Sparse Voronoi Refinement

Hudson, Benoît; Phillips, Todd

doi:10.1007/978-3-540-34958-7_20

Cited by 33 publications

(50 citation statements)

References 17 publications

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“…The minimum such distance in G (or more generally in any PSLG) is called the minimum feature size, denoted by mfs(G). See [Rup93,Dey07,HMP06,Eri03]. We call the ratio mfs(P ) mfs(G) the degradation of the decomposition of P into G.…”

Section: Introductionmentioning

confidence: 99%

Meshes Preserving Minimum Feature Size

Aloupis

Demaine

et al. 2012

Lecture Notes in Computer Science

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Abstract. The minimum feature size of a planar straight-line graph is the minimum distance between a vertex and a nonincident edge. When such a graph is partitioned into a mesh, the degradation is the ratio of original to final minimum feature size. For an n-vertex input, we give a triangulation (meshing) algorithm that limits degradation to only a constant factor, as long as Steiner points are allowed on the sides of triangles. If such Steiner points are not allowed, our algorithm realizes O(lg n) degradation. This addresses a 14-year-old open problem by Bern, Dobkin, and Eppstein.

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Section: Introductionmentioning

confidence: 99%

Meshes Preserving Minimum Feature Size

Aloupis

Demaine

et al. 2012

Lecture Notes in Computer Science

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“…SVR produces a quality conforming mesh that is size-optimal in the number of vertices [HMP06]. One important concern in quality meshing is how we define the quality of tetrahedron.…”

Section: Fig 1 Leftmentioning

confidence: 99%

“…At last year's IMR conference we introduced a new meshing algorithm, Sparse Voronoi Refinement (SVR), which provided the typical guarantees for theoretical meshing algorithms, along with an unusual one that the algorithm ran in near-linear time [HMP06]. The goal in designing SVR was to create a meshing algorithm that was similar in implementation and style to many widely used meshing algorithms, but with the added benefit of very strong worst-case bounds on the runtime complexity and space usage.…”

Section: Introductionmentioning

confidence: 99%

SVR: Practical Engineering of a Fast 3D Meshing Algorithm*

Acar

Hudson

Phillips

Proceedings of the 16th International Meshing Roundtable

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Summary. The recent Sparse Voronoi Refinement (SVR) Algorithm for mesh generation has the fastest theoretical bounds for runtime and memory usage. We present a robust practical software implementation of the SVR for meshing a piecewise linear complex in 3 dimensions. Our software is competitive in runtime with state of the art freely available packages on generic inputs, and on pathological worse cases inputs, we show SVR indeed leverages its theoretical guarantees to produce vastly superior runtime and memory usage. The theoretical algorithm description of SVR leaves open several data structure design options, especially with regard to point location strategies. We show that proper strategic choices can greatly effect constant factors involved in runtime.

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“…The overlay mesh is constructed on the input vertices using the Sparse Voronoi Refinement meshing algorithm, applied to point sets [19]. The output is a Delaunay mesh conforming to the input vertices.…”

Section: Phase 1: the Overlay Meshmentioning

confidence: 99%

“…The runtime of the SVR algorithm used in the overlay phase was analyzed in [19]. This stage is the majority of the work.…”

Section: Work Efficiencymentioning

confidence: 99%

Size Competitive Meshing Without Large Angles

Phillips

Sheehy

Automata, Languages and Programming

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Abstract. We present a new meshing algorithm for the plane, Overlay Stitch Meshing (OSM), accepting as input an arbitrary Planar Straight Line Graph and producing a triangulation with all angles smaller than 170• . The output triangulation has competitive size with any optimal size mesh having equally bounded largest angle. The competitive ratio is O(log(L/s)) where L and s are respectively the largest and smallest features in the input. OSM runs in O(n log(L/s) + m) time/work where n is the input size and m is the output size. The algorithm first uses Sparse Voronoi Refinement to compute a quality overlay mesh of the input points alone. This triangulation is then combined with the input edges to give the final mesh.

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Sparse Voronoi Refinement

Cited by 33 publications

References 17 publications

Meshes Preserving Minimum Feature Size

Meshes Preserving Minimum Feature Size

SVR: Practical Engineering of a Fast 3D Meshing Algorithm*

Size Competitive Meshing Without Large Angles

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