Unconstrained and constrained curve fitting for reverse engineering

Wen Der Ueng, Jiing Yih Lai, Yao Chen Tsai

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

Curve fitting is commonly used in reverse engineering for the reconstruction of curves from measured points, and it is critically important to provide various kinds of curve-fitting algorithms to acquire curves that satisfy different constraint conditions. We divide the curve-fitting problem into unconstrained and constrained types. For the unconstrained type, three curve-fitting algorithms are investigated: general, smooth and extended curve fitting. The general curve fitting considers only the accuracy of the fitted curve; the smooth curve fitting can control both the accuracy and the fairness of the fitted curve, while the extended curve fitting can acquire a curve longer than the range of the measured points. For the constrained type, we propose three curve-fitting conditions: fixed end-points, closed curve and continuity to adjacent curves. Detailed discussion for each of the above cases is presented. Associated examples are also provided to illustrate the feasibility of the proposed algorithms.

Original languageEnglish
Pages (from-to)1189-1203
Number of pages15
JournalInternational Journal of Advanced Manufacturing Technology
Volume33
Issue number11-12
DOIs
StatePublished - Aug 2007

Keywords

  • Constrained curve fitting
  • Smooth curve fitting
  • Unconstrained curve fitting

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