Controlled-distortion constrained global parametrization
| Autor: | Ashish Myles, Denis Zorin |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | ACM Transactions on Graphics. 32:1-14 |
| ISSN: | 1557-7368 0730-0301 |
| DOI: | 10.1145/2461912.2461970 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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