Volumetric Basis Reduction for Global Seamless Parameterization of Meshes

Abstract

We present an efficient method for generating global parameterizations of large meshes. Following the state-of-the art work on global parameterization, we use a cross-field guided approach: we fit the parameterization to a field aligned with surface geometry while constraining the mapping to be seamless, in the sense of local continuity of parametric lines. We extend these approaches by showing that the constraints on the mapping can be decoupled from the mesh tessellation, allowing us to formulate the problem of seamless mesh parameterization over a general function basis. In particular, we show that by adapting a recently proposed volumetric basis, we can develop a highly efficient solver for mesh parameterization.

Using the solver, we compute parameterizations for meshes consisting of up to 20 million vertices in 1600 seconds, providing a solution that outperforms state-of-the-art direct solvers in both time and memory.