ECS 178: Geometric Modeling

Summary of Course Content

1. Basic Theory of Curves and Surfaces
   1. Mathematical representation of shapes
   2. Parametric representation of curves and surfaces
   3. Evaluation of geometrical characteristics
2. Interpolation Methods
   1. Lagrange and Hermite interpolation
   2. Ferguson and Coons surface patches
3. Theory of Splines
   1. Spline functions
   2. Natural splines
   3. Generation of spline curves and surfaces
   4. Best approximation/error-minimizing approximation (e.g., least squares method)
4. Approximation Methods for Curves and Surfaces
   1. Bernstein-Bezier Approximation
   2. B-spline curves and surfaces
   3. Rational polynomial curves and surfaces
   4. NURBS (Non Uniform Rational B-splines)
5. Special Surface Schemes
   1. General surface schemes (e.g., triangular patches, multi-sided patches)
   2. Subdivision schemes (e.g., Doo-Sabin and Catmull-Clark schemes)
   3. Surface interrogation (e.g., normal and curvature behavior)
   4. Scattered data interpolation (e.g., object/function reconstruction)
6. Applications of Geometric Modeling
   1. Elements of computer-aided design systems (e.g., extruded, ruled, rotational surfaces; degree elevation/reduction; implicit vs. parametric representation)
   2. Methods for discretizing/meshing geometry (e.g., triangulation, quadrangulation)
   3. Computer graphics/animation applications (e.g., character modeling)
   4. Scientific data approximation and visualization applications (e.g., Voronoi diagrams; approximation methods for triangulations/tessellations)

Illustrative Reading
G. Farin, Curves and Surfaces for CAGD: A Practical Guide, 5th ed., Morgan Kaufman, 2002.

Potential Course Overlap
None