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

CS 175 – Week 9 B-Splines Blossoming, Bézier Splines. Overview. blossoming algorithms for Bézier curves Bézier splines. Blossoming. replace univariate polynomial by multivariate function (blossom) symmetric multiaffine diagonal property each polynomial has a unique blossom. Algorithms.

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

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  1. CS 175 – Week 9B-SplinesBlossoming, Bézier Splines

  2. Overview • blossoming • algorithms for Bézier curves • Bézier splines

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

  4. Algorithms • subdivision • converges quadratically • degree elevation • proves variation diminishing property • converges, too, but slowly • degree reduction

  5. Bézier Splines • modelling complex shapes • Bézier curve of high degree • piecewise low degree curves • Ck continuity between Bézier curves • tangential condition • A-frame condition • Catmull-Rom splines

  6. Next Session • B-spline basis functions • B-spline algorithms • uniform B-splines and subdivision • interpolation • approximation • B-spline surfaces

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