A functional language to implement the divide-and-conquer Delaunay triangulation algorithm

Moura, Andre Luiz; Camacho, J.R.; Guimarães, Sebastião Carneiro; Salerno, C.H.

doi:10.1016/j.amc.2004.08.033

Cited by 3 publications

(2 citation statements)

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“…Some researchers attempted to improve the efficiency of the in-circle test scheme. 10,11 Conversely, the proposed FBD&C algorithm bypasses the process of searching for conflict triangles and removing them. Instead of a searching and removing scheme, a flip operation, which is generally used in incremental approaches, is applied during the merge process to keep the Delaunay property of the intermediate and resulting triangulations.…”

Section: Contribution Of the Proposed Algorithmmentioning

confidence: 99%

A divide-and-conquer Delaunay triangulation algorithm with a vertex array and flip operations in two-dimensional space

Yang

Choi

Jung

2011

Int. J. Precis. Eng. Manuf.

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Divide-and-conquer algorithms provide computational efficiency for constructing Delaunay triangulations; however, their implementation is complicated. Most divide-and-conquer algorithms for Delaunay triangulation utilize edge-based structures, because triangles are frequently deleted and created during the merge process. However, as our proposed divide-and-conquer algorithm does not require existing edges to be deleted in the merge process, a simple array-based data structure can be used for the representation of the triangulation topology. Rather than deleting the edges of the conflicting triangles, which was used in previous methods, the Delaunay property is also preserved with a new flip propagation method in the merge phase. This array-based data structure is much simpler than the commonly used edge-based data structures and requires less memory allocation. The proposed algorithm arranges sites into a permutation vector that represents a kdtree with an array; thus, the space partitioning information is internally represented in the array without any additional data. Since the proposed divide-and-conquer algorithm is compact, the implementation complexity of conventional divideand-conquer triangulation algorithms can be avoided. Despite of the simplicity of this new algorithm, the experimental results indicate that the computational efficiency is comparable to the previous divide-and-conquer algorithms.

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Section: Contribution Of the Proposed Algorithmmentioning

confidence: 99%

A divide-and-conquer Delaunay triangulation algorithm with a vertex array and flip operations in two-dimensional space

Yang

Choi

Jung

2011

Int. J. Precis. Eng. Manuf.

View full text Add to dashboard Cite

show abstract

“…(2) Divide and conquer algorithm: This algorithm was proposed by Lewis and Robinson [9], and later, Andre, et al carried out improvement [10]. After that, scholars tried to solve the problem in the construction of TIN / Delaunay triangulation with large amounts of data by grid-based block and quadtree algorithm [11].…”

Section: Introductionmentioning

confidence: 99%