAGE 169

)URP 8)'LVVHUWDWLRQV KWWSZHEPDLODWWQHWZPFYZP&$%$)& 3ULQWHG RU 7\SHG 1DPH RI &RS\ULJKW +ROGHU/LFHQVHH 3HUVRQDO LQIRUPDWLRQ EOXUUHG =2R 'DWH RI 6LJQDWXUH 3OHDVH SULQW VLJQ DQG UHWXUQ WR &DWKOHHQ 0DUW\QLDN 8) 'LVVHUWDWLRQ 3URMHFW 3UHVHUYDWLRQ 'HSDUWPHQW 8QLYHUVLW\ R77OEULGD /LEUDULHV 32 b![ *DQHVYLH )/ RI $0


xml record header identifier oai:www.uflib.ufl.edu.ufdc:UF0008228300001datestamp 2009-02-04setSpec [UFDC_OAI_SET]metadata oai_dc:dc xmlns:oai_dc http:www.openarchives.orgOAI2.0oai_dc xmlns:dc http:purl.orgdcelements1.1 xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.openarchives.orgOAI2.0oai_dc.xsd dc:title Augmentable object-oriented parallel processor architectures for real-time computer-generated imagery dc:creator Fleischman, Ross Morrisdc:publisher Ross Morris Fleischmandc:date 1988dc:type Bookdc:identifier http://www.uflib.ufl.edu/ufdc/?b=UF00082283&v=0000120071125 (oclc)001123865 (alephbibnum)dc:source University of Floridadc:language English


xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID EW09BVE8A_FTXYWU INGEST_TIME 2017-07-14T22:28:47Z PACKAGE UF00082283_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES