CS 631 - Computer-Aided Geometric Design

 

Credits: 3

 

Course 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.

 

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

 

Needed Skills

 

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

 

Learning Objectices

 

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.

 

Topics

 

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

Grading

 

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.