Bounded Distortion Mapping Spaces for Triangular Meshes

Lipman, Yaron

doi:10.1145/2185520.2185604

2012-07-01

PRE

Lipman, Yaron *

DOI：10.1145/2185520.2185604

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摘要

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The problem of mapping triangular meshes into the plane is fundamental in geometric modeling, where planar deformations and surface parameterizations are two prominent examples. Current methods for triangular mesh mappings cannot, in general, control the worst case distortion of all triangles nor guarantee injectivity. This paper introduces a constructive definition of generic convex spaces of piecewise linear mappings with guarantees on the maximal conformal distortion, as-well as local and global injectivity of their maps. It is shown how common geometric processing objective functionals can be restricted to these new spaces, rather than to the entire space of piecewise linear mappings, to provide a bounded distortion version of popular algorithms.

Keyword:

triangular meshes

bounded distortion

conformal distortion

quasi-conformal

bijective mapping

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期刊

ACM Transactions on Graphics

IF:

9.5

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4.7K

被引数:

3.6W

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