Optimal development of doubly curved surfaces

Guoxin Yu, Nicholas M. Patrikalakis, Takashi Maekawa

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)


This paper presents algorithms for optimal development (flattening) of a smooth continuous curved surface embedded in three-dimensional space into a planar shape. The development process is modeled by in-plane strain (stretching) from the curved surface to its planar development. The distribution of the appropriate minimum strain field is obtained by solving a constrained nonlinear programming problem. Based on the strain distribution and the coefficients of the first fundamental form of the curved surface, another unconstrained nonlinear programming problem is solved to obtain the optimal developed planar shape. The convergence and complexity properties of our algorithms are analyzed theoretically and numerically. Examples show the effectiveness of the algorithms.

Original languageEnglish
Pages (from-to)545-577
Number of pages33
JournalComputer Aided Geometric Design
Issue number6
Publication statusPublished - 2000 Jul
Externally publishedYes

ASJC Scopus subject areas

  • Modelling and Simulation
  • Automotive Engineering
  • Aerospace Engineering
  • Computer Graphics and Computer-Aided Design


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