Fundamentals part 3

Fundamentals part 3 - Applying Translation I translation...

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Applying Translation n translation leaves vectors unchanged n translation moves points by a vector amount [] 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 = = 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 z y x z y x t t t v T z y x v z y x T H H 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 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 z y x z y x T t z t y t x z y x t t t TP z y x P Inverse of Translation n inverse of a transformation undoes the transformation n check that I T T TT = = 1 1
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Scale n enlarge or shrink an object n scales objects about the x, y, and z-directions u origin is invariant n if 0 < sx < 1, then object shrinks by a factor of sx in x-direction n if sx > 1, then object grows by a factor of sx in x-direction n what if sx < 0? if sx = 0? Inverse of Scale n if an object is scaled by a factor of s u then the inverse scales by a factor of 1/s
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Shear n six basic shearing transformations n first subscript: which coordinate is changed n
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This note was uploaded on 02/13/2012 for the course CSE 4431 taught by Professor Burton during the Winter '12 term at York University.

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Fundamentals part 3 - Applying Translation I translation...

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