Approximation and Modeling with B-Splines

Klaus Höllig and Jörg Hörner

Programs and Demos

Polynomials
- Programs:
  - BERNSTEIN: Bernstein polynomials
  - HERMITE: evaluation of a Hermite Spline
- Demos:
  
  Weierstrass Approximation Hermite Interpolation

Bézier Curves

Programs:

Demos:


Bezier Curve	Geometric Hermite Interpolation	Algorithm of de Casteljau

Rational Bézier Curves
- Programs:
  - RATIONAL_BEZIER_CURVE: evaluation of a rational Bezier curve
  - RATIONAL_BEZIER2MAT: Matrix representation of a conic section
- Demos:
  
  Rational Bezier Curve Conic Section
B-Splines
- Programs:
- Demos:
  
  B-Spline Spline
Approximation
- Programs:
- Demos:
  
  Standard Projector Smoothing Spline
Spline Curves
- Programs:
- Demos:
  
  Spline Curve Uniform Subdivision
Multivariate Splines
- Programs:
  - BSPLINE_MULTIVARIATE: evaluation of a multivariate B-spline
  - SPLINE_EVALUATION_BIVARIATE evaluation of a bivariate spline function
- Demos:
  
  Bivariate B-Spline Bivariate Spline
Surfaces and Solids
- Programs:
- Demos:
  
  Bezier Patch Catmull-Clark Subdivision
Finite Elements
- A program package with demos is available as Supplementary Material of the book Finite Element Methods with B-Splines (SIAM FR26)