Insert and delete algorithms for maintaining dynamic Delaunay triangulations

Devijver, Pierre A.; Dekesel, Michel

doi:10.1016/0167-8655(82)90015-0

Cited by 7 publications

(4 citation statements)

References 6 publications

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“…A survey on triangulations is provided by BERN & EPPSTEIN (1995). One particular algorithm necessary for the following explanations is the incremental insertion of vertices into an existing TIN (e. g. DE BERG ET AL., 1997;DEVILLERS, 1997;EGENHOFER ET AL., 1989;GUIBAS & STOLFI, 1985;DEVIJVER & DEKESEL, 1982). Locations of insertion of spatially independent points of different data sets may be in existing triangles as well as on their respective edges (a point may thus also fall onto an existing point).…”

Section: Integration Of Dtm-tin and 2d Gis Datamentioning

confidence: 99%

“…The major difference in runtime behaviour of incremental algorithms is given by the various spatial access methods to find the location of insertion in the TIN as the actual area influenced by the insertion procedure remains the same for all. It forms a star-shaped polygon around the location of the point (e. g. DEVIJVER & DEKESEL, 1982). Spatial access methods in TINs are treated in particular by DEVILLERS and DEVILLERS (1997) as well as the references in there.…”

Section: Integration Of Dtm-tin and 2d Gis Datamentioning

confidence: 99%

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At the Ministry of the Interior

2017

The Shah’s Iran - Rise and Fall

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Interacting with the topographic map of the future Stephen T`Siobbel (Teleatlas, Gent) 3D and (car) navigation Markus Müller (University of Stuttgart) 3D geo-spatial data requirements in environmental planning 17:00-18:30 Session 2: Acquisition of 3D geo-spatial data Chair: Keith Murray (Ordnance Survey, Southampton) Norbert Haala (University of Stuttgart) and Claus Brenner (Robert Bosch GmbH, Hildesheim) City model data acquisition from laser scanning Eberhard Gülch (Inpho GmbH, Stuttgart) Semi-automatic acquisition of topographic objects from digital imagery Alix Marc (ISTAR, Sophia Antipolis) 3D geo-spatial data acquisition for telecom applications Melanie Hayles (Laser Scan, Cambridge) Integration of photogrammetry and 3D geo-spatial databases Tuesday,

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Section: Integration Of Dtm-tin and 2d Gis Datamentioning

confidence: 99%

Section: Integration Of Dtm-tin and 2d Gis Datamentioning

confidence: 99%

At the Ministry of the Interior

2017

The Shah’s Iran - Rise and Fall

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“…The triangulation is named after Boris Delaunay for his work on this topic from 1934. Many algorithms can generate Delaunay triangulation meshes, such as growth algorithm, divide and conqueralgorithm [5], point-by-point insertionalgorithm [6], etc.…”

Section: A Delaunay Triangulation (Dt)mentioning

confidence: 99%

Optimal layout of borehole location based on Delaunay Refinement

Wan

2013

2013 21st International Conference on Geoinformatics

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During the urban planning, there exists a need for geological disaster investigation. Drilling is the most common way to survey the geological environment of the research area. However, how to determine the locations of the boreholes reasonably is an important problem.We have adopted the Delaunay Refinement technique to determine the location of boreholes. Delaunay Refinement technique can generate relatively well-distributed triangular mesh by inserting some new points at the circumcenter of triangles. In the engineering practice, ZhengDong new district neededto carry out a geological disaster investigation. The government required the distance between any two boreholes not to exceed 1.5 kilometers to guaranteeaccuracy. The existing 40 boreholes data, collected from the constructed buildings,along with the border of ZhengDong new district as the constrained conditions, the locations of new boreholes can be determined the by Delaunay Refinement. The locations of new inserting points just are what we needed. Using this method, the optimal layout of boreholes can be achieved. Thus, this method produces not only a rational result, but also reduces the cost.

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“…One particularly important algorithm is the incremental insertion of points into an existing TIN (e.g., [11], [19]). The major difference between the various approaches for incremental insertion is the employed spatial access method to find the location of insertion into the TIN.…”

Section: Some Backgroundmentioning

confidence: 99%

The Radial Topology Algorithm—A New Approach for Deriving 2.5D GIS Data Models

Lenk¹,

Heipke

2006

Geoinformatica

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In this paper a new method for the combination of 2D GIS vector data and 2.5D DTM represented by triangulated irregular networks (TIN) to derive integrated triangular 2.5D object-based landscape models (also known as 2.5D-GIS-TIN) is presented. The algorithm takes into account special geometric constellations and fully exploits existing topologies of both input data sets, it "sews the 2D data into the TIN like a sewing-machine" while traversing the latter along the 2D data. The new algorithm is called radial topology algorithm. We discuss its advantages and limitations, and describe ways to eliminate redundant nodes generated during the integration process. With the help of four examples from practical work we show that it is feasible to compute and work with such integrated data sets. We also discuss the integrated data models in the light of various general requirements and conclude that the integration based on triangulations has a number of distinct advantages.

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Insert and delete algorithms for maintaining dynamic Delaunay triangulations

Cited by 7 publications

References 6 publications

At the Ministry of the Interior

At the Ministry of the Interior

Optimal layout of borehole location based on Delaunay Refinement

The Radial Topology Algorithm—A New Approach for Deriving 2.5D GIS Data Models

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