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Approximation of high-degree and procedural curves

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Abstract

The objective of this paper is to present an efficient adaptive algorithm to approximate high-degree and procedural continuous parametric curves by integral B-splines. This approximation algorithm covers nonperiodic and periodic curves. The approximation algorithm is motivated and accompanied by an extensive discussion on approximation errors for position and derivatives accuracies. This discussion includes the derivation of local error bounds for position and derivative errors. The practicality and efficiency of the algorithm is demonstrated for a variety of examples in geometric modeling of engineering structures. The approximation algorithm for the curve forms the basis of a similar surface approximation procedure.

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Authors and Affiliations

  1. Department of Ocean Engineering, Design Laboratory, MIT, Room 5-426-A, 77, Massachusetts Avenue, 02139, Cambridge, Massachussetts, USA

    Franz-Erich Wolter & Séamus T. Tuohy

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  1. Franz-Erich Wolter
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  2. Séamus T. Tuohy
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Wolter, FE., Tuohy, S.T. Approximation of high-degree and procedural curves. Engineering with Computers 8, 61–80 (1992). https://doi.org/10.1007/BF01200103

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