Seamless Global Parametrization in a Single Optimization
Résumé
The challenge of computing high quality seamless parametrizations is to account for both the optimal placement of singularity cones and distortion minimization. Existing methods rely either on greedy solvers or on a simplified two steps problem, first finding the cone positions using a cross field and second optimizing the parametrization under fixed topology. Both approaches, however, loosen the link between cone placement and distortion, effectively leading to suboptimal solutions. We instead formulate the problem of global seamless parametrization as a single continuous optimization problem where singularities may appear anywhere inside triangles. To achieve this, the input mesh is subdivided into charts centered at vertices whose orientations are related by rotations along edges. We then exhibit a set of continuous constraints for the parametrization to be seamless, locally injective and aligned with feature and boundary edges. Formulated as a non-linear least-squares problem, these constraints can be easily optimized. We compare our algorithm to previous techniques on a variety of smooth and CAD models, often achieving lower distortion and more practical cone placement for subsequent quad remeshing.
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