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Conference Paper

Dual/Primal Mesh Optimization for Polygonized Implicit Surfaces


Ohtake,  Yutaka
Computer Graphics, MPI for Informatics, Max Planck Society;

Belyaev,  Alexander
Computer Graphics, MPI for Informatics, Max Planck Society;

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Ohtake, Y., & Belyaev, A. (2002). Dual/Primal Mesh Optimization for Polygonized Implicit Surfaces. In Seventh ACM Symposium on Solid Modeling and Applications (SM-02) (pp. 171-178). New York, USA: ACM.

Cite as:
A new method for improving polygonizations of implicit surfaces with sharp features is proposed. The method is based on the observation that, given an implicit surface with sharp features, a triangle mesh whose triangles are tangent to the implicit surface at certain inner triangle points gives a better approximation of the implicit surface than the standard marching cubes mesh \cite{Lorensen} (in our experiments we use VTK marching cubes \cite{VTK}). First, given an initial triangle mesh, its dual mesh composed of the triangle centroids is considered. Then the dual mesh is modified such that its vertices are placed on the implicit surface and the mesh dual to the modified dual mesh is considered. Finally the vertex positions of that ``double dual'' mesh are optimized by minimizing a quadratic energy measuring a deviation of the mesh normals from the implicit surface normals computed at the vertices of the modified dual mesh. In order to achieve an accurate approximation of fine surface features, these basic steps are combined with adaptive mesh subdivision and curvature-weighted vertex resampling. The proposed method outperforms approaches based on the mesh evolution paradigm in speed and accuracy.