Optimal fitting of strain-controlled flattenable mesh surfaces

  • Yunbo ZhangEmail author
  • Charlie C. L. Wang
  • Karthik Ramani


A flattenable mesh surface is a polygonal mesh surface that can be unfolded into a planar patch without stretching any polygon. This paper presents a new method for computing a slightly stretched flattenable mesh surface M from a piecewise-linear surface patch PR 3, where the shape approximation error between M and P is minimized and the strain of stretching on M is controlled. Prior approaches result in either a flattenable surface that could be quite different from the input shape or a (discrete) developable surface has relative simple shape. The techniques investigated in this paper overcome these difficulties. First, we introduce a new surface modeling method to conduct a sequence of nearly isometric deformations to morph a flattenable mesh surface to a new shape which has a better approximation of the input surface. Second, in order to get better initial surfaces for fitting and overcome topological obstacles, a shape perturbation scheme is investigated to obtain the optimal surface fitting result. Last, to improve the scalability of our optimal surface fitting algorithm, a coarse-to-fine fitting framework is exploited so that very dense flattenable mesh surfaces can be modeled and boundaries of the input surfaces can be interpolated.


Surface approximation Flattenable mesh surface Optimization Stretching controlled Coarse-to-fine fitting 


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Copyright information

© Springer-Verlag London 2016

Authors and Affiliations

  • Yunbo Zhang
    • 1
    • 2
    Email author
  • Charlie C. L. Wang
    • 2
    • 3
  • Karthik Ramani
    • 1
  1. 1.School of Mechanical EngineeringPurdue UniversityWest LafayetteUSA
  2. 2.Department of Mechanical and Automation EngineeringThe Chinese Univerity of Hong KongSha TinHong Kong
  3. 3.Shenzhen Institues of Advanced TechnologyShenzhenChina

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