Introduction to Geometric Methods in Computer Science

- Introduction to Polynomial curves and polar forms, I
- Introduction to Polynomial curves and polar forms, II
- Polynomial curves and Control Points
- Polynomial Surfaces (Introduction)
- Basics on Affine spaces, I
- Basics on Affine spaces, II
- Multiaffine maps, affine polynomial maps, and polar forms
- Bezier curves, the de Casteljau algorithm, subdivision methods
- Derivatives of Polynomial Curves. Conditions for C^k continuity
- Spline Curves (B-splines)
- Polynomial Surfaces, the de Casteljau algorithm
- Polynomial Surfaces, subdivision methods for triangular and rectangular patches
- Rectangular and Triangular polynomial spline surfaces
- Subdivision surfaces I, Doo-Sabin, Catmull-Clark, Loop
- Subdivision surfaces II, Analysis of Loop's scheme
- Mathematica programs to draw polynomial curves
- Mathematica programs to draw poly. and rational curves
- Control polys for poly. and rational curves
- Mathematica programs to draw poly. and rational surfaces
- Control polys for rational surfaces
- Mathematica Programs to compute control points
- Parametric curves and surfaces to be polarized
- Embedding an affine space into a vector space