CS284b: Seminar in Computer Science

Topics in Geometric Modeling

Instructors: Profs. Arvo and Schröder

Location: Tu 3:30-5:00, Fr 12:30-2:00, room 121, Beckmann Institute

Online Resources

Description

This course will explore a number of topics that relate to the construction and representation of geometric models on a computer, with the emphasis on three-dimensional surfaces. Rather than attempting to survey the field of geometric modeling, the purpose of the course is to allow students to explore several aspects in depth through programming and reading recently published articles.

The course will begin with a number of lectures aimed at covering the basics of techniques based on approximating and interpolating polynomials. Once the basics are covered we'll move into state of the art algorithms addressing various problems such as

reconstruction of surfaces from unorganized points;
mesh decimation;
smooth interpolation and approximation for arbitrary topologies;
hierarchical, or multi-level, decompositions of geometry;
interactive techniques for surface design;
meshing for finite element methods.

What we'll actually get to during the quarter will be determined by the interests of the participants.

A possible list of basic topics to be covered includes

Spline Curves: Bezier form, B-Spline form, blossoming, polar forms, construction, evaluation, differentiation, knot insertion, subdivision, degree lifting;
Spline Surfaces: Cross product domains, triangular patches, Bezier form, B-Spline form;
Subdivision Surfaces based on Splines: Catmull-Clark, Doo-Sabin, Loop, Reif, Peters;
Interpolating Subdivision Curves: Deslauriers-Dubuc, Donoho, Herley;
Interpolating Subdivsion Surfaces: Dyn.

Requirements

There will be small programming assignments in the beginning of the course to study some of the basic techniques. In the latter part of the course Students will be required to summarize and present one recent research paper related to geometric modeling, and to devise and complete a programming project that builds upon any of the techniques covered in class.

Recommended Background

Mathematics: multi-variable calculus, real analysis, linear algebra.
Computer Science: solid programming ability in at least one language (Java, C++, C, Matlab, Maple, Fortran, Mathematica). Based on the chosen project some familiarity with advanced data structures, 3D computer graphics algorithms, and interactive techniques may be desirable.