Post on 14-Feb-2021
Delaunay Mesh Generation using the GPU http://geomGPU.net
Problem: Generate high-quality Delaunay mesh using the GPU. Input: Point set in ℝ2 or ℝ3 with [constraints] and [point weights].
2D Delaunay Triangulation [1]
A direct application of our framework with any flipping sequence efficiently leads to the 2D Delaunay triangulation.
3D Delaunay Triangulation [3]
(b) Adaptive star splaying locally fix these regions.
(a) After flipping, only a few regions contain locally non-Delaunay facets.
2D Regular Triangulation [2]
• Key techniques: o Identify redundant points through unflippable edges. o Combine flipping of regular and non-regular edges to remove
redundant points.
[1] Computing 2D constrained Delaunay triangulation using the GPU [TVCG ’12]
[2] Flip-Flop: Convex hull construction via star-shaped polyhedron in 3D [i3D ’13]
[3] A GPU accelerated algorithm for 3D Delaunay triangulation [i3D ’14]
References
• Constrained Delaunay triangulation in ℝ3.
• Delaunay refinement in ℝ2 and ℝ3.
• Local transformation in higher dimensions.
Ongoing work
Ashwin Nanjappa
Bioinformatics Institute, Singapore
Input
Points
[Constraints]
[Weights]
Constraint Enforcement
Refinement Output
Framework
Delaunay triangulator
2D flip
3D flip
Point Insertion Flipping
School of Computing, National University of Singapore
Thanh-Tung Cao, Mingcen Gao, Meng Qi, Tiow-Seng Tan
Contour map 3D Delaunay triangulation
TRIANGLE
CGAL
Ours
0
5
10
1
1.4
9
Speedup
2D Delaunay triangulation
TRIANGLE
Ours
0
10
20
30
1
28
Speedup
CGAL
Ours
0
10
20
30
40
1
35
Speedup
2D regular triangulation
CGAL
Ours
0
5
10
15
1
10.7
Speedup
3D Delaunay triangulation
Performance
2D constrained Delaunay triangulation
2D Constrained Delaunay triangulation
2D Constrained Delaunay Triangulation [1]
• Constraint enforcement is performed by repeating two steps: o Identify triangles intersected by constraints. o Flip edges to remove intersections.
• Key techniques:
(a) Flipping edges remove intersections
(b) One step look-ahead
• Key techniques:
Zhiyong Huang
Institute for Infocomm Research, A*STAR
http://geomgpu.net/