An asymptotic decider for robust and topologically correct triangulation of isosurfaces: topologically correct isosurfaces

A set of rules to generate a topologically correct and robust triangulation of isosurfaces across cells borders is presented. Ambiguous cases at cell faces are resolved with the asymptotic decider. The intersection of the isosurface with a face is a hyperbola. If the isovalue equals the asymptotic decider, the hyperbola at the face degenerates into two straight lines intersecting at the hyperbola's center. The center of the hyperbola is in this case a saddle point of the surface. A modified asymptotic decider is proposed to correctly handles this singular case. The method presented solves consistency problems of previously presented algorithms and resolves ambiguous cases efficiently without lookup tables.

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