Shape reconstruction from planar cross sections
Computer Vision, Graphics, and Image Processing
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Robust adaptive floating-point geometric predicates
Proceedings of the twelfth annual symposium on Computational geometry
A comparison of sequential Delaunay triangulation algorithms
Computational Geometry: Theory and Applications
Voronoi diagrams and Delaunay triangulations
Handbook of discrete and computational geometry
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Vectorized image segmentation via trixel agglomeration
Pattern Recognition
Computing two-dimensional Delaunay triangulation using graphics hardware
Proceedings of the 2008 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
Proceedings of the 18th ACM SIGPLAN symposium on Principles and practice of parallel programming
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)
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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We propose the first GPU solution to compute the 2D constrained Delaunay triangulation (CDT) of a planar straight line graph (PSLG) consisting of points and edges. There are many CPU algorithms developed to solve the CDT problem in computational geometry, yet there has been no known prior approach using the parallel computing power of the GPU to solve this problem efficiently. For the special case of the CDT problem with a PSLG consisting of just points, which is the normal Delaunay triangulation problem, a hybrid approach has already been presented that uses the GPU together with the CPU to partially speed up the computation. Our work, on the other hand, accelerates the whole computation by the GPU. Our implementation using the CUDA programming model on NVIDIA GPUs is numerically robust with good speedup, of up to an order of magnitude, compared to the best sequential implementations on the CPU. This result is reflected in our experiment with both randomly generated PSLGs and real world GIS data with millions of points and edges.