L_p shape deformation

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.