Topology Preserving Isosurface Extraction for Geometry Processing

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 adaptive subdivision algorithm to generate a volumetric grid. Our algorithm ensures that every grid cell satisfies certain sampling criteria. We show that these sampling criteria are sufficient to ensure that the isosurface extracted from the grid using Marching Cubes is topologically equivalent to the exact isosurface: both the exact isosurface and the extracted isosurface have the same genus and connectivity. We use our algorithm for accurate boundary evaluation of Boolean combinations of polyhedra and low degree algebraic primitives, Minkowski sum computation, model simplification, and remeshing. The running time of our algorithm varies between a few seconds for simple models composed of a few thousand triangles and tens of seconds for complex polyhedral models represented using hundreds of thousands of triangles.