Transcription of Affine Transformations
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Affine Transformations
University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don FussellAffine TransformationsUniversity of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 2 LogisticsRequired reading:Watt, Section reading:Foley, et al, Chapter F. Rogers and J. Alan Adams, MathematicalElements for Computer Graphics, 2nd Ed., McGraw-Hill, New York, 1990, Chapter :HW #1 handed out MondayProject #1 due on Monday, artifact on of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 3 Geometric transformationsGeometric Transformations will map points in onespace to points in another: (x',y',z') = f(x,y,z).These Transformations can be very simple, such asscaling each coordinate, or complex, such as non-linear twists and 'll focus on Transformations that can berepresented easily with matrix 'll start in of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 4 RepresentationWe can represent a point, p = (x,y), in the planeas a column vectoras a row vector!
The unit square observations also tell us the 2x2 matrix transformation implies that we are representing a point in a new coordinate system: where u =[ a c ] T and v =[ b d ] T are vectors that define a new basis for a
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