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T Schiffer1, F Aurenhammer, M Demuth

  • 1Institute of Computer Graphics and Knowledge Visualization, University of Technology, Graz, Austria.

Discrete Applied Mathematics (Amsterdam, Netherlands : 1988)
|March 6, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces a new computational geometry method using projected Delaunay tetrahedra and maximum independent sets to find large convex quadrangulations. The approach offers improvements over existing triangulation-based pairing methods.

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Area of Science:

  • Computational Geometry
  • Discrete Mathematics
  • Computer Science

Background:

  • Convex quadrangulations are fundamental in computational geometry.
  • Existing methods, like pairing based on triangulations, have limitations in finding large subsets.

Purpose of the Study:

  • To develop an improved algorithm for computing large subsets of convex quadrangulations.
  • To offer a more efficient alternative to current triangulation-based methods.

Main Methods:

  • Utilizing projected Delaunay tetrahedra.
  • Applying a maximum independent set algorithm.
  • Computing convex quadrangulations from point sets.

Main Results:

  • Successfully computed large subsets of convex quadrangulations.

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  • Demonstrated improvement over the pairing method.
  • The new method shows enhanced performance in identifying maximal convex quadrangulations.

    • Conclusions:

    • The projected Delaunay tetrahedra and maximum independent set approach is effective for computing convex quadrangulations.
    • This method provides a significant advancement over traditional triangulation-based techniques.