December 2012
Intermediate to advanced
631 pages
13h 10m
English
Content preview from Graphics Gems III (IBM Version)
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III.2
DECOMPOSING PROJECTIVE TRANSFORMATIONS
Ronald N. Goldman, Rice University, Houston, Texas
Publisher Summary
This chapter discusses how to decompose an arbitrary projective transformation of three-dimensional space into simple, geometrically meaningful factors. The standard way to factor any projective transformation of three-dimensional space is first to embed three-space into four-space, then to apply the 4 × 4 matrix M as a linear transformation in four-space, then to apply a perspective projection of four-space with the eye point at the origin and the perspective hyperplane at w = 1, and finally to project from four-space back to three-space by identifying the four-dimensional hyperplane w = 1 with standard three-dimensional ...
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