vii
TABLE OF CONTENTS
CHAPTER
1
2
TITLE
PAGE
ACKNOWLEDGEMENTS
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
x
LIST OF FIGURES
xii
LIST OF ABBREVIATIONS
xv
LIST OF SYMBOLS
xvi
LIST OF APPENDICES
xvii
INTRODUCTION
1 1.1 Introduction
1 1.2 Background of the Study
2 1.3 Problem Statement
6 1.4 Research Aim
7 1.5 Objectives
7 1.6 Research Scope
7 1.7 Thesis Organization
8 LITERATURE REVIEW
10 2.1 Overview of Surface Reconstruction
10 2.1.1 Surface Reconstruction Process
2.2 Surface Representation
11 11 2.2.1 Bezier Curve and Surface
12 2.2.1.1 Bezier Equations
12 viii
2.2.2 B-Spline
2.2.2.1 B-Spline Equations
2.2.3 Non-Uniform Rational B-Spline (NURBS)
2.2.3.1 NURBS Equations
2.3 Artificial Neural Network for Surface Reconstruction
2.3.1 Overview of Kohonen Network
16 17 18 19 19 2.3.1.2 Kohonen Network Algorithm
22 2.4.1 Overview of Differential Evolution
2.4.1.1 Properties of Differential Evolution
2.4.1.2 Proper Algorithm of Differential
Evolution
2.4.1.3 The Basic Operation of Differential
Evolution
2.5 Related Studies
25 25 28 28 30 31 2.6 Summary
33 METHODOLOGY AND THE PROPOSED METHOD
34 3.1 The Framework of the Study
34 3.1.1 Data Collection
35 3.1.2 Growing Grid Network (GGN) Generation
36 3.1.2.1 Update the Parameter of Growing Grid
Network (GGN)
3.1.3 Parameterization and Knot Vector Generation of
Initial Sketch
3.1.3.1 Parameterization
4
14 2.3.1.1 Kohonen Network Architecture
2.4 Evolutionary Computation for Surface Reconstruction
3
14 44 45 46 3.1.3.2 Knot Vector Generation
47 3.1.4 Differential Evolution Algorithm
48 3.1.4.1 Population
and
Chromosome
initialization
3.1.4.2 Calculation of fitness value
50 50 3.1.4.3 Mutation and Selection
51 3.1.5 Performance Analysis and Comparison
53 3.2 Summary
54 EXPERIMENTAL RESULTS AND ANALYSIS
55 4.1 Experiment Protocol
55 ix
4.1.1 Data Specifications
56 4.1.2 Parameter Setting of Growing Grid Network
(GGN)
4.1.3 Development of the Growing Grid Data Network
58 58 4.1.4 Implementation of Parameterization and Knot
Vector Generation
4.1.5 Parameter Setting of Differential Evolution
Algorithm (DEA)
4.1.6 Parameter Setting of PSO
60 62 4.1.7 Parameter Setting of GA
63 4.2 Performance Assessments
4.2.1 Results and Analysis of Curve and Surface using
GGN – DEA
4.2.2 Results and Analysis of Curve and Surface using
PSO
4.2.3 Results and Analysis of Curve and Surface using
(GA)
4.3 Results Comparison
5
59 64 65 68 69 71 4.4 Experimental Results of Mathematical Function using
Evolutionary Computing
4.4.1 Experimental
Results
for
Mathematical
Functions
4.5 Summary
77 79 CONCLUSIONS AND FUTURE WORK
80 5.1 Research Achievements
80 5.2 Research Contributions
81 5.3 Future Works
82
REFERENCES
83 APPENDICES A-C
88 73 x
LIST OF TABLES
TABLE NO.
TITLE
PAGE
1.1
Previous Related Study on Surface Reconstruction
5 2.1
Comparation of PSO, GA, and DE (Wdaa 2008)
26 3.1
Sample Data for Semi-sphere
36 4.1
Data Specifications
56 4.2
Parameter settings of Growing Grid Network (GGN)
58 4.3
Parameter Value of Mask Data Points
60 4.3
Parameter Settings of DEA
61 4.4
Parameter settings of PSO
62 4.5
Parameter settings of GA
64 4.6
Average error of GGN-DEA for 2D data (curve)
65 4.7
Average error of GGN-DEA for 3D data (surface)
66 4.8
Average error of GGN-PSO for 2D data (curve)
68 4.9
Average error of GGN-PSO for 3D data (surface)
69 4.10
Average error of GGN-GA for 2D data (curve)
70 4.11
Average error of GGN-GA for 3D data (surface)
70 4.12
Average Error between DEA, PSO, and GA for Curve Data
71 4.13
Average Error between DEA, PSO, and GA for Surface Data
72 4.14
Results for Mathematical Functions
77 A.1
Sine Data
89 A.2
Trochoid Data
90 A.3
Spiral Data
91 A.4
Free form curve data
92 A.5
Sample of Mask data
95 A.6
Sample of Ship Hull data
96 xi
A.7
Sample of Saddle data
97 A.8
Sample of Sphere Data
98 A.9
Sample of Buddha statue data
99 A.10
Sample of Free-form surface data
100 B.1
Average error of GGN-DEA for 2D data (curve)
104 B.2
Average error of GGN-DEA for 3D data (surface)
104 B.3
Average error of GGN-PSO for 2D data (curve)
110 B.4
Average error of GGN-PSO for 3D data (surface)
110 B.5
Average error of GGN-GA for 2D data (curve)
116 B.6
Average error of GGN-GA for 3D data (surface)
116 B.7
Comparison of Average Error between DEA, PSO, and GA for
Curve Data
B.8
125 Comparison of Average Error between DEA, PSO, and GA for
Surface Data
126
xii
LIST OF FIGURES
FIGURE NO
TITLE
PAGE
2.1
Kohonen SOM Architecture
20 2.2
Mapping Structure of Kohonen SOM
21 2.3
Mapping Dimension of Kohonen SOM
21 2.4
Lattice Structure of Kohonen SOM
22 2.5
Gaussian Graph Function
24 2.6
Basic pseudo-code for the DE algorithm.
28 2.7
Flowchart of DE algorithm
29 3.1
Framework of the study
35 3.2
Construction of initial sketch using GGN
37 3.3
Neurons Initialization
38 3.4
Initialization Position of Neurons
38 3.5
Initialization Weights for each sample point
39 3.6
Win counter value for each neuron
39 3.7
Sample Points Ps
39 3.8
Winning Neuron
40 3.9
Boundary Neuron
40 3.10
Boundary Neuron Detected
41 3.11
Boundary Neuron Not Detected
41 3.12
Update Position If Boundary Neuron Not Detected
41 3.13
Update Position If Boundary Neuron Detected
42 3.14
Maximum winning counter detected
42 3.15
Node Addition to Column
43 3.16
Node Addition to Row
43 3.17
Differential Evolution Algorithm
49 xiii
3.18
The architecture of population of DE
50 3.19
The Mutation, Recombination, and Selection process of DE
53 4.1
Spiral data
57 4.2
Unstructured Mask
57 4.3
Structured Mask
59 4.4
Generated Spiral Curve using DEA
67 4.5
Generated Semi Sphere Surface using DEA
67 A.1
Sine data
93 A.2
Trochoid data
93 A.3
Spiral data
94 A.4
Free form curve data
94 A.5
Mask data
101 A.6
Ship Hull data
101 A.7
Saddle data
102 A.8
Sphere data
102 A.9
Buddha Statue data
103 A.10
Free Form Surface data
103 B.1
Sine curve, generated by DEA
105 B.2
Trochoid curve, generated by DEA
105 B.3
Spiral curve, generated by DEA
106 B.4
Free form curve, generated by DEA
106 B.5
Sphere in wireframe view, generated by DEA
107 B.6
Ship in wireframe view, generated by DEA
107 B.7
Mask in wireframe view, generated by DEA
108 B.8
Saddle in wireframe view, generated by DEA
108 B.9
Free Form in wireframe view, generated by DEA
109 B.10
Buddha statue in wireframe view, generated by DEA
109 B.11
Sine curve, generated by PSO
111 B.12
Trochoid curve, generated by PSO
111 B.13
Spiral curve, generated by PSO
112 B.14
Free form curve, generated by PSO
112 B.15
Sphere in wireframe view, generated by PSO
113 B.16
Ship in wireframe view, generated by PSO
113 B.17
Mask in wireframe view, generated by PSO
114 xiv
B.18
Saddle in wireframe view, generated by PSO
114 B.19
Free Form in wireframe view, generated by PSO
115 B.20
Buddha statue in wireframe view, generated by PSO
115 B.21
Sine curve, generated by GA
117 B.22
Trochoid curve, generated by GA
117 B.23
Spiral curve, generated by GA
118 B.24
Free form curve, generated by GA
118 B.25
Sphere in wireframe view, generated by GA
119 B.26
Ship in wireframe view, generated by GA
119 B.27
Mask in wireframe view, generated by GA
120 B.28
Saddle in wireframe view, generated by GA
120 B.29
Free Form in wireframe view, generated by GA
121 B.30
Buddha Statue in wireframe view, generated by GA
121
xv
LIST OF ABBREVIATIONS
ABBREVATION
DESCRIPTION
2D
(x, y)-Two dimensional plane
3D
(x, y, z)-Three dimensional plane
CAD
Computer Aided Design
CAM
Computer Aided Manufacturing
CAGD
Computer Aided Geometric Design
DE
Differential Evolution
GA
Genetic Algorithm
GGN
Growing Grid Network
NFL
No Free Lunch
NURBS
Non-Uniform Rational B-Spline
PSO
Particle Swarm Optimization
xvi
LIST OF SYMBOLS
SYMBOLS
DESCRIPTION
Bk,n(t)
-
basis function for Bezier curve at parameter t.
Ni,k(t)
-
B-Spline basis function at parameter t and kth
degree
xvii
LIST OF APPENDICES
APPENDIX
TITLE
PAGE
A
ORIGINAL DATA
B
RESULTS OF THE OPTIMIZATION
104 C
PUBLICATIONS
127 89