Fast and Robust Smallest Enclosing Balls

Gärtner, Bernd

doi:10.1007/3-540-48481-7_29

Cited by 121 publications

(98 citation statements)

References 4 publications

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“…It would be possible to use again the randomized algorithm [Gaertner 1999] which finds the smallest enclosing sphere, but we found that just an approximate enclosing sphere performs better. The approximate enclosing sphere is computed in the same way as in [James and Pai 2004] (but in R 4 in our case), i.e., by taking the average of q 1 ,...,q m as the center and then determining the smallest possible radius which still gives a correct enclosing sphere.…”

Section: Bounding the Spherical Partmentioning

confidence: 97%

Efficient collision detection for spherical blend skinning

Kavan

O’Sullivan

Žára

2006

Proceedings of the 4th International Conference on Computer Graphics and Interactive Techniques in Australasia and Southeast As

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Recently, two algorithms improving the real-time simulation of articulated models in virtual environments have been published: 1) fast collision detection for linear blend skinning and 2) spherical blend skinning. Both linear and spherical blending solve the skinning problem of a skeletally controlled 3D model (e.g., an avatar), but only spherical blending avoids artifacts such as the candywrapper. However, to date, fast collision detection has been limited to linear blending. This paper describes how to perform collision detection for models skinned with the more sophisticated spherical method. As a result, both high-quality skinning and fast and exact collision detection can be achieved -there is no longer any need for a trade-off. The generalization from linear to spherical blending involves the construction of rotation bounds, derived using a quaternion representation. The resulting algorithm is simple to implement and fast enough for real-time virtual reality applications.

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Section: Bounding the Spherical Partmentioning

confidence: 97%

Efficient collision detection for spherical blend skinning

Kavan

O’Sullivan

Žára

2006

Proceedings of the 4th International Conference on Computer Graphics and Interactive Techniques in Australasia and Southeast As

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“…A stochastic algorithm for computing enclosing spheres in expected linear time was proposed by Welzl (1991). A slightly tuned version was given by Gärtner (1999).…”

Section: Robust Euclidean Skeletonmentioning

confidence: 99%

Statistical Analysis of the Local Strut Thickness of Open Cell Foams

Liebscher¹,

Redenbach²

2013

Image Anal Stereol

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Open cell foams are formed by an interconnected network of struts whose thickness varies locally. These variations are known to have an impact on the elastic and thermal properties of the foam. In this paper we quantify the local strut thickness by means of micro computed tomography (µCT) imaging. We develop a fully automatic algorithm to extract the foam's skeleton from a binary image and its topological decomposition into vertices and struts. This allows to estimate the thickness of individual strut segments by the Euclidean distance transform, where an appropriate correction for struts with nonspherical cross-sectional shape is applied. Conflating these estimates based on the strut lengths results in a strut thickness profile for the entire foam. Based on this profile we give a statistical justification that a strut thickness model should depend on the strut length. Furthermore, the investigation of polynomial models for the strut thickness profile by means of regression analysis leads to a new three-parameter strut thickness model.

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“…Summing up the hierarchy creation algorithm: we first compute a bounding sphere for all inner spheres (at the leaves), which becomes the root node of the hierarchy. To do that, we use the fast and stable smallest enclosing sphere algorithm proposed in [Gär99]. Then, we divide the set of inner spheres into subsets in order to create the children.…”

Section: B Building the Istmentioning

confidence: 99%

Inner sphere trees for proximity and penetration queries

Weller¹,

Zachmann²

2009

Robotics: Science and Systems V

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Abstract-We present a novel geometric data structure for approximate collision detection at haptic rates between rigid objects. Our data structure, which we call inner sphere trees, supports different kinds of queries, namely, proximity queries and a new method for interpenetration computation, the penetration volume, which is related to the water displacement of the overlapping region and, thus, corresponds to a physically motivated force.The main idea is to bound objects from the inside with a set of non-overlapping spheres. Based on such sphere packings, a "inner bounding volume hierarchy" can be constructed. In order to do so, we propose to use an AI clustering algorithm, which we extend and adapt here.The results show performance at haptic rates both for proximity and penetration volume queries for models consisting of hundreds of thousands of polygons.

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Fast and Robust Smallest Enclosing Balls

Cited by 121 publications

References 4 publications

Efficient collision detection for spherical blend skinning

Efficient collision detection for spherical blend skinning

Statistical Analysis of the Local Strut Thickness of Open Cell Foams

Inner sphere trees for proximity and penetration queries

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