윤곽선들의 B-spline 곡면 보간을 위한 새로운 방식

A new approach for B-spline surface interpolation to contours

  • 박형준 (조선대학교 산업공학과) ;
  • 정형배 (목포대학교 선박해양공학과) ;
  • 김광수 (포항공과대학교 산업공학과)
  • Park Hyungjun (Department of Industrial Engineering, Chosun University) ;
  • Jung Hyung Bae (Department of Naval Architecture and Ocean Engineering, Mokpo National University) ;
  • Kim Kwangsoo (Department of Industrial Engineering, Pohang University of Science and Technology)
  • 발행 : 2003.05.01

초록

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 lofting approach 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 interpolating them. The approach tends to result in an astonishing number of control points in the resulting 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 avoiding this troublesome situation. The approach includes a novel process of getting a set of compatible B-spline curves from the given contours. The process is based on the universal parameterization [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 realize efficient data reduction and provide a compact representation of a B-spline surface while keeping the desired surface shape. Some experimental results demonstrate its usefulness and quality.

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