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A new approach for lofted B-spline surface interpolation to serial contours

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Abstract

This paper addresses the problem of B-spline surface interpolation to serial contours, where the number of points varies from contour to contour. A traditional approach to the problem creates a set of B-spline curves via B-spline curve interpolation to each contour, makes them compatible via degree elevation and knot insertion and performs B-spline surface lofting to get a B-spline surface that interpolates them. The approach tends to result in an astonishing number of control points in the lofted B-spline surface. This situation arises mainly from the inevitable process of progressively merging different knot vectors to make the B-spline curves compatible. This paper presents a new approach for fixing this problem. The approach includes a novel process of obtaining a set of compatible B-spline curves from the given contours. The process is based on universal parameterisation [1, 2], allowing the knots to be selected freely but leading to a more stable linear system for B-spline curve interpolation. Since the number of control points in each compatible B-spline curve is equal to the highest number of contour points, the proposed approach can realise efficient data reduction and provide a compact representation of a lofted B-spline surface while keeping the desired surface shape. Some experimental results demonstrate its usefulness and quality.

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Acknowledgements

This study was supported in part by research funds from Chosun University, 2002.

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Authors and Affiliations

  1. Department of Industrial Engineering, Chosun University, Gwangju 501-759, South Korea

    H. Park

  2. Department of Naval Architecture and Ocean Engineering, Mokpo National University, Mokpo 534-729, South Korea

    H. B. Jung

  3. Department of Industrial Engineering, Pohang University of Science and Technology, Pohang 790-784, South Korea

    K. Kim

Authors
  1. H. Park
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  2. H. B. Jung
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  3. K. Kim
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Correspondence to H. Park.

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Park, H., Jung, H.B. & Kim, K. A new approach for lofted B-spline surface interpolation to serial contours. Int J Adv Manuf Technol 23, 889–895 (2004). https://doi.org/10.1007/s00170-003-1720-0

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  • DOI: https://doi.org/10.1007/s00170-003-1720-0

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