CS 631 - Computer-Aided Geometric Design

Bulletin Description

Overview of current concepts and issues in CAGD with emphasis on free-form surface design; mathematics of free-form curve and surface representations, including Coons patches, Gregory patches, Bezier method, B-splines, NURBS, triangular interpolants, and their geometric consequences; creating objects with smooth surfaces, covering assembling spline patches, geometric and parametric continuity, texture mapping onto complex shapes, subdivision surfaces, surface evolution, and global optimization.


CS 535 and CS 321, or consent of the instructor.

Expected Preparation

The students should be capable of programming in C++ or Java, and have a general understanding of 3D graphics, data structures, and numerical computing.

Student Learning Outcomes

1. An understanding of the main ideas in CAGD.

2. A geometric insight into curve and surface schemes.

3. The capability of designing large and numerically stable programs for applications in CAD/CAM.

4. The capability to handle more advanced topics such as intersection, rendering, offset and constrained surface design problems.

Syllabus Information

1. Techniques for the Representation of Smooth Curves and Surfaces:
· Bezier curves and surfaces· Coons patches· Gregory patches· B-splines· Triangular interpolants· NURBS· Subdivision surfaces· Geometric continuity, G1, G2· Parametric continuity, C1, C2

2. Creating Objects with Smooth Surface:

· Blending techniques· Rectilinear axis design· Natural axis design· Interpolation and Interproximation techniques· Fairing techniques· Feature Generation· Constrained shape adjustment· Mesh Generation· Shape Sculpting· Surface evolution· Texture mapping onto complex shapes· Global optimization

A student's grade will be determined by a weighted average of homework assignments, programming exercises, projects, midterm examinations, and the final examination. The faculty offering the course will make the details available at the start of the course. A typical weighting is:Homework and programs: 40%
Midterm Examinations (2 @ 15%): 30%
Final Examination: 30%
Possible Textbooks:
Interactive Curves and Surfaces, (with Multimedia Tutorial on CAGD),
A.Rockwood and P. Chambers,
Morgan Kaufman Publishers, Inc.NURB Curves and Surfaces,
Gerald Farin, A K Peters, Wellesley, MA.An Introduction to Splines for Use in Computer Graphics & Geometric Modeling,
R.H. Bartels, J.C. Beatty, and B.A. Barsky, Morgan Kaufman Publishers, Inc.