Post optimiza tion of delaunay tetrahedrization
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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

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


Content
Content

  • tetrahedrization

  • incremental algorithm

    + local transformations

  • measuring of the mesh quality

  • post-optimization

  • results


Delaunay tetrahedrization
Delaunay tetrahedrization

  • tetrahedrization

    • decomposition of convex hull

    • tetrahedra are not overlapping

  • Delaunay criterion

    • empty circumsphere


Algorithm 1

dividing of tetrahedron

DAG structure

Algorithm (1)


Algorithm 2
Algorithm (2)

  • configurations of 5 points

  • local transformations


Algorithm 3
Algorithm (3)

create boundary tetrahedron

while (input set is not empty)

insert new point

find and divide tetrahedron

do local optimization

remove boundary tetrahedron


Properties quality
Properties – quality

  • relative volume

  • radius ratio

  • edge ratio

  • aspect ratio

  • solid angle

  • minimum / maximum solid angle


Post optimization
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


Criteria of post optimization
Criteria of post-optimization

  • geometrical

    • simple

    • compound

  • max / min number of tetrahedra







Conclusion
Conclusion

  • degradation

    • MaxThNo, MinMaxSA, MaxVol

  • improvement

    • MinThNo, MaxMinSA, MaxMinVol, MaxMinRR

  • improvement up to 10%


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