The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Star splaying: an algorithm for repairing delaunay triangulations and convex hulls
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Fast Two Dimensional Convex Hull on the GPU
WAINA '11 Proceedings of the 2011 IEEE Workshops of International Conference on Advanced Information Networking and Applications
Flipping to robustly delete a vertex in a delaunay tetrahedralization
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
Computing 2D constrained Delaunay triangulation using the GPU
I3D '12 Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games
Applications of Geometry Processing: CudaHull: Fast parallel 3D convex hull on the GPU
Computers and Graphics
SMI 2012: Full GPU accelerated convex hull computation
Computers and Graphics
Computational Geometry: Theory and Applications
A GPU accelerated algorithm for 3D Delaunay triangulation
Proceedings of the 18th meeting of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games
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Flipping is a local and efficient operation to construct the convex hull in an incremental fashion. However, it is known that the traditional flip algorithm is not able to compute the convex hull when applied to a polyhedron in R3. Our novel Flip-Flop algorithm is a variant of the flip algorithm. It overcomes the deficiency of the traditional one to always compute the convex hull of a given star-shaped polyhedron with provable correctness. Applying this to construct convex hull of a point set in R3, we develop ffHull, a flip algorithm that allows nonrestrictive insertion of many vertices before any flipping of edges. This is unlike the well-known incremental fashion of strictly alternating between inserting a single vertex and flipping. The new approach is not only simpler and more efficient for CPU implementation but also maps well to the massively parallel nature of the modern GPU. As shown in our experiments, ffHull running on the CPU is as fast as the best-known convex hull implementation, qHull. As for the GPU, ffHull also outperforms all known prior work. From this, we further obtain the first known solution to computing the 2D regular triangulation on the GPU.