TL;DR
The paper introduces a method for embedding simplicial complexes into bounded-degree, low-volume simplicial balls, enabling space simplification or complexification with controlled geometric properties.
Contribution
It provides a novel construction for embedding simplicial complexes into simplicial balls with bounded degrees and low volume, facilitating space manipulation.
Findings
Embedding into simplicial balls with bounded degrees
Applications in space simplification and complexification
Controlled metric properties inherited from embedded complexes
Abstract
We construct embeddings of simplicial complexes into a (surface of a) simplicial ball whose triangulation has bounded degrees and low volume. This construction can be used either to efficiently "simplify a complicated space" by realizing it as a part of a ball/sphere, or to "complexify" a sphere - to give it a specific metric that inherits desired properties from an embedded complex.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Data Management and Algorithms · Computational Geometry and Mesh Generation