lecture15 - CSE472 Computer Graphics Curves II Blending...

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1 CSE472 Computer Graphics Curves II Blending Functions Bernstein Polynomials Bézier Surface Patches

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2 CSE472 Computer Graphics A Bézier Curve p 0 p 1 p 3 p 2
3 CSE472 Computer Graphics Bézier Curve Geometry Matrix The matrix we computed for the Bézier Curve is called a Geometry Matrix = - - - - 3 2 1 0 3 2 1 0 1 3 3 1 0 3 6 3 0 0 3 3 0 0 0 1 c c c c p p p p - - - - = 1 3 3 1 0 3 6 3 0 0 3 3 0 0 0 1 B M

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4 CSE472 Computer Graphics How a Geometry Matrix is used - - - - = 3 2 1 0 3 2 1 0 1 3 3 1 0 3 6 3 0 0 3 3 0 0 0 1 p p p p c c c c - - - - = 1 3 3 1 0 3 6 3 0 0 3 3 0 0 0 1 B M p M c B = or… [ ] = 3 2 1 0 3 2 1 ) ( c c c c u u u u p c u u p T = ) ( p M u u p B T = ) (
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This note was uploaded on 07/25/2008 for the course CSE 472 taught by Professor Owen during the Spring '08 term at Michigan State University.

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lecture15 - CSE472 Computer Graphics Curves II Blending...

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