BSNS102 Study Guide - Final Guide: Rotation Matrix, Determinant, Invertible Matrix
28 Jan 2021
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From section 7. 1. 6 we know that matrix multiplication is associative, and so we can compute one matrix to transform directly from object to camera space: Thus, we can concatenate the matrices outside the loop and have only one matrix multiplication inside the loop (remember there are many vertices): So we see that matrix concatenation works from an algebraic perspective using the associative property of matrix multiplication. Let"s see if we can"t get a more geometric interpretation of what"s going on. Recall our breakthrough discovery from section 7. 2 that the rows of a matrix contain the basis vectors after transformation. This is true even in the case of multiple transforma- tions. Notice that in the matrix product ab, each resulting row is the product of the corresponding row from a times the matrix b. In other words, let the row vectors a1, a2, and a3 stand for the rows of a. Then matrix multiplication can alternatively be written like this:
