Geometric Modeling For Computer Graphics
Wed 5:00 pm-7:00 pm
719 Broadway, room 1221
Denis Zorin, office hours:
Tue 11-12pm and by appointment
Description
This course will survey a number of topics in geometric modeling, concentrating
on computer representations of surfaces used in computer graphics applications.
The following topics will be covered: Spline curves and surfaces, subdivision,
multiresolution representations, polygonal representations, mesh simplification,
overview of representation of solids and image-based techniques.
Prerequisites
Mathematics: linear algebra, multivariate calculus.
Computer Science: solid programming ability in at least one
language (Java, C++, C). An introductory graduate class in computer graphics
is recommended.
Requirements
There will be several written assignments and a course project. The grade
will be primarily based on the course project. There is a list of suggested
projects; however, students may choose their own project. In either case,
the intended project should be discussed with the instructor.
Deadlines
October 7 A detailed description of the proposed project.
November 11 Progress report.
Finals week Projects due.
Outline
Spline curves and surfaces. Bezier form, B-spline form, blossoming,
knot insertion. NURBS. Tensor product and triangular patches. Applications
of splines in computer graphics.
Subdivision curves and surfaces. Subdivision as generalization
of splines. Convergence. Subdivision matrices. Catmull-Clark, Doo-Sabin,
Butterfly subdivision schemes. Smoothness criteria. Modeling surface features
using subdivision. Implementation issues.
Multiresolution representations of surfaces. Wavelet representation.
Pyramid representation.
Polygonal representations. Mesh simplification algorithms: Schroeder,
Rossigniac, Garland. Hoppe's progressive mesh representation and variations.
Taubin's mesh smoothing. Mesh compression. Connectivity and geometry compression.
Overview of other representations. Constructive solid geometry.
Volume representations. BSP trees. Image-based rendering and combining
geometry and image-based representations.
Denis Zorin
