Proceedings ArticleDOI
Dual/Primal mesh optimization for polygonized implicit surfaces
Yutaka Ohtake,Alexander Belyaev +1 more
- pp 171-178
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TLDR
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.read more
Citations
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Proceedings ArticleDOI
Multi-level partition of unity implicits
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Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids
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Noise removal using smoothed normals and surface fitting
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A Multi-scale Approach to 3D Scattered Data Interpolation with Compactly Supported Basis Functions
TL;DR: The numerical experiments suggest that the approach integrates the best aspects of scattered data fitting with locally and globally supported basis functions and is essentially faster than the state-of-the-art scattered data approximation with globally supported RBFs and much simpler to implement.
Proceedings ArticleDOI
A multi-scale approach to 3D scattered data interpolation with compactly supported basis functions
TL;DR: In this article, a hierarchical approach to 3D scattered data interpolation with compactly supported basis functions is proposed, which integrates the best aspects of scattered data fitting with locally and globally supported RBFs.
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The Visualization Toolkit: An Object-Oriented Approach to 3-D Graphics
William Schroeder,Bill Lorenson +1 more
TL;DR: The book/CD package offers readers the opportunity to practice visualization using a complete C++ programming environment developed by the authors.
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Estimation of planar curves, surfaces, and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation
TL;DR: It is shown how this unified representation can be used for object recognition, object position estimation, and segmentation of objects into meaningful subobjects, that is, the detection of 'interest regions' that are more complex than high curvature regions and, hence, more useful as features for object Recognition.
Proceedings ArticleDOI
Dual contouring of hermite data
TL;DR: This paper describes a new method for contouring a signed grid whose edges are tagged by Hermite data (i.e; exact intersection points and normals) and develops an octree-based method for simplifying contours produced by this method.