Postoptimization of Delaunay tetrahedrization

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
Algorithm (1)

• dividing of tetrahedron

• DAG structure

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