lecture8_correction

lecture8_correction - Note the Bezier blending functions...

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Bézier Basis Matrix We can derive the Bézier basis matrix, M B , by pre-multiplying the Hermite basic M matrix by the Bézier-Hermite conversion matrix shown on the previous slide p p 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 p p 3 3 0 0 0 0 3 3 1 1 2 2 1 2 3 3 ] 1 [ ) ( 4 3 2 3 2 t t t t Q p 0 0 3 3 0 0 0 1 1 p p p 1 3 3 1 0 3 6 3 ] 1 [ ) ( 4 3 2 3 2 t t t t Q Brown 32 Bezier Basis Matrix, call it M B Correction to original post
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Bézier Examples Brown 33 http://www.sunsite.ubc.ca/LivingMathematics/V001N01/UBCExamples/Bezier/bezier.html http://www.sunshine2k.de/stuff/Java/Curves/Curves.html
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Bézier Blending Functions Just like Hermite curves, we can think of this as blending functions.
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Unformatted text preview: Note the Bezier blending functions don’t change, only the user supplied control points p1, p2, p3, p4.         p 1 1                      p p p 1 3 3 1 3 6 3 3 3 ] 1 [ ) ( 4 3 2 3 2 t t t t Q 3 2 3 3 1 t t t B     Correction to original post 3 2 3 3 2 2 1 3 3 3 6 3 t t B t t t B      Brown 34 3 4 t B  There are also known as the Bernstein polynomial...
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lecture8_correction - Note the Bezier blending functions...

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