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An Accurate Implicit Field Representation for Meshes and Its Adapted Triangulation Algorithms

The classic implicit scalar field distance transform representation of a mesh is very useful to perform many mesh processing operations and to obtain better results than with other methods. In this paper we propose a new and more accurate implicit vector field distance transform representation of a mesh. We adapt Marching Cube and Marching Triangle, the two most widely used triangulation algorithms, to our new vector field representation to correctly reconstruct the final mesh after data processing in the implicit domain. According to a reliable surface error metric, we show our new vector field is more accurate than the classic scalar field to implicitly represent a mesh. We adapt to our vector field a previously introduced mesh denoising algorithm performed on the scalar field. Results show mesh denoising with our vector field outperforms the one with classic scalar field in terms of an error metric comparison.