math - Decompose complex matrix transformation into a series of simple transformations? -


I wonder if this is possible (and if this happens) to re-index an indexed M3 matrix conversion In other words: How to calculate the matrix of MCMplex, MScLe, Mrotate, MKKU from MComplex so that the following equation is correct:

P>

MComplex = MTranslate * MScale * MRotate * MSkew (or other order) In this structure, an arbitrary matrix changes in the structure of the 3 matrix:

Orthogonal + diagonal + orthogonal Orthogonal matrix rotation matrix; Diagonal matrix represents skewing with primary axes = scaling.

A monkey throws a translation in the wrench, but what you should do is to take the translated part of the matrix so that you have 3x3 matrix on it to run the SVD to give you rotation + skiving, then Add translation part back. In this way you have to translate a rotation + scale + rotation + 4 matrix. It is possible that this is possible in 3 matrix (axes + rotating + scaling with some set of translations), but I'm not sure that ... maybe a QR decomposition (Q = orthogonal = rotation), but I'm not sure That R is only skewed or is a rotating part.)


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