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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Vydáno v:	Computer Graphics Forum Ročník 38; číslo 2; s. 37 - 48
Hlavní autor:	Takayama, Kenshi
Médium:	Journal Article
Jazyk:	angličtina japonština
Vydáno:	Oxford Wiley 01.05.2019 Blackwell Publishing Ltd
Témata:	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
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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.
AbstractList	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. 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.
Author	Kenshi Takayama
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Snippet	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... 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...
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SubjectTerms	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
Title	Dual Sheet Meshing: An Interactive Approach to Robust Hexahedralization
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