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Computational Visual Media

, Volume 4, Issue 4, pp 305–321 | Cite as

Deforming generalized cylinders without self-intersection by means of a parametric center curve

  • Ruibin Ma
  • Qingyu Zhao
  • Rui Wang
  • James Damon
  • Julian Rosenman
  • Stephen Pizer
Open Access
Research Article
  • 47 Downloads

Abstract

Large-scale deformations of a tubular object, or generalized cylinder, are often defined by a target shape for its center curve, typically using a parametric target curve. This task is non-trivial for free-form deformations or direct manipulation methods because it is hard to manually control the centerline by adjusting control points. Most skeleton-based methods are no better, again due to the small number of manually adjusted control points. In this paper, we propose a method to deform a generalized cylinder based on its skeleton composed of a centerline and orthogonal cross sections. Although we are not the first to use such a skeleton, we propose a novel skeletonization method that tries to minimize the number of intersections between neighboring cross sections by means of a relative curvature condition to detect intersections. The mesh deformation is first defined geometrically by deforming the centerline and mapping the cross sections. Rotation minimizing frames are used during mapping to control twisting. Secondly, given displacements on the cross sections, the deformation is decomposed into finely subdivided regions. We limit distortion at these vertices by minimizing an elastic thin shell bending energy, in linear time. Our method can handle complicated generalized cylinders such as the human colon.

Keywords

generalized cylinder deformation skeleton self-intersection 

Notes

Acknowledgements

We gratefully thank Dr. Saad Nadeem and Dr. Arie Kaufman from Stony Brook University and Dr. Sarah McGill from UNC Medical School for sharing their results, data, and suggestions. This work was supported by National Institutes of Health grant R01 CA158925.

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© The Author(s) 2018

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Authors and Affiliations

  • Ruibin Ma
    • 1
  • Qingyu Zhao
    • 1
  • Rui Wang
    • 1
  • James Damon
    • 2
  • Julian Rosenman
    • 3
    • 1
  • Stephen Pizer
    • 1
    • 3
  1. 1.Computer ScienceUniversity of North Carolina at Chapel HillChapel HillUSA
  2. 2.MathematicsUniversity of North Carolina at Chapel HillChapel HillUSA
  3. 3.Radiation OncologyUniversity of North Carolina at Chapel HillChapel HillUSA

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