Curvature Variation Based Sampling for Delaunay Triangulations of Manifolds
Offered By: Applied Algebraic Topology Network via YouTube
Course Description
Overview
Explore a 50-minute lecture on adaptive sampling techniques for Delaunay triangulations of Riemannian manifolds. Delve into new quality bounds for point clouds that ensure successful manifold triangulation, particularly effective for manifolds with locally constant non-zero sectional curvature. Examine the method's approach of comparing the manifold to a constant curvature space using a map with small metric distortion. Analyze the impact of distortion on Voronoi and Delaunay decompositions, and understand the conditions for creating a correct triangulation of the manifold. Learn about the joint work of Hana Dal Poz Kouřimská and Mathijs Wintraecken, covering topics such as good point sampling, Voronoi diagrams, and the mapping process.
Syllabus
Introduction
The procedure
What is a good point sample
The Voronoi diagram
The map
The set
Voronoi diagram
Summary
Observations
Questions
Taught by
Applied Algebraic Topology Network
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