Fast computation of generalized Voronoi diagrams using graphics hardware

Hoff, Kenneth E.; Culver, Tim; Keyser, John; Manocha, Dinesh

doi:10.1145/336154.336226

Cited by 59 publications

(66 citation statements)

References 2 publications

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“…Computing Delaunay diagrams using our algorithm, we can easily obtain Voronoi diagrams. Compared with the algorithm by [3], our algorithm can change the size of the window on which we draw images. The efficiency of the algorithm depends on the size of the window.…”

Section: Discussionmentioning

confidence: 99%

“…We describe the algorithm with which to make the image of the Voronoi diagram from given points, reported by [3]. To make the image, we first consider a cone.…”

Section: Drawing a Voronoi Diagram With Graphics Hardwarementioning

confidence: 99%

“…Using graphics hardware, we can effectively generate several types of Voronoi diagrams [3,9]. Although these algorithms can generate Voronoi diagram images very rapidly, they cannot extract the information from regions adjacent to these Voronoi diagrams.…”

Section: Introductionmentioning

confidence: 99%

“…Hoff at al. reported an algorithm to draw Voronoi diagrams using graphics hardware [3]. Our algorithms are based on the same technique used by [3].…”

mentioning

confidence: 99%

“…reported an algorithm to draw Voronoi diagrams using graphics hardware [3]. Our algorithms are based on the same technique used by [3]. However, our algorithm employs an analyzing phase of the images and obtains topological information from the image.…”

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confidence: 99%

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Fast computation of three-dimensional convex hulls using graphics hardware

Yamamoto

2005

Japan J. Indust. Appl. Math.

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This paper describes an algorithm for computing three-dimensional convex hulls. First, we introduce a simple algorithm to compute two-dimensional convex hulls using graphics hardware. This algorithm computes the edges and the facets of the convex hulls by analyzing bitmap images drawn using given points. Graphics hardware can generate bitmap images of three-dimensional objects very rapidly. We then expand the algorithm to compute three-dimensional convex hulls. Finally, we apply the algorithm to compute Delaunay diagrams. The algorithm is very simple. Hoff at al. reported an algorithm to draw Voronoi diagrams using graphics hardware [3]. Our algorithms are based on the same technique used by [3]. However, our algorithm employs an analyzing phase of the images and obtains topological information from the image.The diagrams produced by our algorithm are not strict Delaunay diagrams, because the images we obtain using graphics hardware are bitmap images and are not continuous. Therefore, they may contain some errors but, because of the simplicity of the algorithm, they are stable compared with ordinary algorithms, without a requirement for special techniques, such as symbolic perturbation. The algorithms can be easily implemented.

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Section: Discussionmentioning

confidence: 99%

“…We describe the algorithm with which to make the image of the Voronoi diagram from given points, reported by [3]. To make the image, we first consider a cone.…”

Section: Drawing a Voronoi Diagram With Graphics Hardwarementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Hoff at al. reported an algorithm to draw Voronoi diagrams using graphics hardware [3]. Our algorithms are based on the same technique used by [3].…”

mentioning

confidence: 99%

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confidence: 99%

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Fast computation of three-dimensional convex hulls using graphics hardware

Yamamoto

2005

Japan J. Indust. Appl. Math.

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Umbrella spherical integration: a stable meshless method for non‐linear solids

Kucherov

Tadmor

Miller

2006

Numerical Meth Engineering

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SUMMARYA stable meshless method for studying the finite deformation of non-linear three-dimensional (3D) solids is presented. The method is based on a variational framework with the necessary integrals evaluated through nodal integration. The method is truly meshless, requiring no 3D meshing or tessellation of any form. A local least-squares approximation about each node is used to obtain necessary deformation gradients. The use of a local field approximation makes automatic grid refinement and the application of boundary conditions straightforward. Stabilization is achieved through the use of special 'umbrella' shape functions that have discontinuous derivatives at the nodes. Novel efficient algorithms for constructing the nodal stars and computing the nodal volumes are presented. The method is applied to four test problems: uniaxial tension, simple shear and bending of a bar, and cylindrical indentation. Convergence studies at infinitesimal strain show that the method is well-behaved and converges with the number of nodes for both uniform and non-uniform grids. Typical of meshless methods employing nodal integration, the total energy can be underestimated due to the approximate integration. At finite deformation the method reproduces known exact solutions. The bending example demonstrates an interesting example of torsional buckling resulting from the bending.

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Navigation and steering for autonomous virtual humans

Kapadia

Badler

2013

WIRES Cognitive Science

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The ever-increasing applicability of interactive virtual worlds in industry and academia has given rise to the need for robust, versatile autonomous virtual humans to inject life into these environments. There are two fundamental problems that must be addressed to produce functional, purposeful autonomous populaces: (1)Navigation: finding a collision-free global path from an agent's start position to its target in large complex environments, and (2) Steering: moving an agent along the path while avoiding static and dynamic threats such as other agents. In this review, we survey the large body of contributions in steering and navigation for autonomous agents in dynamic virtual worlds. We describe the benefits and limitations of different proposed solutions and identify potential future research directions to meet the needs for the next generation of interactive virtual world applications. WIREs Cogn Sci 2013, 4:263-272. doi: 10.1002/wcs.1223 For further resources related to this article, please visit the WIREs website.

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Fast computation of generalized Voronoi diagrams using graphics hardware

Cited by 59 publications

References 2 publications

Fast computation of three-dimensional convex hulls using graphics hardware

Fast computation of three-dimensional convex hulls using graphics hardware

Umbrella spherical integration: a stable meshless method for non‐linear solids

Navigation and steering for autonomous virtual humans

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