On Faster Sphere-Box Overlap Testing

Larsson, Thomas; Akenine-Möller, Tomas; Lengyel, Eric

doi:10.1080/2151237x.2007.10129232

Cited by 16 publications

(23 citation statements)

References 3 publications

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“…The original partitioning schemes always result in partitions defined by axis-aligned bounding boxes. Therefore, the intersection test in Line 8 in Algorithm 1 can be performed using the fast box-sphere overlap test of Larsson et al [23]. However, using the more advanced partitioning algorithms presented in this paper, this is no longer true.…”

Section: Geometric Primitivesmentioning

confidence: 97%

“…A crude approximation uses the bounding box of each partition and the fast intersection test of Larsson et al [23] to determine the simplices that belong to the border of a partition. While computationally cheap, the bounding box can overestimate the extent of a partition.…”

Section: Bounding Box Intersection Testmentioning

confidence: 99%

“…The root node of the tree corresponds to the bounding box from Section 3.2.1. This allows for a more accurate test whether a given simplex s of partition i intersects with partition j using log |C j | box-sphere intersection tests [23].…”

Section: Grid-based Intersection Testmentioning

confidence: 99%

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Load-Balancing for Parallel Delaunay Triangulations

Funke

Sanders

Winkler

2019

Lecture Notes in Computer Science

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Computing the Delaunay triangulation (DT) of a given point set in R D is one of the fundamental operations in computational geometry. Recently, Funke and Sanders [18] presented a divide-and-conquer DT algorithm that merges two partial triangulations by re-triangulating a small subset of their vertices -the border vertices -and combining the three triangulations efficiently via parallel hash table lookups. The input point division should therefore yield roughly equal-sized partitions for good load-balancing and also result in a small number of border vertices for fast merging. In this paper, we present a novel divide-step based on partitioning the triangulation of a small sample of the input points. In experiments on synthetic and real-world data sets, we achieve nearly perfectly balanced partitions and small border triangulations. This almost cuts running time in half compared to non-data-sensitive division schemes on inputs exhibiting an exploitable underlying structure.Recently, we presented a novel divide-and-conquer (D&C) DT algorithm for arbitrary dimension [18] that lends itself equally well to shared and distributed memory parallelism and thus hybrid parallelization. While previous D&C DT algorithms suffer from a complex -often sequential -divide or merge step [12,24], our algorithm reduces the merging of two partial triangulations to re-triangulating a small subset of their vertices -the border vertices -using the same parallel algorithm and combining the three triangulations efficiently via hash table lookups. All steps required for the merging -identification of relevant vertices, triangulation and combining the partial DTs -are performed in parallel.The division of the input points in the divide-step needs to address a twofold sensitivity to the point distribution: the partitions need to be approximately equal-sized for good load-balancing, arXiv:1902.07554v1 [cs.DS]

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Section: Geometric Primitivesmentioning

confidence: 97%

Section: Bounding Box Intersection Testmentioning

confidence: 99%

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Load-Balancing for Parallel Delaunay Triangulations

Funke

Sanders

Winkler

2019

Lecture Notes in Computer Science

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“…Our proposed D&C scheme relies on combinatorial computations on hash values except for the detection of the border [16] to determine if the (hyper)-circumsphere of a given simplex intersects with the bounding box of the opposite partial triangulation. The test does not suffer from floating-point inaccuracies like the orientation-and inSphere-tests required by the base case algorithm [21].…”

Section: Implementation Detailsmentioning

confidence: 99%

Parallel d-D Delaunay Triangulations in Shared and Distributed Memory

Funke

Sanders

2017

2017 Proceedings of the Ninteenth Workshop on Algorithm Engineering and Experiments (ALENEX)

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Computing the Delaunay triangulation (DT) of a given point set in R D is one of the fundamental operations in computational geometry. In this paper we present a novel divide-and-conquer (D&C) algorithm that lends itself equally well to shared and distributed memory parallelism. While previous D&C algorithms generally suffer from a complex -often sequential -merge or divide step, we reduce the merging of two partial triangulations to re-triangulating a small subset of their vertices using the same parallel algorithm and combining the three triangulations via parallel hash table lookups. In experiments we achieve a reasonable speedup on shared memory machines and compare favorably to CGAL's three-dimensional parallel DT implementation on some inputs.In the distributed memory setting we show that our approach scales to 2048 processing elements, which allows us to compute 3-D DTs for inputs with billions of points.

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“…At present time, there are several famous bounding volumes such as spheres (Weller and Zachmann, 2009, Madera et al, 2009, Rocha and Maria Andre'ia Formico, 2008, Larsson et al, 2007, Spillmann et al, 2007, Benitez et al, 2005, Gareth and Carol, 2004, Bradshaw and O'Sullivan, 2002, Axis Aligned Bounding Box (AABB) , Zhang and Kim, 2007, Oriented Bounding Box (OBB) , Discrete Oriented Polytope (k-DOP) [3], new type of bounding volume; Oriented Convex Polyhedra (Suaib et al, 2008, Bade et al, 2006, and hybrid combination bounding volume (Tu andYu, 2009, Kockara, 2007). Most large scale 3D simulations used bounding box because it iss simple, require small space of storage, fast response of collision, and easy to implement (Lin and Manocha, 2004).…”

Section: Fig 4 Common Bounding Volume In Previous Researchesmentioning

confidence: 99%