Mesh Deformation Based on Preserving Distances and Angles

A novel method for the interactive detail preserving deformation of 3D meshes is proposed in this paper. It is based on preserving the distances between each vertex and its adjacent vertices and the angles between edges formed by each vertex and its adjacent vertices. The distances and the angles are invariant over the rigid transformations. If preserving the distances and the angles it can preserve the local details and volumetric details of the mesh, which is important requirement of mesh deformation. The mesh is deformed by specifying constraints of vertices positions. These constraints are incorporated in the distances and the angles reconstruction equations, and their solution produces a deformed surface geometry that preserves the local detail in the least-squares sense. We demonstrate the effectiveness of our method with several detail-preserving deformation operators.