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Controlled-Distortion Constrained Global Parametrization
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DOI：10.1145/2461912.2461970.png)
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Abstract
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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 compared to the state-of-the art field-based method, yet maintain feature and boundary alignment. In the most extreme cases, parametrization collapse due to alignment constraints is eliminated.
Keywords:
geometric modeling
parametrization
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9.5
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