Dual Sheet Meshing: An Interactive Approach to Robust Hexahedralization

Abstract

The combinatorial dual of a hex mesh induces a collection of mutually intersecting surfaces (dual sheets). Inspired by Campen et al.'s work on quad meshing [CBK12,CK14], we propose to directly generate such dual sheets so that, as long as the volume is properly partitioned by the dual sheets, we are guaranteed to arrive at a valid all-hex mesh topology. Since automatically generating dual sheets seems much harder than the 2D counterpart, we chose to leave the task to the user; our system is equipped with a few simple 3D modeling tools for interactively designing dual sheets. Dual sheets are represented as implicit surfaces in our approach, greatly simplifying many of the computational steps such as finding intersections and analyzing topology. We also propose a simple algorithm for primalizing the dual graph where each dual cell, often enclosing singular edges, gets mapped onto a reference polyhedron via harmonic parameterization. Preservation of sharp features is simply achieved by modifying the boundary conditions. We demonstrate the feasibility of our approach through various modeling examples.