CS 175

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