L p shape deformation

Lin Gao, Guo-Xin Zhang, Yu-Kun Lai

Abstract: Shape deformation is a fundamental tool in geometric modeling. Existing methods consider preserving local details by minimizing some energy functional measuring local distortions in the L 2 norm. This strategy distributes distortions quite uniformly to all the vertices and penalizes outliers. However, there is no unique answer for a natural deformation as it depends on the nature of the objects. Inspired by recent sparse signal reconstruction work with non L 2 norm, we introduce general L p norms to shape deformation; the positive parameter p provides the user with a flexible control over the distribution of unavoidable distortions. Compared with the traditional L 2 norm, using smaller p, distortions tend to be distributed to a sparse set of vertices, typically in feature regions, thus making most areas less distorted and structures better preserved. On the other hand, using larger p tends to distribute distortions more evenly across the whole model. This flexibility is often desirable as it mimics objects made up with different materials. By specifying varying p over the shape, more flexible control can be achieved. We demonstrate the effectiveness of the proposed algorithm with various examples.