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Controlled-distortion Constrained Global Parametrization by Ashish Myles; Denis Zorin is a Computer Science article available to read on EtoBox.

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The quality of a global parametrization is determined by a number of factors, including amount of distortion, number of singularities (cones), and alignment with features and boundaries. Placement of cones plays a decisive role in determining the overall distortion of the parametrization; at the same time, feature and boundary alignment also affect the cone placement. A number of methods were proposed for automatic choice of cone positions, either based on singularities of cross-fields and emphasizing alignment, or based on distortion optimization. In this paper we describe a method for placing cones for seamless global parametrizations with alignment constraints. We use a close relation between variation-minimizing cross-fields and related 1-forms and conformal maps, and demonstrate how it leads to a constrained optimization problem formulation. We show for boundary-aligned parametrizations metric distortion may be reduced by __cone chains__ , sometimes to an arbitrarily small value, and the trade-off between the distortion and the number of cones can be controlled by a regularization term. Constrained parametrizations computed using our method have significantly lower distortion

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Author

Ashish Myles; Denis Zorin

Publisher

ACM

Published

2013

Language

EN

Field

Computer Science (Physical Sciences)