Efficient Parallel Convex Hull Algorithms
IEEE Transactions on Computers
Algorithms for diametral pairs and convex hulls that are optimal, randomized, and incremental
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
An NC parallel 3D convex hull algorithm
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
A randomized parallel 3D convex hull algorithm for coarse grained multicomputers
Proceedings of the seventh annual ACM symposium on Parallel algorithms and architectures
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
Faster output-sensitive parallel algorithms for 3D convex hulls and vector maxima
Journal of Parallel and Distributed Computing
Star splaying: an algorithm for repairing delaunay triangulations and convex hulls
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Particle-based immiscible fluid-fluid collision
GI '06 Proceedings of Graphics Interface 2006
Computing two-dimensional Delaunay triangulation using graphics hardware
Proceedings of the 2008 symposium on Interactive 3D graphics and games
Convex hull covering of polygonal scenes for accurate collision detection in games
GI '08 Proceedings of graphics interface 2008
Evaluating Protein Similarity from Coarse Structures
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Parallel Banding Algorithm to compute exact distance transform with the GPU
Proceedings of the 2010 ACM SIGGRAPH symposium on Interactive 3D Graphics and Games
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
Recognition of 3d object using attributed relation graph of silhouette's extended convex hull
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
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
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A novel algorithm is presented to compute the convex hull of a point set in ℝ3 using the graphics processing unit (GPU). By exploiting the relationship between the Voronoi diagram and the convex hull, the algorithm derives the approximation of the convex hull from the former. The other extreme vertices of the convex hull are then found by using a two-round checking in the digital and the continuous space successively. The algorithm does not need explicit locking or any other concurrency control mechanism, thus it can maximize the parallelism available on the modern GPU. The implementation using the CUDA programming model on NVIDIA GPUs is exact and efficient. The experiments show that it is up to an order of magnitude faster than other sequential convex hull implementations running on the CPU for inputs of millions of points. The works demonstrate that the GPU can be used to solve nontrivial computational geometry problems with significant performance benefit.