The hole system of triangulated shapes

K. Ölsböck, The Hole System of Triangulated Shapes, IST Austria, 2020.

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Thesis | Published | English
Department
Series Title
IST Austria Thesis
Abstract
Many methods for the reconstruction of shapes from sets of points produce ordered simplicial complexes, which are collections of vertices, edges, triangles, and their higher-dimensional analogues, called simplices, in which every simplex gets assigned a real value measuring its size. This thesis studies ordered simplicial complexes, with a focus on their topology, which reflects the connectedness of the represented shapes and the presence of holes. We are interested both in understanding better the structure of these complexes, as well as in developing algorithms for applications. For the Delaunay triangulation, the most popular measure for a simplex is the radius of the smallest empty circumsphere. Based on it, we revisit Alpha and Wrap complexes and experimentally determine their probabilistic properties for random data. Also, we prove the existence of tri-partitions, propose algorithms to open and close holes, and extend the concepts from Euclidean to Bregman geometries.
Publishing Year
Date Published
2020-02-10
Page
155
ISSN
IST-REx-ID

Cite this

Ölsböck K. The Hole System of Triangulated Shapes. IST Austria; 2020. doi:10.15479/AT:ISTA:7460
Ölsböck, K. (2020). The hole system of triangulated shapes. IST Austria. https://doi.org/10.15479/AT:ISTA:7460
Ölsböck, Katharina. The Hole System of Triangulated Shapes. IST Austria, 2020. https://doi.org/10.15479/AT:ISTA:7460.
K. Ölsböck, The hole system of triangulated shapes. IST Austria, 2020.
Ölsböck K. 2020. The hole system of triangulated shapes, IST Austria, 155p.
Ölsböck, Katharina. The Hole System of Triangulated Shapes. IST Austria, 2020, doi:10.15479/AT:ISTA:7460.
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