# Dual/Primal mesh optimization for polygonized implicit surfaces

TL;DR: A new method for improving polygonizations of implicit surfaces with sharp features is proposed, which outperforms approaches based on the mesh evolution paradigm in speed and accuracy.

Abstract: 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 Lorensen(in our experiments we use VTK marching cubes 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.

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##### Citations

766 citations

### Cites methods from "Dual/Primal mesh optimization for p..."

...We find it attractive to combine a low resolution Bloomenthal polygonization with a postprocessing mesh optimization technique developed in [Ohtake and Belyaev 2002], as shown in the top middle, top right, and bottom middle images of Figure 7....

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...An alternative is to use adaptive polygonization strategies such as those in [Kobbelt et al. 2001; Ohtake and Belyaev 2002; Ju et al. 2002]....

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726 citations

### Cites background from "Dual/Primal mesh optimization for p..."

...new concepts [12,50] useful to mesh implicit surfaces....

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209 citations

### Cites methods from "Dual/Primal mesh optimization for p..."

...As a postprocessing step we can also employ a method proposed in [28] in order to improve the mesh quality....

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208 citations

199 citations

##### References

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### "Dual/Primal mesh optimization for p..." refers methods in this paper

...Similar to [10] we use the singular value decomposition [17] to find a minimum-norm least squares solution to (1)....

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3,347 citations