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

2. CS175 2003 2 Overview blossoming algorithms for Bézier curves Bézier splines

3. CS175 2003 3 Blossoming replace univariate polynomial by multivariate function (blossom) symmetric multiaffine diagonal property each polynomial has a unique blossom

4. CS175 2003 4 Algorithms subdivision converges quadratically degree elevation proves variation diminishing property converges, too, but slowly degree reduction

5. CS175 2003 5 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

6. CS175 2003 6 Next Session B-spline basis functions B-spline algorithms uniform B-splines and subdivision interpolation approximation B-spline surfaces