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Reverse engineering of complex geometry using rational B-splines

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Abstract

Rational B-splines have become the new standard for representing free-form curves and surfaces. This paper presents a method for approximating rational B-splines using digitised data. Instead of using the classical optimisation approach to solve the multivariable nonlinear equations, a new method based on iterations of least-squares solutions and single variable mimimisation is developed. This is made possible by modifying the original objective function to avoid the rational format. Simulation of fitting a 90° arc shows that the algorithm can produce accurate solutions close to nominal values. The efficiency of the algorithm also makes it possible to apply the method to day-to-day reverse engineering problems using rational B-splines.

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Chung Cheng University, Cha-Yi, Taiwan

    Hong-Tzong Yau & Jenq-Shyong Chen

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  1. Hong-Tzong Yau
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  2. Jenq-Shyong Chen
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Yau, HT., Chen, JS. Reverse engineering of complex geometry using rational B-splines. Int J Adv Manuf Technol 13, 548–555 (1997). https://doi.org/10.1007/BF01176298

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  • DOI: https://doi.org/10.1007/BF01176298

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