# 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.