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Spatial Separation of Molecular Conformers and Clusters
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Sampling Conditions for Conforming Voronoi Meshing by the VoroCrust Algorithm.

Ahmed Abdelkader1, Chandrajit L Bajaj2, Mohamed S Ebeida3

  • 1Dept. of Computer Science, University of Maryland, College Park.

Lipics : Leibniz International Proceedings in Informatics
|January 29, 2019
PubMed
Summary
This summary is machine-generated.

VoroCrust provides the first provably correct algorithm for decomposing volumes with smooth boundaries into Voronoi cells. This method generates unweighted Voronoi cells conforming to surfaces, offering guarantees on cell convexity and fatness.

Keywords:
Voronoipolyhedral meshingsampling conditionssurface reconstruction

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Area of Science:

  • Computational geometry
  • Computer graphics
  • Surface reconstruction

Background:

  • Decomposing volumes with smooth boundaries into Voronoi cells is a challenging problem.
  • Existing methods like clipping-based algorithms and the power crust algorithm have limitations.
  • A principled solution for generic smooth surfaces was previously elusive.

Purpose of the Study:

  • To develop the first provably correct algorithm for decomposing volumes with smooth boundaries into unweighted Voronoi cells.
  • To ensure Voronoi cells conform to the surface and possess convexity and fatness guarantees.
  • To offer a flexible alternative to existing methods for surface and volume meshing.

Main Methods:

  • Leveraging weighted α-shapes and the power crust algorithm.
  • Utilizing balls of a specific radius centered at sample points on the surface.
  • Identifying Voronoi sites from the corners of the union of these balls.
  • Constructing a watertight surface reconstruction from the cell interfaces.

Main Results:

  • VoroCrust successfully generates unweighted Voronoi cells that conform to smooth surfaces.
  • The algorithm provides guarantees on the convexity and fatness of the resulting Voronoi cells.
  • The method allows for further decomposition of the enclosed volume using internal sites.

Conclusions:

  • VoroCrust represents a significant advancement in surface and volume decomposition.
  • It offers a provably correct and flexible approach compared to prior methods.
  • The algorithm facilitates robust meshing of complex geometric domains.