Computer-Aided Geometric Design

Computer-Aided Geometric Design
Mathematical theory of free-form curves and surfaces and solid geometric modeling. Bezier and B-spline curve and surface theory, parametric and implicit forms, intersection algorithms, topics in computer algebra, and free-form deformation. Several programming projects.
CE EN
572
 Hours 3.0 Credit, 3.0 Lecture, 0.0 Lab Prerequisites Proficiency in C programming. Taught Programs Containing CE EN 572
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.

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.

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.

B-Spline Curves

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

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.

Tensor Product Surfaces

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