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Post-optimiza tion of Delaunay tetrahedrization

Post-optimiza tion of Delaunay tetrahedrization. Pavel Maur, Ivana Kolingerová Department of Computer Science and Engineering University of West Bohemia Czech Republic Supported by the Ministry of Education of Czech Republic project MSM 235200005. Content. tetrahedrization

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Post-optimiza tion of Delaunay tetrahedrization

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  1. Post-optimizationof Delaunay tetrahedrization Pavel Maur, Ivana Kolingerová Department of Computer Science and Engineering University of West Bohemia Czech Republic Supported by the Ministry of Education of Czech Republic project MSM 235200005

  2. Content • tetrahedrization • incremental algorithm + local transformations • measuring of the mesh quality • post-optimization • results

  3. Delaunay tetrahedrization • tetrahedrization • decomposition of convex hull • tetrahedra are not overlapping • Delaunay criterion • empty circumsphere

  4. dividing of tetrahedron DAG structure Algorithm (1)

  5. Algorithm (2) • configurations of 5 points • local transformations

  6. Algorithm (3) create boundary tetrahedron while (input set is not empty) insert new point find and divide tetrahedron do local optimization remove boundary tetrahedron

  7. Properties – quality • relative volume • radius ratio • edge ratio • aspect ratio • solid angle • minimum / maximum solid angle

  8. Post-optimization • use of flips again put all non convex hull triangles into the queue while (queue is not empty) do flips according to the selected criterion • criteria of post-optimization

  9. Criteria of post-optimization • geometrical • simple • compound • max / min number of tetrahedra

  10. Results

  11. relative volume

  12. radius ratio

  13. minimum solid angle

  14. maximum solid angle

  15. Conclusion • degradation • MaxThNo, MinMaxSA, MaxVol • improvement • MinThNo, MaxMinSA, MaxMinVol, MaxMinRR • improvement up to 10%

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