Computing Surface PolyCube-Maps by Constrained Voxelization

Abstract

We present a novel method to compute bijective PolyCube-maps with low isometric distortion. Given a surface and its preaxis- aligned shape that is not an exact PolyCube shape, the algorithm contains two steps: (i) construct a PolyCube shape to approximate the pre-axis-aligned shape; and (ii) generate a bijective, low isometric distortion mapping between the constructed PolyCube shape and the input surface. The PolyCube construction is formulated as a constrained optimization problem, where the objective is the number of corners in the constructed PolyCube, and the constraint is to bound the approximation error between the constructed PolyCube and the input pre-axis-aligned shape while ensuring topological validity. A novel erasing-and-filling solver is proposed to solve this challenging problem. Centeral to the algorithm for computing bijective PolyCube-maps is a quad mesh optimization process that projects the constructed PolyCube onto the input surface with high-quality quads. We demonstrate the efficacy of our algorithm on a data set containing 300 closed meshes. Compared to state-of-the-art methods, our method achieves higher practical robustness and lower mapping distortion.