CIS 510/CSE410, Fall 2002

Curves and Surfaces: Theory and Applications

Formerly called

Introduction to Geometric Methods in Computer Science

Some Slides

• 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