[talks] Talk by Yaron Lipman today at noon

[Tom Funkhouser]

Yaron Lipman from Tel Aviv University will give a talk
today at noon in CS 401.

Title:

Geometric Deformations.


Abstract:

Deforming objects in a "shape preserving" manner is a challenging
problem with various applications in geometric modeling and computer
graphics. In this talk I will examine two geometric-driven approaches
to the problem.

First, reformulating the problem using the notion of Cartan's moving
frames reveals an intriguing relationship between harmonic maps into
the group of rotations and shape preserving deformations. The moving
frames are known in differential geometry for their ability to
simplify some surface theory argumentation. Their employment leads to
rather simple algorithms for shape deformation and shape blending of
discrete surfaces (meshes). I will present the moving frames as
rigid-motion invariant surface representation which is suited for
deformations and shape blending. Then I will discuss the optimal
rotation field between two isometric surfaces and its use in the
context of surface deformation.

Second, I will present a recent result demonstrating a closed-form
solution to shape preserving space deformations. The new scheme
guarantees a pure conformal mapping in 2D and quasi-conformal mappings
in 3D. This generalizes recent interesting affine-invariant free form
deformation techniques and provides an extremely fast algorithm for
shape preserving deformations.



Short Bio:

Yaron Lipman is a PhD candidate at Tel-Aviv University. He received
the BSc degree in mathematics and computer science from Tel Aviv
University in 2003. His research interests are in applied geometry,
approximations and computer graphics.