Geometric algebra and computer graphics

摘要

What is the best representation for doing euclidean geometry on computers? This question is a fundamental one for practitioners of computer graphics, as well as those working in computer vision, 3D games, virtual reality, robotics, CAD, animation, geometric processing, discrete geometry, and related fields. While available programming languages change and develop with reassuring regularity, the underlying geometric representations tend to be based on vector and linear algebra and analytic geometry (VLAAG for short), a framework that has remained virtually unchanged for 100 years. These notes introduce projective geometric algebra (PGA) as a modern alternative for doing euclidean geometry and shows how it compares to VLAAG, both conceptually and practically. In the next section we develop a basis for this comparison by drafting a wishlist for doing euclidean geometry.