Topology Preserving Surface Extraction Using Star-shaped Subdivision

We address the problem of computing a topology preserving isosurface from a volumetric grid using Marching Cubes for geometry processing applications. We present a novel topology preserving subdivision algorithm to generate an adaptive grid. Our algorithm ensures that every grid cell satisfies two local geometric properties: a complex cell property and a star-shaped property. We show that these two properties are sufficient to ensure that the surface extracted from the grid using Marching Cubes has the same genus and connectedness as that of the exact isosurface. We use our subdivision algorithm for accurate boundary evaluation of CSG models, model simplification and remeshing. The running time of our algorithm varies between a few seconds for simple models composed of a few thousand triangles to tens of seconds for complex models represented using hundreds of thousands of triangles.