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
Interactive 3D distance field computation using linear factorization
I3D '06 Proceedings of the 2006 symposium on Interactive 3D graphics and games
Parallel Banding Algorithm to compute exact distance transform with the GPU
Proceedings of the 2010 ACM SIGGRAPH symposium on Interactive 3D Graphics and Games
Collision-streams: fast GPU-based collision detection for deformable models
I3D '11 Symposium on Interactive 3D Graphics and Games
gHull: a three-dimensional convex hull algorithm for graphics hardware
I3D '11 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
Applications of Geometry Processing: CudaHull: Fast parallel 3D convex hull on the GPU
Computers and Graphics
Computing 2D Constrained Delaunay Triangulation Using the GPU
IEEE Transactions on Visualization and Computer Graphics
Flip-flop: convex hull construction via star-shaped polyhedron in 3D
Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games
gHull: A GPU algorithm for 3D convex hull
ACM Transactions on Mathematical Software (TOMS)
Approximate polytope ensemble for one-class classification
Pattern Recognition
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We present a hybrid algorithm to compute the convex hull of points in three or higher dimensional spaces. Our formulation uses a GPU-based interior point filter to cull away many of the points that do not lie on the boundary. The convex hull of remaining points is computed on a CPU. The GPU-based filter proceeds in an incremental manner and computes a pseudo-hull that is contained inside the convex hull of the original points. The pseudo-hull computation involves only localized operations and maps well to GPU architectures. Furthermore, the underlying approach extends to high dimensional point sets and deforming points. In practice, our culling filter can reduce the number of candidate points by two orders of magnitude. We have implemented the hybrid algorithm on commodity GPUs, and evaluated its performance on several large point sets. In practice, the GPU-based filtering algorithm can cull up to 85M interior points per second on an NVIDIA GeForce GTX 580 and the hybrid algorithm improves the overall performance of convex hull computation by 10-27 times (for static point sets) and 22-46 times (for deforming point sets).