Computer-Aided Geometric Design

Computer-Aided Geometric Design
Free-form curves and surfaces; mathematical theory and algorithms. Bezier and B-spline curves and surfaces, subdivision surfaces, T-splines, free-form deformation, and intersection algorithms. Several programming projects.
 Hours3.0 Credit, 3.0 Lecture, 0.0 Lab
 PrerequisitesC S 240, Math 343; or equivalents.
 ProgramsContaining C S 557
Course Outcomes

Bezier Curves

Understand the theory, properties, and algorithms for Bezier curves: de Casteljau algorithm, degree elevation, hodographs, curve intersection algorithms, convex hull property, variationa diminishing property, rational Bezier curves, explicit Bezier curves.

B-Spline Curves

Understand polar form, the de Boor algorithm, the Boehm algorithm, knot intervals.

Tensor product surfaces

Understand tensor product Bezier and B-Spline surfaces, including the de Casteljau algorithm, partial derivatives, parametric continuity, tesselation.