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how does matrix represent the 3D world?

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i wonder if these components of a matrix are just data that represent x-rotation, y-rotation, position and etc. regards, Tim

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If you are talking about matrices in 3D graphics then I believe so.

Not too much of an expert myself, but (for OpenGL):
http://www.morrowland.com/apron/tutorials/gl/gl_matrix.php

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This is a good introductory text that might help you get up to speed on matrix and vector math.

As to your question, a 4x4 matrix can be used to represent quite a few things. Quite often it represents, as you suggested, a rotation and a translation. The translation vector is stored in the bottom row or right column. The upper-left 3x3 sub-matrix stores in its rows or columns the orthonormal basis vectors that represent the rotation. The remaining row or column is set to [0 0 0 1].

The 3x3 sub-matrix can also incorporate other transformations such as scale, shear, and reflection. Other uses for 4x4 matrices include projecting from 3d to 2d.

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