3D Computer Graphics: A Mathematical Introduction with OpenGLThis textbook, first published in 2003, emphasises the fundamentals and the mathematics underlying computer graphics. The minimal prerequisites, a basic knowledge of calculus and vectors plus some programming experience in C or C++, make the book suitable for self study or for use as an advanced undergraduate or introductory graduate text. The author gives a thorough treatment of transformations and viewing, lighting and shading models, interpolation and averaging, Bézier curves and B-splines, ray tracing and radiosity, and intersection testing with rays. Additional topics, covered in less depth, include texture mapping and colour theory. The book covers some aspects of animation, including quaternions, orientation, and inverse kinematics, and includes source code for a Ray Tracing software package. The book is intended for use along with any OpenGL programming book, but the crucial features of OpenGL are briefly covered to help readers get up to speed. Accompanying software is available freely from the book's web site. |
Contents
Introduction | 1 |
Transformations and Viewing | 17 |
Lighting Illumination and Shading | 67 |
Averaging and Interpolation | 99 |
Texture Mapping | 126 |
Color | 146 |
Bézier Curves | 155 |
BSplines | 200 |
Intersection Testing | 257 |
Radiosity | 272 |
Animation and Kinematics | 289 |
A Mathematics Background | 319 |
B RayTrace Software Package | 332 |
| 353 | |
| 359 | |
Ray Tracing | 233 |
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Common terms and phrases
3-space affine transformation algorithm ambient axis B-spline curve Bézier curves Bézier patches blending functions buffer calculate called Catmull-Rom color commands computer graphics control points Cook-Torrance cross product curve q(u cylinder defined degree three Bézier diffuse direction discussed dot product double environment map equal Equation example Exercise float form factors formula geometric Gouraud homogeneous coordinates illumination jittered joint angles kinematics knot positions light source line segment linear interpolation linear transformation matrix method mipmap multiple nonzero normal vector numbers objects OpenGL orientation p₁ partial derivatives Phong lighting Phong lighting model pixel plane polygons polynomial projection properties quadrilateral quaternions radiosity ray tracing recursive reflection rendering represent rotation routines scalar scene shading shadow shown in Figure specified specular sphere splines subpixel supersampling surface normal texture coordinates texture map Theorem three Bézier curve triangle u₁ Ui+1 unit vector values vertex vertices viewer weighted average zero