Remeshing triangulations based on constructing and resampling geometry images

In this paper, we present a general and robust algorithm to remesh triangular meshes with genus-0 topology based on their geometric properties. Our algorithm first parameterizes an given original mesh onto planar area, and creates several geometry images for it according to its intrinsic geometric properties, e.g. per-vertex density, per-face normal or texture, etc. Then the algorithm replaces the geometric properties in parameter space by the grey-level images. The images can be further dealt with by techniques of digital image process to build a controllable image in interactive way, this provides user a tool to edit the grey-level images in order to obtain desired number of vertices. Finally, a binary-value image constructed by half-toning technique would be connected to form planar Delaunay triangulation, and at the same time, a Laplacian smoothing process is performed to optimize the output meshes.