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Fundamentals part 3

# Fundamentals part 3 - Applying Translation I translation...

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Applying Translation translation leaves vectors unchanged 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 inverse of a transformation undoes the transformation check that I T T TT = = 1 1

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Scale enlarge or shrink an object scales objects about the x, y, and z-directions origin is invariant if 0 < sx < 1, then object shrinks by a factor of sx in x-direction if sx > 1, then object grows by a factor of sx in x-direction what if sx < 0? if sx = 0? Inverse of Scale if an object is scaled by a factor of s then the inverse scales by a factor of 1/s
Shear six basic shearing transformations

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