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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 \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.
