We construct smooth parameterizations of irregular connectivity triangulations of arbitrary genus 2-manifolds. Our algorithm uses hierarchical simplification to efficiently induce a parameterization of the original mesh over a base domain consisting of a small number of triangles. This initial parameterization is further improved through a hierarchical smoothing procedure based on Loop subdivision applied in the parameter domain. Our method supports both fully automatic and user constrained operations. In the latter, we accommodate point and edge constraints to force the align-
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