Geometric Reasoning in Sketch-Based Volumetric Decomposition Framework for Hexahedral Meshing

  • Jean Hsiang-Chun Lu
  • Inho Song
  • William Roshan Quadros
  • Kenji Shimada


This paper presents a sketch-based volumetric decomposition framework using geometric reasoning to assist in hex meshing. The sketch-based user interface makes the framework user-friendly and intuitive; and the geometric reasoning engine makes the framework smarter and improves the usability. The system first creates a data structure containing B-Rep and 3D medial to capture the exterior and interior of the input model, respectively. The four-step geometric reasoning process consists of (1) Determining sweeping direction and two types of sweepable regions, (2) Providing visual aids on sweeping direction and sweepable region for decomposition, (3) Understanding user’s intent by using prioritized B-Rep and medial entities, and (4) smart decomposition operation. Imprint and merge operations are then performed on the decomposed model before passing it to the sweeping algorithm to create hex meshes. The sketch-based framework has been tested on industrial models.


3D medial object geometric reasoning hexahedral meshing sketch-based decomposition 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jean Hsiang-Chun Lu
    • 1
  • Inho Song
    • 1
  • William Roshan Quadros
    • 2
  • Kenji Shimada
    • 1
  1. 1.Carnegie Mellon UniversityPittsburghUSA
  2. 2.Sandia National LaboratoriesAlbuquerqueUSA

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