From Real-Time Shape Deformation to Geometric Flows in Shape Space
11:30 - 12:00
The optimization of deformable, flexible or non-rigid shapes is essential for many tasks in geometric modeling and processing. In the first part of this talk, I will introduce model reduction techniques that can be used to construct fast approximation algorithms for shape optimization problems. The goal is to obtain run times that are independent of the resolution of the discrete shapes to be optimized. As an example, we will discuss a method for real-time elasticity-based shape interpolation.
In the second part, we will broaden the perspective and discuss how concepts from elasticity can be used to obtain geometric structures on shape spaces, in which a shape is a single point. We will see how these structures can be used for the processing of motion and animations of non-rigid shapes. The idea is to treat the motions as curves in shape space and to transfer concepts from curve processing in Euclidean space to the processing of motion of non-rigid shapes. We will discuss explicit examples including a geometric flow of curves in shapes space that can be used for reducing jittering artifacts in motion capture data, the construction of subdivision curves in shape space and the efficient computation of geodesics in shape space.