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Integration part 1

# Integration part 1 - Composition or Concatenation of...

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Composition or Concatenation of Transformations rare to perform only one elementary transformation composition of affine transformations is also affine order transformations are applied in matters matrix multiplication does not commute example: translate then scale vs. scale then translate ú ú ú ú û ù ê ê ê ê ë é = ú ú ú ú û ù ê ê ê ê ë é ú ú ú ú û ù ê ê ê ê ë é 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 z y x z y x t t t s s s ú ú ú ú û ù ê ê ê ê ë é = ú ú ú ú û ù ê ê ê ê ë é ú ú ú ú û ù ê ê ê ê ë é 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 z y x z y x s s s t t t Composition or Concatenation of Transformations reading left to right transformation matrices appear in reverse order example: apply A then B then C overall transformation is )) ( ( a A B C d d c C c b B b a A H H H H H H H H = = = = CBA T =

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Composition or Concatenation of Transformations (cont) example: scale about arbitrary point P = (px, py, pz) translate P to origin scale translate back to original point P ú ú ú ú û ù ê ê ê ê ë
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