Dual Sheet Meshing: An Interactive Approach to Robust Hexahedralization

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,...

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Bibliographic Details
Published in:Computer Graphics Forum Vol. 38; no. 2; pp. 37 - 48
Main Author: Takayama, Kenshi
Format: Journal Article
Language:English
Japanese
Published: Oxford Wiley 01.05.2019
Blackwell Publishing Ltd
Subjects:
Algorithms
Boundary conditions
CCS Concepts
Combinatorial analysis
Computing methodologies → Mesh models
Finite element method
Graph theory
Intersections
Mesh generation
Mesh geometry models
Parameterization
Sheets
Three dimensional models
Topology
Volumetric models
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary: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.
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.13617