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, W.E., and Cline, H.E., 1987, Computer Graphics (Proceedings of SIGGRAPH ’87), 21(3), pp. 163–169] (in our experiments we use VTK Marching Cubes [Schroeder, W., Martin, K., and Lorensen, W., 1998, The Visualization Toolkit: An Object-Oriented Approach to 3-D Graphics, Prentice Hall]). 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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December 2002
Technical Papers
Dual-Primal Mesh Optimization for Polygonized Implicit Surfaces With Sharp Features
Yutaka Ohtake,
Yutaka Ohtake
Computer Graphics Group, Max-Planck-Institut fu¨r Informatik, 66123 Saarbru¨cken, Germany
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Alexander G. Belyaev
Alexander G. Belyaev
Computer Graphics Group, Max–Planck–Institut fu¨r Informatik, 66123 Saabru¨cken, Germany
University of Aizu, Aizu-Wakamatsu 965-8580, Japan
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Yutaka Ohtake
Computer Graphics Group, Max-Planck-Institut fu¨r Informatik, 66123 Saarbru¨cken, Germany
Alexander G. Belyaev
Computer Graphics Group, Max–Planck–Institut fu¨r Informatik, 66123 Saabru¨cken, Germany
University of Aizu, Aizu-Wakamatsu 965-8580, Japan
Contributed by the Engineering Simulation and Visualization Committee for publication in the Journal of Computing and Information Science in Engineering. Manuscript received September 2002; revised manuscript received January 2003. Associate Editors N. Patrikalakis and K. Lee.
J. Comput. Inf. Sci. Eng. Dec 2002, 2(4): 277-284 (8 pages)
Published Online: March 26, 2003
Article history
Received:
September 1, 2002
Revised:
January 1, 2003
Online:
March 26, 2003
Citation
Ohtake, Y., and Belyaev, A. G. (March 26, 2003). "Dual-Primal Mesh Optimization for Polygonized Implicit Surfaces With Sharp Features ." ASME. J. Comput. Inf. Sci. Eng. December 2002; 2(4): 277–284. https://doi.org/10.1115/1.1559153
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