CS-631  Computer-Aided Geometric Design (new course)

Proposed by Fuhua (Frank) Cheng

Credits: 3


Course Description:

Introduction to 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.

Prerequisites:  CS-535, CS321

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 Outcomes:

The students will have a understanding of the main ideas in CAGD,
with a geometric insight into curve and surface schemes, and the
capability of designing large and numerically stable programs for
applications in CAD/CAM. The knowledge they learn in this course will
prepare them to handle more advanced topics such as intersection,
rendering, offset and constrained surface design problems.



Course Content:

*  Techniques for the representation of smooth curves and surfaces:

   Bezier curves and surfaces; 
   Coons patches;
   Gregory patches; 
   B-splines; 
   Triangular interpolants;
   (Quadrics and cyclids;)
   NURBS;
   Subdivision surfaces;
   Geometric continuity, G1, G2;
   Parametric continuity, C1, C2;

*  Creating Objects with Smooth Surfaces

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


Textbooks: 

1. Interactive Curves and Surfaces," (with Multimedia Tutorial on CAGD),
   A. Rockwood and P. Chambers, Morgan Kaufman Publishers, Inc.

2. NURB Curves and Surfaces," Gerald Farin, A K Peters, Wellesley, MA.

3. 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.