Seamless Parametrization with Cone and Partial Loop Control

We present a method for constructing seamless parametrization surfaces of any genus, which can handle feasible cone configuration with type cones. The mapping is guaranteed to be locally injective, due careful construction simple domain boundary polygon. polygon’s complexity depends on the cones in field, and it independent mesh geometry. result small polygon that optimized prior interior mapping, contributes robustness pipeline. For surface genus > 0, non-contractible loops play an important role, their holonomies significantly affect quality. enable holonomy prescription, where local injectivity guaranteed. Our however, limited cannot all monotonicity constraints keep our simple. Yet, this work step towards fully solving prescription problem.