Vector geometry for computer graphics

摘要

Computer graphics and modeling rely on mathematical operations on points and vectors. The author advocates using vector geometric analysis to simplify required derivations. He presents the basic language and methods of vector geometric analysis and characterizes the situations favoring vector geometric versus coordinate based analysis. A set of C++ classes is developed which includes methods and definitions of overloaded operators implementing nearly all of the low level operations and matrix construction algorithms presented in this article and its companion (J.R. Miller, see ibid., vol.19, no.4, 1999). Sample code using these tools to perform representative common operations is presented.