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Markus Wilhelm Jahn and Patrick Erik Bradley
Geometrically induced topology plays a major role in applications such as simulations, navigation, spatial or spatio-temporal analysis and many more. This article computes geometrically induced topology useful for such applications and extends previous r...
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Markus Wilhelm Jahn and Patrick Erik Bradley
In order to perform topological queries on geographic data, it is necessary to first develop a topological access method (TOAM). Using the fact that any (incidence or other binary) relation produces a topology which includes the common usage of topology ...
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Alessio Martino, Alessandro Giuliani and Antonello Rizzi
This paper investigates a novel graph embedding procedure based on simplicial complexes. Inherited from algebraic topology, simplicial complexes are collections of increasing-order simplices (e.g., points, lines, triangles, tetrahedrons) which can be int...
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Uznir Ujang, Francesc Anton Castro and Suhaibah Azri
In spatial science, the relationship between spatial objects is considered to be a vital element. Currently, 3D objects are often used for visual aids, improving human insight, spatial observations, and spatial planning. This scenario involves 3D geometr...
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Kevin P. Knudson
We define the notion of an approximate triangulation for a manifold M embedded in Euclidean space. The basic idea is to build a nested family of simplicial complexes whose vertices lie in M and use persistent homology to find a complex in the family whos...
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