Mathematical Foundations of 3D Computer Graphics with OpenGL

This book serves as an introduction to 3D computer graphics, focusing on the mathematical principles that underpin the field. It covers the OpenGL programming environment, offering source code for a ray tracing software package. Topics include transformations, viewing, lighting, shading models, interpolation, B´ezier curves, B-splines, ray tracing, radiosity, and ray intersection testing. It also briefly addresses texture mapping, color theory, and animation aspects such as quaternions, orientation, and inverse kinematics. The book includes a review of vector and matrix mathematics in an appendix and is suitable for advanced undergraduates, introductory graduate students, or self-learners with a basic understanding of calculus, vectors, and C/C++ programming. It complements other OpenGL programming resources. Samuel R. Buss, the author, is a Professor of Mathematics and Computer Science at the University of California, San Diego, with extensive experience in computer science and mathematical logic.