Getting Started p. 1
Introduction p. 1
Access to Libraries p. 2
Data Types p. 2
Terminology p. 3
The OpenGL Utility Toolkit-GLUT p. 3
Our First Program p. 4
Drawing Primitives p. 7
Gaps, Lines and Blobs p. 10
Other Line Types p. 11
Surface Patterns and Polygon Stippling p. 12
Character Generation p. 15
Parametric Representation of Curves p. 17
The Growth or Logarithmic Spiral p. 19
Approximation and Processing Efficiency p. 21
Line Drawing p. 22
The Digital Difference Analyser p. 23
Bresenham's Algorithm p. 25
Bresenham's Algorithm for a Circle p. 27
Problem Solving Through Graphics p. 31
The Application Programming Interface (API) p. 34
The OpenGL Utility Toolkit (GLUT) Library p. 34
Mouse Interaction p. 35
Keyboard Interaction p. 36
Exercises p. 37
Conclusion p. 37
Image File Formats p. 39
Introduction p. 39
The Bitmap File p. 39
Bitmap-file Structure p. 40
A Typical File Layout p. 41
Reading and Drawing a Bitmap File p. 42
Creating a Display Window p. 45
Creating the Image for Display p. 46
Monochrome Bitmaps p. 46
A General Class for Input of Bit Map Files p. 47
Manipulating Bit Maps - Embossing p. 49
Audio/Video Interleaved (AVI) File Format p. 51
Chunk Hierarchy p. 53
An Example of Web Cam Display p. 55
Exercises p. 59 Conclusion p. 59 Image Processing p. 61 Introduction p. 61 Finding Objects p. 61 Edge Detection p. 62 Numerical Implementation p. 63 Sobel Operator p. 63 Convolution p. 64 Laplacian Operator p. 66
Smoothing and Edge Finding p. 69
Histogram Equalisation p. 71
Component (object) Labelling p. 73
Exploring Connectivity (1) p. 74
Exploring Connectivity (2) p. 76
Multiple Regions p. 77
Drawing on the Screen and Data Capture p. 77
Outlining of Areas of Interest on Images p. 80
An Approach to Automating Edge Detection p. 82
Exercises p. 85
Conclusion p. 85
Transformations p. 87
Introduction p. 87
Representing Points and Vectors p. 87
Vector Dot Products p. 89
The Vector Cross Product p. 89
Using the Cross Product to Provide Colour Variation to a Cylinder p. 91
Coordinate Systems p. 94
Transformations p. 95
Rotation p. 96
A Simple Example of Rotation p. 98
General Rotations About Any Point p. 99
The Model View Matrix p. 103
Adding Some Movement p. 103
Movement of Composite Objects p. 104
The Orrery p. 104
The Internal Combustion Engine p. 107
Arms, Robots, Actuators and Movement p. 113
Data Capture of Limb Movement p. 114
Animation - A Walking Robot p. 116
Exercises p. 124
Conclusion p. 124
Viewing and Projection p. 125
Introduction p. 125
Vertex Pipeline p. 125
The Viewing Process p. 126
Engineering Drawings p. 128
Orthographic or Parallel Projection p. 132
From Real World to Screen Window p. 132
Inside the Matrix p. 134
Getting to Grips with Where Things Are p. 137
Perspective Projection p. 139
Understanding the View p. 143
Exercises p. 145
Conclusion p. 146
Lighting and Colour p. 147
Introduction p. 147
The Electromagnetic Spectrum p. 147
Colour p. 148
Mixing Colours p. 149
The Shading Model p. 150
Lighting and Illumination p. 151
Setting up the Lighting p. 152
Addition of Specular Light p. 157
A Synthetic Face p. 162
Getting the Vertex Coordinates p. 162
Moving the Eye and Light Source Together p. 163
Shadows - A Projection p. 164
Derivation of the Shadow Outline Using Equation of a Line p. 164
A Polygon Moving Shadow p. 166
Exercises p. 168
Conclusion p. 169
Texture Mapping p. 171
Introduction p. 171
The Mapping Process p. 171
Setting up Textures p. 172
Drawing the Texture p. 174
Mapping onto Curved Surfaces p. 176
Mercator Lines of Projection p. 176
Quadric Surfaces p. 177
Mapping one Image to Sphere p. 182
Cylinder Texturing Mapping p. 184
Mapping to a Circle p. 185
Mapping to a Cone p. 186
Mapping onto a General Surface p. 189
Mapping onto a Contour Surface p. 191
Adding Some Movement - A Rotating Hemisphere p. 193
Movement via the Mouse p. 196
Using Bit Maps to Provide Context p. 200
Blending p. 202
Manipulating Pixels p. 206
Three-Dimensional Texturing p. 212
Simulation of a Spherical Object p. 213
Building a Solid Model of a Head p. 219
Exercises p. 226
Conclusion p. 226
Objects to Artefacts p. 227
Introduction p. 227
Artefact Hierarchy p. 227
Construction Double Sided Squares p. 228
A Box as a Basic Building Block p. 232
Building a Table p. 233
Integrating to a System p. 235
Changing the Furniture Style p. 243
Exercises p. 247
Conclusion p. 247
Curves, Surfaces and Patterns p. 249
Introduction p. 249
Fitting a Line or a Curve p. 250
Straight Line Fitting to Data Points p. 250
Lagrange Polynomials and Curve Fitting p. 251
A Practical Approach to Curve Fitting p. 251
Curve Fitting Using Cubic Splines p. 252
Surface Construction from Contour Maps p. 256
A Spline Surface Construction p. 258
Bezier Curves p. 260
General Curve Representation p. 263
The Beginning's of a Bezier Surface p. 267
Using Rotation to Sweep Out a Ring p. 271
Patching a Surface p. 271
Introductory Concepts p. 275
Reduction Copying p. 276
Implementation of a Sierpinski Gasket p. 278
Pascal's Triangle p. 280
The Sierpinski Gasket in 3 Dimensions p. 280
Order Out of Chaos - A Non-deterministic Gasket? p. 284
An Alternative Idea for a Tree or Plant p. 290
Koch Curves p. 292
Further Thoughts on the Koch Snowflake p. 295
Self-Similarity p. 296
Random Koch Fractals p. 298
Back to Trees and Bushes p. 300
Brownian Motion p. 304 Fractalised Lines p. 305 Fractal Surfaces p. 307 Exercises p. 310 Conclusion p. 311 Appendix A p. 313 Starting up VC++ 6.0 p. 313 Appendix B p. 317
Bresenham's Line Algorithm - General Conditions p. 317
Appendix C p. 319
Matrix and Vector Algebra p. 319
Matrix Addition or Subtraction p. 319
Matrix Multiplication p. 319
Matrix Vector Multiplication p. 320
Example of Matrix Multiplication p. 321
Shearing Matrices p. 321 Appendix D p. 323 Equation of a Plane p. 323 References p. 325 Index of Functions p. 327 Index p. 329
