Physically-based Geometry Processing

This talk splits in two parts. In the first part, we will discuss a scheme for real-time nonlinear interpolation of a set of shapes. The scheme exploits the structure of the shape interpolation problem, in particular, the fact that the set of all possible interpolated shapes is a low-dimensional object in a high-dimensional shape space. The interpolated shapes are defined as the minimizers of a nonlinear objective functional on the shape space. Our approach is to construct a reduced optimization problem that approximates its unreduced counterpart and can be solved in milliseconds. In the second part, we will be broaden the perspective and consider the geometric structure of shape spaces. Then we will see how this structure can be used for the processing of motion and animation of non-rigid shapes. The idea is to treat animations and motions of deformable shapes as curves in shape space and to transfer concepts from curve processing in R^n to the processing of motion of non-rigid shapes. We will discuss explicit examples including a geometric flow for curves in shapes space that can be used for reducing jittering artifacts in motion capture data, the construction of Bezier curves in shape space and the efficient computation of geodesics in shape space.