A robust surface fitting and reconstruction algorithm for form characterization of ultra-precision freeform surfaces

M. J. Ren, Chi Fai Cheung, L. B. Kong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

10 Citations (Scopus)


Ultra-precision freeform surfaces are non-rotational symmetric surfaces possessing sub-micrometer form accuracy and nanometric surface finish. Although they can be fabricated accurately by ultra-precision machining technology, their surface quality is difficult to be characterized. Surface reconstruction is a vital task in the form characterization of ultra-precision freeform surfaces. This paper presents a robust surface fitting algorithm to reconstruct a high fidelity surface from measured discrete points while the surface smoothness can be ensured as well. A fitting threshold named confidence interval of fitting error is proposed to strike the balance between fitting accuracy and surface smoothness in the fitting process. The fitting algorithm is in two steps. In the first step, bidirectional sampling method is developed to extract a curve network from measured points cloud to construct an initial surface. In the second step, the fitting error of the initial surface is minimized to meet the prescribed fitting error threshold. A series of experimental work has been conducted and the results show that the proposed algorithm is able to provide effective means for increasing the accuracy in the form characterization of ultra-precision freeform surfaces.
Original languageEnglish
Pages (from-to)2068-2077
Number of pages10
JournalMeasurement: Journal of the International Measurement Confederation
Issue number10
Publication statusPublished - 1 Dec 2011


  • Freeform surfaces
  • Precision engineering
  • Precision metrology
  • Precision surface measurement
  • Robust surface fitting
  • Ultra-precision machining

ASJC Scopus subject areas

  • Instrumentation
  • Electrical and Electronic Engineering

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