Teaching

Advanced Computer Graphics (Fall 2006)

Advanced topics in computer graphics, vision and medical imaging will be introduced. It covers major theorems in algebraic topology, differential geometry and Riemann surface theory. Computational algorithms will be taught for computing homology, cohomology, harmonic maps, conformal structure, Ricci flow, uniformization metrics. The methods for computing affine structure, real projective structure and hyperbolic structure will be covered.

Students will apply these algorithms for various applications, such as parameterization, geometry images, real time raytracing, conformal brain mapping and colon flattening.

Computational Structures in Computer Graphics (Spring 2006)

Computer Graphics is the introductory graphics course. Students will learn to program interactive graphics environments, basic illumination and modeling of curved geometry (camera, light and actors). Currently, OpenGL (with extensions) and C, C++ form the learning environment. Central concepts are composition, such as matrix multiplication or parametrization, and convolution.

Advanced Computer Graphics (Fall 2005)

Students will learn advanced topics in computer graphics and geometric modeling. The major goal is to computer various geometric structures on surfaces, including Euclidean structure, Real projective structure, hyperbolic structure, spherical structure etc. The geometric algorithms for computing fundametal domain, unversial cover, homology and cohomology, holomorphic 1-forms, uniformization metrics, surface Ricci flow will be explained in details. The applications in graphics, geometric modeling and medical imaging will be covered as well.

Seminar

Shape Space (2006 Fall)

We study the theorems and algorithms related to shape anylasis, surface registration, recogonition and calssification. Especially large scale geometric database indexing and shape retrieval.

Computational Ricci Flow (2006 Spring)

We discuss the theory and implementations of Ricci flow, including surface Ricci flow, circle packing metric, combinatorial Ricci flow, Euclidean and hyperbolic surface parameterizations based on Ricci flow.

The current version of the lecture notes can be accessed by emailing to gu AT cs DOT sunysb DOT edu.

Computational Conformal Geometry (2005 Fall)

This seminar focuses on the computational aspects of Riemann surface theory. The topics on algebraic topology, differential geometry, Riemannian geometry, algebraic curves will be discussed as well.

For this term, the major focus is characteristic class of vector bundles and the goal is to construct manifold splines.

The current version of the lecture notes can be accessed by emailing to gu AT cs DOT sunysb DOT edu.