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Flattening topologically spherical surface

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Abstract

The problem of optimal surface flattening in 3-D finds many applications in engineering and manufacturing. However, previous algorithms for this problem are all heuristics without any quality guarantee and the computational complexity of the problem was not well understood. In this paper, we prove that the optimal surface flattening problem is NP-hard. Further, we show that the problem of flattening a topologically spherical surface admits a PTAS and can be solved by a (1+ε)-approximation algorithm in O(nlog n) time for any constant ε>0, where n is the input size of the problem.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    Danny Z. Chen

  2. Mathematics Department, Saint Mary’s College, Notre Dame, IN, 46556, USA

    Ewa Misiołek

Authors
  1. Danny Z. Chen
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  2. Ewa Misiołek
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Corresponding author

Correspondence to Ewa Misiołek.

Additional information

This research was supported in part by the National Science Foundation under Grants CCF-0515203, CCF-0916606.

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Chen, D.Z., Misiołek, E. Flattening topologically spherical surface. J Comb Optim 23, 309–321 (2012). https://doi.org/10.1007/s10878-010-9296-8

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  • DOI: https://doi.org/10.1007/s10878-010-9296-8

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