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Mastering Bézier Splines: Algorithms and Applications

Dive into the world of Bézier splines, exploring blossoming algorithms, diagonal properties, and degree elevation while modeling complex shapes with Ck continuity and tangential conditions. Get ready for B-spline basis functions and uniform B-splines in the next session!

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Mastering Bézier Splines: Algorithms and Applications

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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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