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Optimal fitting of strain-controlled flattenable mesh surfaces

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Abstract

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 P∈R 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.

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Authors and Affiliations

  1. School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA

    Yunbo Zhang & Karthik Ramani

  2. Department of Mechanical and Automation Engineering, The Chinese Univerity of Hong Kong, Sha Tin, Hong Kong

    Yunbo Zhang & Charlie C. L. Wang

  3. Shenzhen Institues of Advanced Technology, Shenzhen, China

    Charlie C. L. Wang

Authors
  1. Yunbo Zhang
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  2. Charlie C. L. Wang
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  3. Karthik Ramani
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Correspondence to Yunbo Zhang.

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Zhang, Y., Wang, C.C.L. & Ramani, K. Optimal fitting of strain-controlled flattenable mesh surfaces. Int J Adv Manuf Technol 87, 2873–2887 (2016). https://doi.org/10.1007/s00170-016-8669-2

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  • DOI: https://doi.org/10.1007/s00170-016-8669-2

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