v

ABSTRACT

Splitting process in Bounding-Volume Hierarchies (BVH) for collision

detection is one of the most challenging issues in computer graphics. The splitting

process requires an object with their set of triangles to be splitted into two parts

using binary tree. The problem exists where most of objects do not have similar

triangle size and thus creating unbalanced tree when reaching the final level of

tree construction. It is very crucial to make sure that the BVH tree construction is

always in balanced as the speed of BVH tree traversal algorithm dropped for

unbalanced tree. In this thesis, we introduce the Spatial Object Median Splitting

(SOMS) Rule to enhance the capability of BVH construction by efficiently

splitting the irregular triangles so that each of them can be bounded with single

Axis-Aligned Bounding Box (AABB). The process starts by splitting the longest

axis between the midpoint of the triangles based on their minimum and maximum

points. Result show that SOMS is capable of creating an optimum level of BVH

where more leaf nodes containing a single triangle bounded with AABB are

produced compared to Spatial Median technique. From the BVH construction

experiments, SOMS managed to create the AABB tree in 43 milliseconds for

object that have 948 triangles or 8% faster compared to the Spatial Median

technique. Furthermore, experiment to create BVH also showed that SOMS

produced 26% more nodes with single triangle compared to the Spatial Median

technique given that the total object triangle count for the complex environment

are 5672 triangles. The E-Node traversal approach that is specially designed to

perform traversal testing for SOMS technique is able to detect overlap between

dynamic and static models in an average of 0.2 milliseconds for the same complex

environment. As a conclusion, BVH can easily be constructed using SOMS

approach to create a more balanced tree and an E-Node traversal algorithm that is

more efficient and faster.

vi

ABSTRAK

Proses pemisahan di dalam Isipadu Persempadanan Berhierarki (BVH)

untuk pengesanan pelanggaran adalah salah satu isu paling mencabar dalam

bidang grafik berkomputer. Proses pemisahan ini memerlukan set segitiga objek

dipisahkan kepada dua bahagian menggunakan pepohon binari. Masalah muncul

apabila objek tersebut tidak mempunyai saiz segitiga yang sama dan membuatkan

proses pemisahan membina pepohon BVH yang tidak seimbang. Kepantasan

algorithma penyusuran pepohon juga menurun jika pepohon BVH tidak seimbang.

Di dalam tesis ini, satu teknik yang dipanggil Peraturan Pemecahan Ruang

Median berdasarkan Objek (SOMS) telah diperkenalkan untuk meningkatkan

keupayaan pembinaan BVH dengan membahagikan secara efisien set segitiga

supaya setiap segitiga dilitupi oleh Isipadu Persempadanan Paksi Sejajar (AABB).

Proses bermula dengan memotong paksi terpanjang yang dikira antara titik tengah

segitiga-segitiga berdasarkan titik minimum dan maksimum. Hasilnya adalah

SOMS berupaya membina pepohon BVH yang lebih optimum di mana terdapat

lebih banyak nod dedaun yang mengandungi satu segitiga yang disempadani oleh

AABB dihasilkan berbanding dengan teknik Ruang Median Terbuka (Spatial

Median). Ujian kepantasan pembinaan BVH menunjukkan SOMS berupaya

membina pepohon AABB dalam 43 milisaat bagi objek yang mengandungi

sebanyak 948 segitiga atau 8% lebih pantas daripada teknik Ruang Median

Terbuka. Tambahan pula, hasil ujikaji untuk membina BVH menunjukkan SOMS

dapat menghasilkan 26% lebih banyak nod yang mengandungi satu segitiga

berbanding teknik Spatial Median di mana jumlah segitiga untuk membentuk

persekitaran kompleks tersebut adalah sebanyak 5672 segitiga. Pendekatan

susuran E-Node yang direka khas untuk teknik SOMS membolehkan penyusuran

antara nod yang bersentuhan antara objek dinamik dan statik dihasilkan dalam

sela masa purata 0.2 milisaat bagi persekitaran kompleks yang sama. Sebagai

kesimpulan, teknik SOMS membolehkan pembinaan pepohon BVH dilakukan

dengan pantas dan mampu membina peringkat pepohon BVH yang lebih

seimbang di samping algorithma penyusuran E-Node yang efisien dan pantas.

vii

TABLE OF CONTENTS

CHAPTER TITLE PAGE

TITLE i

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES xii

LIST OF FIGURES xiv

LIST OF ABBREVIATIONS xx

LIST OF APPENDICES xxii

1 INTRODUCTION 1

1.1 Introduction 1

1.2 Problem Background 3

1.3 Research Aim 8

1.4 Research Objectives 8

1.5 Scope of the study 9

1.6 Significance of the study 10

1.7 Contribution of this thesis 11

1.8 Structure of the thesis 12

viii

2 LITERATURE REVIEW 13

2.1 Introduction 13

2.2 Complex Environments 14

2.3 Collision Detection in Complex Environments 19

2.3.1 Collision Detection Between Rigid Bodies 23

2.3.2 Collision Detection for Deformable Models 25

2.4 Hierarchical Approaches 26

2.4.1 Concept of Hierarchical Tree Creation 27

2.5 Bounding-Volume Hierarchies 30

2.5.1 BVH Construction 31

2.5.1.1 Binary Tree 31

2.5.1.2 Splitting Rules for BVH Construction 33

2.5.1.2.1 Object Median 35

2.5.1.2.2 Object Mean and other Splitting

Rules

36

2.5.1.2.3 Spatial Median 36

2.5.2 BVH Characteristics 38

2.6 Bounding-Volume 40

2.6.1 Axis-Aligned Bounding Boxes (AABB) 42

2.6.2 Spheres BV 43

2.6.3 Oriented Bounding Box (OBB) 44

2.6.4 Oriented Convex Polyhedra

(Oriented-Dops)

46

2.7 Collision Detection Evaluation and Testing 47

2.8 Discussion and Summary 48

3 METHODOLOGY 52

3.1 Introduction 52

3.2 Research Design and Methodology 54

3.3 BVH Framework 55

3.4 PLY 3D Object and Complex Environment Design 58

3.5 BVH Construction Phase 59

3.5.1 Load BVH 59

ix

3.5.2 BVH Node Creation 60

3.5.3 Construct Balanced Level 61

3.5.4 Splitting Axis and Optimization 62

3.5.5 Tree ID Implementation 63

3.5.6 Bound with BVH 64

3.6 Collision Detection Module Phase 65

3.6.1 Traversal Algorithm 65

3.7 Testing and Reporting 66

3.8 Complex Environment Testing Parameter and Procedure 67

3.9 Testing Controlled Environment 67

3.9.1 PLY Object Testing 67

3.9.2 Orientation Object Testing 69

3.9.3 Complex Environment Testing 70

3.10 Summary 71

4 SPATIAL OBJECT MEDIAN SPLITTING (SOMS)

RULES

72

4.1 Introduction 72

4.2 SOMS 73

4.3 Implementation of SOMS Rules 82

4.3.1 The AABB Construction 82

4.3.2 Drawing an AABB 85

4.3.3 AABB Transformation Update 87

4.4 AABB BVH tree 88

4.4.1 Top-Down Approach for AABB BVH Construction 89

4.4.2 Finding Tree Depth 91

4.4.3 Tree ID Implementation 93

4.4.4 Splitting Procedure 94

4.4.4.1 Midpoint Calculation 95

4.4.4.2 SOMS Midpoint Calculation 98

4.4.4.3 Storing Variables 98

4.4.5 AABB BVH tree Rendering 100

4.5 Traversal Algorithm 102

x

4.5.1 Details on BVH Collision Traversal Algorithm 103

4.5.2 DFS Traversal Algorithm 106

4.5.2.1 Ericson DFS Algorithm 108

4.5.2.2 Larrson DFS Algorithm 109

4.6 Urban Simulation Construction for Complex Environment 110

4.6.1 Urban Simulation Layout Design and Building

Placement

110

4.6.2 Implementation of BVH in Urban Simulation 115

4.7 Summary 116

5 SOMS TESTING 117

5.1 Introduction 117

5.2 PLY Object BVH Tree Construction Test 118

5.2.1 Tree Construction Time Test for Fixed Balanced

Level of Spatial Median

119

5.2.2 Tree Construction Time Test for Fixed Balanced

Level of SOMS

121

5.2.3 Time Construction per Node Test 123

5.2.4 BVH Level 15 Test 126

5.2.5 Hierarchies of Balance Tree Test 128

5.3 Construction of Complex Environment BVH 130

5.3.1 Tree Construction Time for Fixed Balanced Level

of Spatial Median

130

5.3.2 Tree Construction Time Test for Fixed Balanced

Level of SOMS

131

5.3.3 Time Construction per Node Test 133

5.4 Traversal Testing 136

5.4.1 Orientation Test Using DFS Generic Algorithm 137

5.4.2 BVH Balance Tree Test 140

5.5 Introduction of Earlier Node Detection Traversal

Algorithm (E-Node)

142

5.5.1 Construction of E-Node Traversal Algorithm 143

5.5.2 Experimental Result of E-Node Traversal Algorithm 146

xi

5.6 Summary of Urban Simulation BVH 147

6 CONCLUSION AND FUTURE WORK 148

6.1 Summarization and Discussion 148

6.2 List of Contribution 151

6.3 Future Work 152

6.3.1 Construction of BVH 153

6.3.2 Traversal of BVH 154

REFERENCES 156

APPENDIX A – LIST OF PUBLICATION 165

APPENDIX B – BVH MODEL 168

xii

LIST OF TABLES

TABLE NO. TITLE PAGE

2.1 Researches on BVH concerning Splitting Rules 36

2.2 BVH Test Parameters by Previous Researchers 47

3.1 Object Specification (PLY) 68

3.2 Four Orientation Tests for CD 69

3.3 Object Specification (3DS) 71

5.1 Time Construction Per Each Node 124

5.2 Percentage of Time Construction from Different Level 127

5.3 Total Nodes with One Triangle for BVH Level 15

(Maximum Declared Array List can support)

117

5.4 Balance Mode (Set of Leaf Nodes less than Five

Triangles) for Bunny, Teapot and Venus

128

5.5 Total Nodes with Set of Nodes that contain node that

cannot be divided (No Triangle) for PLY Objects with

Different Level of BVH

129

5.6 Time Construction Per Each Node 133

5.7 Percentage of Time Construction from Different Level 134

5.8 Average Time to Perform Splitting BVH Level 12 (100

Times Construction) for Urban Simulation

135

5.9 Total Nodes with One Triangle for BVH Level

13(Maximum Level Supported by Declared Array for

Urban Simulation)

135

5.10 Nodes with Leaf Nodes contain less than Five 140

xiii

Triangles according to Splitting Rules for Urban

Environment

5.11 Total Nodes with Set of Triangles that cannot perform

further Splitting for Level 13 of BVH

141

xiv

LIST OF FIGURES

FIGURE NO. TITLE PAGE

2.1 Complex Environments of Urban Simulation Virtual

Los Angeles (Team 2010)

15

2.2 Important Purposes of Complex Environment Design 16

2.3 Urban Environment that has been built by using

Automatic System proposed by (Laycock, Ryder et

al. 2007)

17

2.4 Collision Detection Technique Classifications 22

2.5 (a) Tangential Collision and (b) Boundary Collision

(Lin 1994)

24

2.6 The Differences between DCD Method (A) and CCD

Method (B). DCD check for certain Time Steps,

while CCD using Advance Motion Calculation

Technique that continuously checks for intersection

which is more expensive in term of Computation

Cost (Kipfer 2007).

25

2.7 Space Subdivision (a) and BVH (b). From (a), it

encloses whole environment and divides the whole

environment into two equal sizes while (b) only

covers The Whole Objects and divides using Splitting

Rules into certain sizes.

26

2.8 Hierarchy Tree based of Four Objects using (a) Top-

Down, (b) Bottom-Up, and (c) Insertion Construction

27

xv

(Ericson 2004)

2.9 Rule 1(left) Group o has p as a Child. Rule 2(Middle)

merging Two Primitive to create new o‟. Rule

3(right) recursively insert Primitive into Parent

Nodes (Goldsmith and Salmon 1987).

29

2.10 The Left Hand Side Image shows a BVH with Sphere

BV while on The Right Hand Side Image, shows

Unbalanced Hierarchical Form using Binary Type

Hierarchy

30

2.11 BVH Traversal Algorithm proposed by (Nguyen

2006) for Collision Detection between Two BVH

31

2.12 (a) Object Median Splitting (b) Object Mean

splitting (c) Spatial Median Splitting

33

2.13 Splitting along The Farthest Axis of Object Bounded

with OBB using Centre Points (Gottschalk, Lin et al.

1996)

34

2.14 OBB Tree recursively divided The Object into Two

Parts using Binary Type Tree and Top-Down

Approach (Gottschalk 2000).

35

2.15 Hierarchical Tree Characteristics 38

2.16 Traversal Algorithm will traverse down the BVH tree

by visiting only nodes that is confirmed to be

intersected with the other nodes (Zachmann and

Langetepe 2006). When collision occurs between

node A and node 1, A child nodes will checks

potential collision with 1 child nodes (2 and 3).

Further traversing will be required in order to find

accurate intersection point.

40

2.17 Examples of Common BVs as described in (Bade,

Suaib et al. 2006)

41

2.18 AABB Representation: (a) Min-Max; (b) Min-

Widths; (c) Centre-Radius. The point of AABB is

mapped into Cartesian Coordinate in this example

(source (Ericson 2004)).

42

xvi

2.19 Sphere Representations. “r” is The Radius while “c”

is The Sphere Centre

43

2.20 Creation of OBB. “e[0..2] is The World Coordinate

for Axis while “u[0..2]” is The Coordinate of OBB

itself. “X” is The Midpoint for The OBB located at

very Centre of The OBB.

45

2.21 Construction of Slab from Two Parallel Planes by

(Bade, Suaib et al. 2006)

45

2.22 Two Sample of 3D Set Models (Santa and Dragon)

bounded by Oriented Dops (Bade, Suaib et al. 2006)

46

2.23 Four Attributes of BV 50

3.1 Research Methodology 53

3.2 BVH Frameworks (Phase 2 of Research

Methodology)

57

3.3 The Architecture of Complex Environment Setup

Procedures with Testing and Evaluation System.

58

3.4 Steps for BVH Node Creation 60

3.5 Procedures of BVH Construction and Updating The

BVH

64

3.6 Testing Procedure 66

3.7 Three 3D PLY Object for Simple Testing 68

3.8 Conditional for Four Orientation Test 70

3.9 Complex Environment (Right) and Test Object (Left) 71

4.1 Common Splitting Rules (a) Splitting at The Object

Median. (b) Splitting at The Object Mean. (c)

Splitting at The Spatial Median (Ericson 2004).

73

4.2 An Example of BVH Splitting Process using both

techniques. SOMS intends to properly divide the

triangles into two nodes that have many triangles and

can produce more level of Balanced BVH compared

to Spatial Median Technique.

75

4.3 Condition where Separating Axis Plane cannot

continue to divide (Triangle not in the same sizes)

76

4.4 Splitting Process of Group of Triangles using both 77

xvii

techniques. Top: BVH generated by Spatial Median.

Bottom: BVH generated by SOMS Technique. Red

Box describes The Minimum and Maximum points of

both techniques.

4.5 Pseudo Code for creating SOMS 78

4.6 An Example on how the SOMS Rule split The Object

Triangle into two parts using the Spatial Midpoint

between Midpoints of Two Triangles which will

become their Separating Plane

78

4.7 An Example to show the situation of common

splitting and SOMS where (a) Splitting at Object

Median. (b) Splitting at Spatial Median. (c) Splitting

at Object Mean. (d) SOMS.

81

4.8 Continuous Loops on finding The Best Maximum

and Minimum points for all axes in order to construct

AABB based on The Maximum and Minimum points

83

4.9 Coordination of AABB 84

4.10 Number Assignment of Each Point for drawing

AABB Surfaces

85

4.11 Pseudo Code of drawing AABB 86

4.12 GL_QUADS Function to draw six faces from AABB

Vertices where each arrow represents Sequence of

Reading glVertex3f

86

4.13 Transformation Update for AABB 87

4.14 Definitions of AABB BVH Tree Class 88

4.15 Initialization of AABB BVH Tree 89

4.16 Tree Construction for Depth = 3 where Root of The

BVH tree is equal to 0

90

4.17 Pseudo Code to Call Split Function 91

4.18 Calculation to determine The Depth or Level of The

BVH Tree

91

4.19 Pseudo Code for Tree Creation Node 92

4.20 Pseudo Code for creating AABB BVH Tree Node 93

4.21 TreeID Assignments for each BVH Tree Node. For 93

xviii

Example, if Left Node is TreeID = 1, then The

Parents is (1-1)/2 = 0 and if Right Node is TreeID =

4, then its Parent is (4-1)/2 = 1.

4.22 Boolean Functions to determine The Longest Axis 94

4.23 Centre of Triangle. The Midpoint between A and B is

not always 90 Degrees in Direction of C. The key is

to find the Midpoint between A and B and then

calculate The Midpoint between f and C to get Centre

of Triangle.

95

4.24 Storing Left and Right Vertex of Triangles and Total

Triangles Count

96

4.25 Triangles to be stored into Left and Right AABB

BVH Tree

96

4.26 Pseudo Code of Object Splitting Procedure 97

4.27 Store each New Total Triangles and Triangle Vector

Point into Array for Each Object by TreeID

99

4.28 Splitting Process of AABB BVH 100

4.29 Process of AABB BVH Tree Rendering 101

4.30 Complete AABB BVH Tree using Stanford Bunny

Model. Display above is BVH of Level 1 (One big

BV), Level 3, Level 5 and Level 6.

101

4.31 Pseudo Code for Collision Detection Traversal

between Two BVH

102

4.32 Roots Checking for Broad Phase CD 103

4.33 Simple Overlap Checking between Two AABB 104

4.34 Pseudo Code to check for Internal Node 104

4.35 Illustration on how Traversal Algorithm detects

collision between Two BVH (Red Colour) Without

Pruning Capabilities and With Pruning Capabilities

107

4.36 Pseudo Code of DFS Traversal 108

4.37 Pseudo Code of Ericson Generic Traversal 109

4.38 Google Sketchup Version 7.0 Software is used for

implementation of Urban Environment

111

4.39 Placing 3D Terrain and Building into Google 111

xix

Sketchup Software. Approximately nearly 2 KM x 2

KM Square Radius is used to represent Urban

Environment.

4.40 Part 1 of Urban Environment Construction Design 112

4.41 Approximation of 4km x 4km radius of Complete

Urban Environments

113

4.42 The Urban Environment has been loaded into Main

Program using Visual Studio C++ 2008

114

4.43 Process of Reading and Loading 3DS File into C++

Programming

115

4.44 Complex Environment of Urban Simulation with

specific level of BVH

116

5.1 SOMS Testing Procedure 118

5.2 Average times to construct BVH for each three PLY

object consists of Bunny, Teapot and Venus model.

Each objects on their balance level using Spatial

Median Splitting Rules.

119

5.3 Average times to construct BVH for each three PLY

Object consists of Bunny, Teapot and Venus model.

Each objects on their Balance Level using SOMS

Rules.

121

5.4 Average times to construct 1000 times BVH for 3DS

Urban Simulation using Spatial Median and SOMS

Method

130

5.5 Average times to construct 1000 times BVH for 3DS

Urban Simulation using Spatial Median and SOMS

Method. The Level of BVH is fixed at level 7 (SOMS

Balanced BVH).

131

5.6 Collision Test using Right Orientation Test of BVH 138

5.7 Collision Test using Left Orientation Test of BVH 139

5.8 Collision Test using Top Orientation Test of BVH 139

5.9 E-Node Traversal Algorithm for SOMS technique 144

5.10 Traversal Testing using E-Node Traversal Algorithm

by comparing to Larrson DFS Algorithm

146

xx

LIST OF ABBREVIATIONS

CG - Computer Graphics

3D - Three-Dimensional

FPS - Frame per-second

BVH - Bounding-Volume Hierarchies

CA - Cellular Automata

UTM - Universiti Teknologi Malaysia

UCLA - University of California, Los Angeles

LAX - Los Angeles International Airport

GJK - Gilbert-Johnson-Keerthi

CCD - Continuous Collision Detection

AABB - Axis Aligned Bounding Box

OBB - Oriented Bounding Box

BV - Bounding-Volume

DOP - Discrete Oriented Polytope

Min - Minimum

Max - Maximum

Ghz - Giga Hertz

DDR - Double Data Rate

RAM - Random Access Memory

GB - Gigabyte (1,000,000,000 Bytes)

xxi

JPEG - Joint Photographic Experts Group

MB - Megabyte (1,000,000 Bytes)

PLY - Polygon File Format

3DS - 3D Studio Max File Format

TXT - Text File

DFS - Depth First Search

BFS - Breadth First Search

SOMS - Spatial Object Median Splitting

SKP - Google SketchUp 3D File Format

xxii

LIST OF APPENDICES

APPENDIX TITLE PAGE

A List of Publication 146

B BVH Model 149

1

CHAPTER 1

INTRODUCTION

1.1 Introduction

The visualization of complex environments in recent years has tremendously

caught attention from various types of user especially for three-dimensional (3D)

applications such as games, animation and simulation. Researchers, gaming

programmer, animator, or normal people will be able to experience the uniqueness of

complex environments. From the beginning of 3D era, various types of technique

also be implemented and tools have been developed in order to create an efficient

and realistic 3D applications. For example, films such as Transformers, 2012,

Dragon Wars, Star Trek, and 3D animation films such as Shrek and Toy Story have

shaped the future requirement of complex environments. Computer games also have

increased their level of realism to produce better complex environments complete

with good story line and realistic complex environments. This also helps to

encourage some of the researchers to continue producing better system in visualizing

the complex environments.

2

There was a significant amount of researches concerning on complex

environments proposed by various researchers (Bittner, Wonka et al. 2001; Willmott,

Wright et al. 2001; Wonka 2001; Hamill and Carol 2003; Waddell and Borning

2004; Brosnan, Hamill et al. 2005; Himanshu, Subhrajit et al. 2006; Laycock, Ryder

et al. 2007; Xiaoping, Xia et al. 2007; Batya, Alan et al. 2008; Borning, Hana et al.

2008; Haciomeroglu, Laycock et al. 2008). Most of these researchers proposed

techniques to be used in Urban Simulation that represent complex environments. For

instance, the urban planner such as architect can properly show their design of urban

planning using 3D tools. It also helps to envision urban issues in urban economies,

social and political structures and norms, transportation and other infrastructure

systems and technologies.

Simulating complex environments consumes lot of resources as it needs to

load multiple objects that has thousand of polygons (Wonka 2001; Hamill and Carol

2003). In order to design better system and to visualize the complex environments,

several important issues must be considered by programmer or researchers. For

instance in most 3D applications, there are needs to maintain the suitable frame rates

such as 30 – 60 frame per seconds (FPS) [(Hamill and Carol 2003; Luiz Gonzaga da

and Soraia Raupp 2006; Spillmann, Becker et al. 2007; Sulaiman, Bade et al. 2008)].

To achieve that requirement, the 3D applications should be able to perform some

optimization methods that could reduce the complexity of the complex environments.

Such requirements also raised other issues which there are also a need to balance

between the realism and the complexity of the applications [(Cohen, Manocha et al.

1994), (Luiz Gonzaga da and Soraia Raupp 2006)].

Among optimization technique that is implemented for complex

environments is collision detection. Collision detection is very essential for realistic

effects in complex environments where it involves static and moving objects. For

example, the meteorite effects such as in 3D films required high performance

collision detection method where it is involved lot of mathematical calculation.

Every trajectory of meteorite needs to be calculated and when the collision occurs, it

requires sophisticated mathematical calculation just to measure the impact. The

3

response of such collision also needs to be calculated in order to visualize the

complex environments after the impact has occurred. Thus, the computational cost is

increased just to confirm the collision detection that has been inserted into complex

environments produced realistic effects (Tecchia and Chrysanthou 2000; Hamill and

Carol 2003; Ryder, Flack et al. 2005; Luiz Gonzaga da and Soraia Raupp 2006;

Laycock, Ryder et al. 2007).

The common approach that had been used by researchers when required to

perform collision detection is Bounding-Volume Hierarchies (BVH) technique

(Somchaipeng, Erleben et al. 2005; Nguyen 2006; Chang, Wang et al. 2008;

Sulaiman, Bade et al. 2009; Tu and Yu 2009). BVH technique provides a

hierarchical representation of object that could be used for complex environments by

successfully dividing the object into several parts. When performing collision

detection checking, only potential colliding parts is going to be further testing for

collision. BVH used various type of hierarchical volume called Bounding Volume

(BV) (Zachmann 2000; Bade, Suaib et al. 2006; Nguyen 2006; Kockara 2007). BV

provides a representation group of primitives reducing the need to perform earlier

primitive-primitive testing. Performing BV-BV testing is faster compared to

primitive-primitives testing as it only checks for certain parts of BVH that collides

with another object. Therefore, the computation cost of detecting object interference

for complex environments can be lowered as the complexity of the object is reduced.

1.2 Problem Background

Detecting object interference in large-scaled virtual environment such as

complex environment becomes a challenge since decades ago as it requires the

simulation to run smoothly at interactive frame-rates (Cohen, Manocha et al. 1994).

(Hubbard 1993) proposed a method that increases the speed of pair wise test between

4

objects but they traded with the accuracy. By making object intersection faster,

performance of the simulation will become faster than normal. However, it degrades

the accuracy of object intersection. This is not always the best choice as exact contact

determination always takes some time to produce collision pairs (Cohen, Lin et al.

1995).The objectives of detecting object interference is quite vague as it heavily

depends on the simulation itself. For medical such as surgeon simulation, accuracy is

more important than speed of the intersection as it must precisely contact the patient

body but for complex environment, faster intersection is more relevant compared to

accuracy. However, we still need to realize that it depends on what are the important

things to consider for specific environment.

In 2000, (Tecchia and Chrysanthou 2000) suggested that in order to make

realistic complex environment, simulating human movement using crowd simulation

becomes important aspect to bring complex environment to „life‟. However, human

crowds not only bring additional cost in the simulation but also decrease the

performance of complex environment by making collision detection test slower

(Tecchia and Chrysanthou, 2000). For example, complex environment may consist

thousands of human crowds freely walking in different directions. If one tries to

perform standard exact collision detection method between human crowds and static

objects in complex environment, it is time consuming as every entity needs to be

checked for collision (Tecchia and Chrysanthou, 2000). Hence, they decided not to

compute the accuracy of detecting object interference in this case.

In order to tackle this problem, they used a simple and fast method such as

height map to detect collision in complex city cramps with human and other 3D

models (Tecchia and Chrysanthou, 2000). They introduced two different approaches

which involves predicting the future or final position of the object. They reallocate

the task to detect collision away from current object position or they focused on

detecting object interference between moving particles and static objects only. Inter-

particle collision is not performed to make sure the proposed method is fast enough.

Accuracy has to be abandoned in order to make sure that complex environment run

smoothly in exchange for faster intersection (Tecchia and Chrysanthou, 2000).

5

Later in 2003, (Hamill and Carol 2003) had presented Virtual Dublin

complex environment that can be used as a prototype to test various projects such as

crowd and traffic simulation, land design, and disseminated graphics studies. They

implemented a Moller Ray-Triangle Intersection Algorithm for detecting collision in

complex environment (Möller and Trumbore 1997). (Nurminen 2006) had suggested

a 3D mobile map, called m-LOMA city. The city was designed with special mobile

features that can keep the location-based information of the city. In m-LOMA,

collision detection had been used to detect intersection between user moving line and

the objects of the city. (Pelechano, Allbeck et al. 2007) created HiDAC system (High

Density Autonomous Crowd) and they used collision detection technique to detect

overlapping direction of human crowd. The proposed approach only occur in one

single room between other human crowd and it allows faster intersection between

hundreds of human crowd (Pelechano, Allbeck et al. 2007).

Hierarchical representation has not been the main focus in term of using them

for collision detection in complex environment. From thorough discussion of

collision detection in complex environment above, the method that involving

hierarchical representation is on grid system and height map system to detect

collision (Cohen, Manocha et al. 1994; Tecchia and Chrysanthou 2000; Laycock,

Ryder et al. 2007). By using so called grid system, the collision is to be determined

once the object or crowd has intersected with any grid boxes. However, this method

is far from more specific approach of hierarchical representation which is Space

subdivision and bounding-volume hierarchies (BVH). BVH usage is more on general

collision detection in virtual environment and from the study, BVH has only very

little literature in large-scaled simulation such as massive environment simulation

and complex environment.

In BVH, there are generally three phase of BVH construction. First phase is

to determine its characteristics such as types of the tree, bounding-volume to use,

splitting point, and any other characteristics. Second phase involved the construction

of defined tree after all characteristics have been decided. Last phase involved the

traversal scheme when it uses to detect collision between BVH of other objects.

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However, looking at BVH construction in details, most researchers used common

splitting algorithm to split their node into two equal sizes especially in binary type

tree which is the most common BVH tree that has been used. This common method

has been used along with heuristic determination in order to reach desired stopping

criteria. Spatial Median technique is the most common splitting technique after

Object Median technique and any other techniques (Cormen, Leiserson et al. 1990;

Lin and Manocha 2004; Spillmann, Becker et al. 2007; Kun, Qiming et al. 2008;

Masatake, Yasuyuki et al. 2008). They work in different ways as Spatial Median cut

the object into two equal parts while Object Median calculate median point and split

at the centre of object median.

Most objects that are designed using 3D tools theoretically contain almost the

same triangle size. But in practise, most 3D designer prefers to give some

modification to the object in order to draw their object according to their own

specification. Thus, the triangle of the corresponding object is not the same as in

theory. Hence, by enclosing the object with BVH could produce the BVH to certain

levels but eventually stop when it reaches non splitting condition such as irregular

size of triangles. Hence researchers come out with heuristic determination in order to

continue split the object into desired stopping point according to stopping criteria or

until each node contain only one triangle. Among splitting that used is that kind of

heuristic in their implementation are both spatial median and object median which

are the most common implementation for BVH construction or more general in

hierarchical representation (Rusinkiewicz and Levoy 2000; Sobottka and Weber

2005; C.Watcher and A.Keller 2006; Ernst and Greiner 2007; Liu, Wang et al. 2007;

Otaduy, Chassot et al. 2007; Yi, Kim et al. 2007; Steinemann, Otaduy et al. 2008).

In this research, the splitting technique will be improved by increasing the

level of BVH that can be generated automatically without using heuristic at the

earlier phase. It reduces time to construct tree and increase the efficiency in collision

detection handling for large complex environment. As complex environment consist

lot of buildings, performing collision in large area could become problem as it could

consumes memory and constantly test for object intersection. Hierarchical

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representation could reduces the problem into certain degrees by making only parts

of object that within the hierarchical section is tested for intersection leaving any

non-colliding pairs.

In this research, our main research question is.

What kind of optimization approach that is suitable in BVH technique that

will improved the capabilities of BVH construction in order to create fast and

efficient technique to perform collision detection between static and moving object

for complex environments.

In order to find the solution of creating faster collision detection method

using BVH technique for complex environments, few questions need to be detailed

up as follows:-

1. How to find the correct improvement on BVH that possibly improve the

collision detection method for complex environments.

2. What type of tree construction must be used? Is it binary tree, quad tree, or

oct-tree?

3. How to choose the tree construction approach? Is it top-down, bottom-up and

insertion method?

4. How to choose to splitting/merging criteria for each branch of the tree

hierarchies?

5. Why each splitting rule give differences result when it is used for BVH?

6. What types of bounding-volumes suitable for proposed technique?

7. Does the chosen technique speed up the process of detecting object

interference? And how fast compared to the previous one and how to measure

the „accuracy‟ of the technique.

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For each question described above, the answer for all research questions

invoked will be answered in chapter two, three, and four.

1.3 Research Aim

The aim of this research is:-

To enhance the splitting rule technique using Binary BVH of Axis-Aligned

Bounding Boxes (AABB) in detecting object interference for complex environments

therefore the performance of collision detection handling can be optimized.

1.4 Research Objectives

The objectives for this research study are as follows:

1. To develop Spatial Object Median Splitting (SOMS) Rules

2. To develop E-Node Traversal Algorithm for SOMS technique

3. To evaluate and benchmark the proposed techniques with previous method of

BVH splitting rules.

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1.5 Scope of the study

The scope of this research is as follows:

1. Two common 3D data files which are Polygon (PLY) data file and 3D Studio

Max (3DS) data file were used in this research implementation. For PLY

object, three models were chosen for simple collision testing. These models

can be downloaded from Stanford University Repository model library.

a) Stanford Bunny Model

b) Stanford Teapot Model

c) Stanford Venus Model

2. The Urban Simulation that represents the complex environments is developed

using 3D modeling tools: Google Sketchup 6.4 version. It contains all the

complex environments basic requirements which are multiple objects, basic

texturing and lighting.

3. The propose method is only focusing at the improvement of splitting

algorithm for BVH. Other elements such as data management, culling system,

texturing, and lighting will not be discussed. This is because the technique

only requires the object triangle in order to find the differences between other

splitting techniques.

4. An OpenGL library and C++ language will be used for the programming

parts as well as implementing the Class and Data Structure concept.

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5. Testing procedure will be conducted using orientation test between moving

object and static object. Orientation test consists of basic directional

movement of moving object either from left, right, top, and bottom towards

the static object for collision detection test. The parameters involves are:-

a) Time in milliseconds

b) Frame

c) Frame per second (FPS)

1.6 Significance of the study

BVH technique can be reproduced by enclosing geometry objects with

AABB bounding-volumes without having to slow down the process of detecting

interference in complex environments. This research intends to achieve all the

objectives according to the scope of this research towards development of efficient

collision detection technique for complex environments. The proposed technique is

able to minimize the computation cost and increase the performance for complex

environments when collision occurred. As a result, the frame-rate of complex

environments increases regardless number of object being tested.

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1.7 Contribution of this thesis

The contribution of this thesis consists of:-

1. New Spatial Object Median Splitting Rules in Bounding-Volume Hierarchies

for Complex environments.

2. E-Node Traversal Algorithm that is embedded with the new Splitting Rules to

include in BVH technique for collision detection.

1.8 Structure of the thesis

This report consists a total of six chapters. The organisation of this report has

been arranged into following orders.

Chapter 1 discusses the fundamental elements of this research. It consists

introduction to this research, related work, problem statement, objective and scope of

the research, as well as research contribution.

Chapter 2 discusses thoroughly about literature review of this research.

Discussion starts by explaining complex environments, hierarchical representation

and collision detection. Various techniques or methods have been discussed here to

provides enough evidence to support this research implementation.

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Chapter 3 provides a research methodoly of this research. Every phase has

been thoroughly discussed. All phases are well-explained starting from literature

review, data collection and analysing of previous techniques and few other phases.

Chapter 4 introduced the Spatial Object Median Splitting (SOMS) Rules

technique in BVH. All discussions about how the implementation of SOMS is

carried out, the justification of SOMS, and related information regarding SOMS will

be explained in this chapter.

Chapter 5 is the results and discussion chapter for our proposed technique in

details. The chapter also will discuss in details about all testing and results were

made along with the justification on each experiement. Each implementation is

explained thoroughly and why the testing must be done such way.

Chapter 6 is the final chapter where the summarization of our work. The

conclusion and future work is also discussed.