Towards a 3D Feature Overlay through a Tetrahedral Mesh Data Structure

Verbree, E.; Most, A. van der; Quak, Wilko; Oosterom, Peter van

doi:10.1559/152304005775194791

Cited by 7 publications

(3 citation statements)

References 11 publications

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“…Simplexes offer not only support for calculations, but also for more complex spatial operations like buffer (de Vries 2001) and overlay (van der Most 2004). Verbree et al (2005) describe the possibilities of executing these classic GIS operators on tetrahedrons. Validation is another operation that can be performed on both simplexes and features.…”

Section: Definitionmentioning

confidence: 99%

3D Topography. A Simplicial Complex-based Solution in a Spatial DBMS

Penninga¹

2008

Publications on Geodesy

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An 'oliebol' is a typical Dutch treat, traditionally eaten on New Year's Eve, and can be described roughly as a doughnut ball. The 'oliebollenbar' was a theme night at the Snelliusbar (the bar of the students association Snellius of the faculty of Geodesy, Delft University of Technology), organised by staff members of the GIS Technology group. Wiebke, Yahaya) and our guest researchers (Chen, João, Ludvig, Rod). I really enjoy working with this young, dynamic and enthusiastic group of researchers.Other OTB colleagues also contributed to the pleasant atmosphere in which I have worked for four years. Thanks to the 12 o'clock lunch crew, the 20 year OTB committee, the PhD council and board (I enjoyed both the work and the drinks) and all other colleagues that I met during joint projects, off-sites, OTBorrels and coffee breaks. Thanks to Itziar Lasa for the cover design of the dissertation version.A lot of people outside OTB also contributed in one way or the other. The week Peter and I spent at Oracle USA was invaluable (thanks to Siva Ravada, Ravi Kothuri, Baris Kazar, John Herring, Han Wammes), even though the annual 'A Quilters Gathering' created the most surreal atmosphere in the Nashua Sheraton. Discussing spatial data types during the day and being surrounded by hundreds of quilters with humongous trolleys with sewing kits and machines by night; it's quite a gap.

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Section: Definitionmentioning

confidence: 99%

3D Topography. A Simplicial Complex-based Solution in a Spatial DBMS

Penninga¹

2008

Publications on Geodesy

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“…While there has been some work by previous researchers on cutting tetrahedral meshes by a plane 10–12, it has been primarily for the purpose of visualization. To the best of our knowledge, this is the first time this problem—subdividing polyhedral meshes along a set of disjoint planes and creating a conformal mesh for the purpose of solving PDEs, and particularly in parallel—has been addressed in the literature.…”

Section: Introductionmentioning

confidence: 99%

Solution of the diffusion equation in multi‐material domains by sub‐division of elements along reconstructed interfaces

Garimella

Lipnikov

2011

Numerical Methods in Fluids

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SUMMARYThis paper describes the accurate solution of the diffusion equation in three-dimensional multi-material domains where some mesh elements contain more than one material. Given the volume fractions of each material in mesh elements, the method first recreates the material interfaces in the elements using interface reconstruction methods. Then the mesh is subdivided along the interfaces making sure that the final polyhedral mesh is conforming. Finally, the diffusion equation is solved on the sub-divided mesh containing all single material elements. It is shown that the method produces second-order accurate solutions with a lower error than methods that average the material properties in the multi-material elements. Published in

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“…[12,13] The inclusion test is not a complex problem, but a robust, correct and efficient algorithm is needed because the basic test has to be applied many times in the geometric intersection test that should be performed within reasonable computational time. [14,15] Moreover, the point inclusion test lays the foundation of other geometric computation for complex 3D models, e.g., geometric intersection for general polyhedra.…”

Section: Introductionmentioning

confidence: 99%

Point-in-polyhedra test with direct handling of degeneracies

Cui

Zhang

Chen

et al. 2011

Geo-spatial Information Science

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The Point-In-Polyhedron problem is to check whether a point is inside or outside of a given polyhedron. When a degenerate case is detected, the traditional ray-crossing algorithms avoid the case by selecting a different ray or erase the case by perturbing input data. This paper introduces a Threshold-Based Ray-Crossing (TBRC) algorithm for solving the Point-In-Polyhedron problem. The TBRC algorithm copes directly with degenerate cases by checking whether to count the face intersecting with the ray.It is worth mentioning that the TBRC algorithm can handle all degeneracies without extra computation and storage. Moreover, we analyze the basic algorithm and examine how to accelerate it. The experimental results show that TBRC algorithm is highly efficient and robust for the Point-In-Polyhedron problem, compared to a classical tetrahedron-based algorithm without pre-processing.

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Towards a 3D Feature Overlay through a Tetrahedral Mesh Data Structure

Cited by 7 publications

References 11 publications

3D Topography. A Simplicial Complex-based Solution in a Spatial DBMS

3D Topography. A Simplicial Complex-based Solution in a Spatial DBMS

Solution of the diffusion equation in multi‐material domains by sub‐division of elements along reconstructed interfaces

Point-in-polyhedra test with direct handling of degeneracies

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