Localizing the Delaunay Triangulation and its Parallel Implementation
- Slides: 18
Localizing the Delaunay Triangulation and its Parallel Implementation Renjie Chen Craig Gotsman Technion – Israel Institute of Technology
• Introduction of Delaunay triangulation(DT) • Localize DT • Parallel DT • Experimental results & conclusion 2021/3/6 Outline 2
2021/3/6 Delaunay Triangulation 3
2021/3/6 Delaunay Triangulation - Voronoi Diagram 4
• Edge flip non-Delaunay triangulation • (Randomized) Incremental construction • Divide and conquer • Sweepline • Sweephull • Half-plane intersecting • … 2021/3/6 Delaunay Triangulation - Algorithms 5
• Empty circumcircle • Convex hull • Nearest neighbor • … 2021/3/6 Delaunay Triangulation - Properties 6
2021/3/6 Delaunay Triangulation Delaunay neighbor can be far away Can we localize it? 7
2021/3/6 Localize Delaunay Triangulation Please refer the paper for proof Given a containing polygon formed by points in the set 8
2021/3/6 Localize Delaunay Triangulation 9 Given an open polygon?
Half-plane intersecting for DT Convergence of the alg. ? The approximate Voronoi polygon always shrinks 2021/3/6 • Start from some initial (Delaunay) 1 -ring 10
2021/3/6 Parallel Delaunay Triangulation 11 Find the Delaunay 1 -ring for each point in parallel
Avoiding redundant computation 2021/3/6 • Each Delaunay triangle found 3 times • Each Delaunay edge found 4 times 12
2021/3/6 Periodic DT 13
2021/3/6 Periodic DT 14
2021/3/6 Results - Performance 15
• Local Delaunay triangulation • Localize DT • Parallel DT • Future work • GPU implementation • Optimization for non-uniform distribution • High dimensions • Manifold surfaces 2021/3/6 Conclusion 16
2021/3/6 Thank you for your attention! 17
2021/3/6 Recovering regular DT from Periodic DT 18
