CS175 2003 1 CS 175 – Week 9 B-Splines Blossoming, Bézier Splines.

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Presentation transcript:

CS CS 175 – Week 9 B-Splines Blossoming, Bézier Splines

CS Overview blossoming algorithms for Bézier curves Bézier splines

CS Blossoming replace univariate polynomial by multivariate function (blossom) symmetric multiaffine diagonal property each polynomial has a unique blossom

CS Algorithms subdivision converges quadratically degree elevation proves variation diminishing property converges, too, but slowly degree reduction

CS Bézier Splines modelling complex shapes Bézier curve of high degree piecewise low degree curves C k continuity between Bézier curves tangential condition A-frame condition Catmull-Rom splines

CS Next Session B-spline basis functions B-spline algorithms uniform B-splines and subdivision interpolation approximation B-spline surfaces