A Note on Point Location in Delaunay Triangulations of Random Points

Devroye, Luc; Mücke, Ernst P.; Zhu, Binhai

doi:10.1007/pl00009234

Cited by 58 publications

(44 citation statements)

References 19 publications

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“…Obviously if the search-hint is proximal to the target, fewer elements will be walked through and fewer orientation tests will be performed. Devroye et al [17][18][19] 4 ) for BinSearch and Walk (1D search tree is used), O(n 0.056 ) for search based on a random 2D tree, and O(lg n) for search aided by a 2D median tree.…”

Section: A New Order From Breadth-first Travel Of a Kd-treementioning

confidence: 99%

A new insertion sequence for incremental Delaunay triangulation

Liu

Yan

2013

Acta Mech Sin

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Incremental algorithm is one of the most popular procedures for constructing Delaunay triangulations (DTs). However, the point insertion sequence has a great impact on the amount of work needed for the construction of DTs. It affects the time for both point location and structure update, and hence the overall computational time of the triangulation algorithm. In this paper, a simple deterministic insertion sequence is proposed based on the breadth-first-search on a Kd-tree with some minor modifications for better performance. Using parent nodes as search-hints, the proposed insertion sequence proves to be faster and more stable than the Hilbert curve order and biased randomized insertion order (BRIO), especially for non-uniform point distributions over a wide range of benchmark examples.

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Section: A New Order From Breadth-first Travel Of a Kd-treementioning

confidence: 99%

A new insertion sequence for incremental Delaunay triangulation

Liu

Yan

2013

Acta Mech Sin

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“…Each method has its advantages and disadvantages (Wen, 2007;Devroye, 1998). In spite of the fact that laser scanning has been recognized as the most precise method and the gathered results are the most extensive (human body measurement data, a 3D virtual mannequin, a reflection of the actual texture, surface relief measurements, etc.…”

Section: Fig 5 Types Of Anthropometrical Data Acquisitionmentioning

confidence: 99%

Virtual Garment Creation

Loureiro¹,

Santos²,

Bettencourt³

2012

Applications of Virtual Reality

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“…The first application is the randomized incremental construction of the Delaunay Triangulation using the Jump-andWalk strategy, introduced by Mücke, Zhu et al [12], [13]. This strategy proceeds in an incremental way.…”

Section: Convex Hull (2d-hull) and The Construction Of The Twodimensmentioning

confidence: 99%

Robust thread-level speculation

García-Yágüez

Llanos

González-Escribano

2011

2011 18th International Conference on High Performance Computing

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Robustness is a key issue on any runtime system that aims to speed up the execution of a program. However, robustness considerations are commonly overlooked when new software-based, thread-level speculation (STLS) systems are proposed. This paper highlights the relevance of the problem, showing different situations when the use of incorrect data can irreversibly alter the speculative execution of an algorithm, despite the efforts of a given STLS system to maintain sequential consistency. We show that the management of speculative exceptions is a common factor to these problems. Based on this fact, we propose a novel solution to handle speculative exceptions. Our solution eagerly tries to solve the issue before the non-speculative thread arrives to the instruction that rose the exception. We compare our solution to a more conservative approach found in the bibliography. The comparison is done both qualitatively, through a detailed analysis of the tradeoffs involved, and quantitatively, evaluating the effects of both solutions in the execution of three different benchmarks on a real system. Both studies conclude that our solution handles the occurrence of speculative exceptions more efficiently. Under heavy loads intended to push to its limits a STLS system, our solution leads to execution times reduced by up to 52.02% with respect to earlier proposals. Our solution does not affect the performance when speculative exceptions do not appear. We believe that our proposal makes STLS systems robust enough to be used in production environments.

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A Note on Point Location in Delaunay Triangulations of Random Points

Cited by 58 publications

References 19 publications

A new insertion sequence for incremental Delaunay triangulation

A new insertion sequence for incremental Delaunay triangulation

Virtual Garment Creation

Robust thread-level speculation

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