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The Power of Orthogonal Duals (Invited Talk)

Desbrun, Mathieu and de Goes, Fernando (2014) The Power of Orthogonal Duals (Invited Talk). In: Mathematical Progress in Expressive Image Synthesis I. Mathematics for Industry. No.4. Springer , Tokyo, Japan, pp. 3-6. ISBN 978-4-431-55006-8.

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Triangle meshes have found widespread acceptance in computer graphics as a simple, convenient, and versatile representation of surfaces. In particular, computing on such simplicial meshes is a workhorse in a variety of graphics applications. In this context, mesh duals (tied to Poincaré duality and extending the well known relationship between Delaunay triangulations and Voronoi diagrams) are often useful, be it for physical simulation of fluids or parameterization. However, the precise embedding of a dual diagram with respect to its triangulation (i.e., the placement of dual vertices) has mostly remained a matter of taste or a numerical after-thought, and barycentric versus circumcentric duals are often the only options chosen in practice. In this chapter we discuss the notion of orthogonal dual diagrams, and show through a series of recent works that exploring the full space of orthogonal dual diagrams to a given simplicial complex is not only powerful and numerically beneficial, but it also reveals (using tools from algebraic topology and computational geometry) discrete analogs to continuous properties.

Item Type:Book Section
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Desbrun, Mathieu0000-0003-3424-6079
Additional Information:© 2014 Springer. 30 May 2014. Pooran Memari, Patrick Mullen, Houman Owhadi, and Pierre Alliez have significantly contributed to various parts of this work.
Subject Keywords:Orthogonal dual · Blue noise · Masonry structure · Discrete exterior calculus
Series Name:Mathematics for Industry
Issue or Number:4
Record Number:CaltechAUTHORS:20170622-124548469
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78466
Deposited By: Ruth Sustaita
Deposited On:22 Jun 2017 20:49
Last Modified:03 Mar 2020 13:01

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