"Lecture notes prepared for the American Mathematical Society course Discrete Differential Geometry held in San Diego, California, January 8-9, 2018." Includes bibliographical references.
Contents:
Discrete Laplace operators / Max Wardetzky -- Discrete parametric surfaces / Johannes Wallner -- Discrete mappings / Yaron Lipman -- Conformal geometry of simplicial surfaces / Keenan Crane -- Optimal transport on discrete domains / Justin Solomon.
Summary:
Discrete Differential Geometry (DDG) is an emerging discipline at the boundary between mathematics and computer science. It aims to translate concepts from classical differential geometry into a language that is purely finite and discrete, and can hence be used by algorithms to reason about geometric data. In contrast to standard numerical approximation, the central philosophy of DDG is to faithfully and exactly preserve key invariants of geometric objects at the discrete level. This process of translation from smooth to discrete helps to both illuminate the fundamental meaning behind geometric ideas and provide useful algorithmic guarantees.--Provided by publisher.
Series:
Proceedings of symposia in applied mathematics ; volume 76
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