Piecewise Linear Approximation of Isovalued Surfaces
Continuation methods provide a frame for the efficient approximation of isovalued surfaces in 3D space. We discuss two related algorithms in this field. The first one is based on subdividing space into cubes, while the second one uses a triangulation approach. For the latter, an efficient implementation is presented. The algorithms determine all cubes (or simplices) intersecting the surface and then generate an oriented polygonal approximation. Comparison shows that the cube approach takes less time and memory. The resulting surfaces have different properties concerning symmetry and connectedness. For demonstration and comparison we use several fractal and smooth surfaces. These surfaces are implicitly defined by a function, however it is also possible to apply both methods to 3D volume data.
KeywordsManifold Rubber Hull
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