CSE 167 Lecture 12: L12 2/14/19
14 Feb 2019
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Homogeneous 4x4 matrices for: translate by +5 units in x dir. [ 0 0 0 | 1 : rotate by 30 degrees about the x axis. 1 : rotation, followed by translation above, followed by scaling by a factor of 2, rotation, translation. [ i3x3 t3x1 ] [ r3x3 03x1 ] = For rotation matrices: rtr = i rt = r-1. For translation matrices: t-1 = -t (only the translation part!!!) [ r (t-rt) ] t" = t - rt (center point) => axis becomes aligned with the x axis! Consider flatland (w/o homogeneous coordinates) 2x2 transformation matrices. Let"s say we want to scale by 1. 5 (increase length 50%) not about coordinate axes, but about an axis at -45 degrees to the horizontal. Idea: first rotate, then scale, then rotate back! Any symmetric matrix m = mt can be decomposed into: u ut = rsrt. = ( u ) [ 1 0 ] ( ut )
