DECOMPOSING LINEAR AND AFFINE TRANSFORMATIONS
Ronald N. Goldman, Rice University, Houston, Texas
Publisher Summary
Every nonsingular linear transformation of three-dimensional space is the product of three scales, two shears, and one rotation. This chapter explains how to decompose any arbitrary, singular or nonsingular, linear, or affine transformation of three-dimensional space into simple, geometrically meaningful factors. Linear transformations of three-dimensional space are generally represented by 3 × 3 matrices. The parallel projection can be replaced by a shear followed by an orthogonal projection. Every nonsingular affine transformation of three-dimensional space can be factored into the product of three scales, two shears, ...
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