An ANSI C program to determine in expected linear time the vertices of the convex hull of a set of planar points

Larkin, Brett J.

doi:10.1016/0098-3004(91)90050-n

Cited by 13 publications

(4 citation statements)

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“…The larger the data set, the greater the saving of time. Partitioning points in this manner runs in linear time, or O(N), for a uniform distribution of points, but in O(N 2, for the worst possible case (Larkin 1991). Similar data structures are also used to store the centroids of triangles for quick search of triangles whose circumcircles enclose the inserted point or which intersect a constraint segment.…”

Section: A Complete Convex Hull Insertion Algorithmmentioning

confidence: 99%

“…Thus it is preferred in runtime programmes to leave the points unsorted such that these indices point to correct points while partitioning them into cells. A faster alternative is to create a one-dimensional array to store the index of the first point in each cell, then store along with each point the index of next point lying in the same cell (Larkin 1991). Figure 9 shows the partitioning cell structures of a simplified data set containing 12 points.…”

Section: A Complete Convex Hull Insertion Algorithmmentioning

confidence: 99%

“…(a) Initial boundaries 7.9, 12 and 6; (b) find hull vertices 11, 5 and 4; (c) the convex hull. the algorithm improved byLarkin (1991), the following procedures are involved in computing the Convex Hull of the partitioned set as depicted infigure 10. (A) Find the points with the minimum x -y , x f y , and maximum x -y , and x + y values respectively.…”

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confidence: 99%

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Delaunay triangulations in TIN creation: an overview and a linear-time algorithm

Tsai

1993

International journal of geographical information systems

149

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The Delaunay triangulation is commonly used to generate triangulared irregular network (TIN) models for a best description of the surface morphology in a variety of applications in geographic information systems (GIs). This paper discusses the definitions and basic properties of the standard and constrained Delaunay triangulations. Several existing Delaunay algorithms are reviewed and classified into three categories according to their procedures: ( I ) divide-and-conquer methods, (2) incremental insertion methods, and (3) triangulation growth methods. Furthermore, a linear-time Convex Hull Insertion algorithm is presented to construct T l N s for a set of points as well as specific features such as constraint breaklines and exclusion boundaries. Empirical results over various sets of up to 50000 points on personal computers show that the proposed algorithm efficiently expedites the construction of TIN models in approximately O ( N ) for N randomly distributed points.

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Section: A Complete Convex Hull Insertion Algorithmmentioning

confidence: 99%

Section: A Complete Convex Hull Insertion Algorithmmentioning

confidence: 99%

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Delaunay triangulations in TIN creation: an overview and a linear-time algorithm

Tsai

1993

International journal of geographical information systems

149

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“…The initial triangulation can be obtained in a number of ways. The approach adopted here is to produce a Delaunay triangulation of those points which define the convex hull of the points to be triangulated, Algorithms for constructing the convex hull of a set of points and computing the Delaunay triangulation of a convex polygon are given by Larkin (1991) and Derijver and Maybank (1982) respectively.…”

Section: Ground Surfnce Triangulationmentioning

confidence: 99%

A data model for representing geological surfaces

Ware

Jones

1997

Proceedings of the 5th ACM International Workshop on Advances in Geographic Information Systems

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This paper provides details of a technique which enables the automatic creation of a geological surface model from terrain, outcrop and subsurface horizon data The model is created in such a way that each data set provides constraints on the interpretation of others. Both terrain and subsurface formation boundaries are represented by adjoining triangulated irregular networks that am constmined by the linear boundaries of outcrop regions. This approach to model creation demonstrates a step toward automated integration of sparse da@ from multiple sources, that may allow complex geological structures to be stored within JD-GIS. IntroductionThe aims of this paper are three-fold. Firstly, it presents, in a 3D-GIS context, the concept of combining terrain, outcrop and subsurface data for the purpose of constructing geological surface data models. Secondly, the paper outlines a data model construction methodoiogy based on, and motivated by, the previously mentioned concept. This methodology, many aspects of which can be adapted for use within existing surface modeling packages, is intended as a useful guide to those with an interest in computer-based geological surface modeling. The third aim of the paper is to give de&ails of specific algorithms. that include some novel techniques, which, when combined and applied in accordance with thk model construction methodology, automatically produce a geological surface model.

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C

Howarth¹

2017

Dictionary of Mathematical Geosciences

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An ANSI C program to determine in expected linear time the vertices of the convex hull of a set of planar points

Cited by 13 publications

References 9 publications

Delaunay triangulations in TIN creation: an overview and a linear-time algorithm

Delaunay triangulations in TIN creation: an overview and a linear-time algorithm

A data model for representing geological surfaces

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