Searching geometry-aware pants decomposition in different isotopy classes

We propose an optimization framework to compute the desirable pants decomposition of surfaces. A pants decomposition partitions a surface into a set of genus-0 sub-patches with 3 boundaries. Any surface with non-trivial topology admits infinitely many pants decompositions that are isotopically inequivalent. We traverse different classes of pants decompositions to search for the optimal one with the pre-determined geometric criterion. Our proposed framework is general, and can be used to construct different suitable segmentations according to different applications. We also generalize this algorithm for consistent decomposition of multiple surfaces, which can be used to construct compatible cross-surface parameterization.