There is a planar graph almost as good as the complete graph
SCG '86 Proceedings of the second annual symposium on Computational geometry
Numerical computation of internal & external flows: fundamentals of numerical discretization
Numerical computation of internal & external flows: fundamentals of numerical discretization
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Regridding surface triangulations
Journal of Computational Physics
Automatic unstructured grid generators
Finite Elements in Analysis and Design
Algorithm 772: STRIPACK: Delaunay triangulation and Voronoi diagram on the surface of a sphere
ACM Transactions on Mathematical Software (TOMS)
Crust and anti-crust: a one-step boundary and skeleton extraction algorithm
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Exact and efficient construction of planar Minkowski sums using the convolution method
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Sweep-line algorithm for constrained Delaunay triangulation
International Journal of Geographical Information Science
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A standard use of triangulation in GIS is to model terrain surface using TIN. In many simulation models of physical phenomena, triangulation is often used to depict the entire spatial domain, which may include buildings, landmarks and other surface objects in addition to the terrain surface. Creating a seamless surface of complex building structures together with the terrain is challenging and existing approaches are laborious, time-consuming and error-prone. We propose an efficient and robust procedure using computational geometry techniques to derive triangulated building surfaces from 2D polygon data with a height attribute. We also propose a new method to merge the resultant building surfaces with the triangulated terrain surface to produce a seamless surface for the entire study area. Using Oklahoma City data, we demonstrate the proposed method. The resultant surface is used as the input data for a simulated transport and dispersion event in Oklahoma City. The proposed method can produce the seamless surface data to be used for various types of physical models in a fraction of the time required by previous methods.