In this paper, we present a novel method to triangulate variational implicit surfaces. The core of the algorithm is an incremental Delaunay tetrahedralization of the constraint points defining the surface; it can be refined over time by adding new points around the surface as needed. Each tetrahedron that crosses the surface can then be triangulated to locally approximate the surface. This method allows getting several meshes of the same shape at different resolutions, which can be updated dynamically when adding new constraint points. This level-of-detail property makes variational surfaces more appealing for applications such as interactive modeling
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