Journal of the Korea Computer Graphics Society (한국컴퓨터그래픽스학회논문지)

Korea Computer Graphics Society (한국컴퓨터그래픽스학회)
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Knot Removal of B-spline Curves using Hausdorff Distance

하우스도르프 거리를 이용한 B-spline 곡선의 낫제거

  • Oh, Jong-Seok (Department of Multimedia Engineering, Dongguk University) ;
  • Yoon, Seung-Hyun (Department of Multimedia Engineering, Dongguk University)
  • 오종석 (동국대학교 대학원 멀티미디어공학과) ;
  • 윤승현 (동국대학교 대학원 멀티미디어공학과)
  • Received : 2011.07.18
  • Accepted : 2011.08.26
  • Published : 2011.09.01
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Abstract

We present a new technique for removing interior knots of parametric B-spline curves. An initial curve is constructed by continuous $L_{\infty}$ approximation proposed by Eck and Hadenfeld. We employ Hausdorff distance to measure the shape difference between the original curve and the initial one. The final curve is obtained by minimizing their Hausdorff distance. We demonstrate the effectiveness of our technique with experimental results on various types of planar and spatial curves.

본 논문에서는 B-spline 곡선의 낫 제거 (knot removal)를 위한 새로운 기법을 제안한다. 제안된 기법은 낫 제거 전후, 두 곡선의 형상의 차이를 측정하기 위해 하우스도르프 거리 (Hausdorff distance)를 이용한다. 먼저 Eck와 Hadenfeld의 연속 $L_{\infty}$ 근사법[1]을 이용하여 낫이 제거된 곡선을 생성한다. 수치적 최적화 (numerical optimization) 기법을 통해 생성된 곡선의 제어점 위치를 조정하여, 낫 제거 전 곡선과의 하우스도르프 거리가 최소화 되도록 한다. 본 논문에서는 다양한 형태와 차수의 곡선들(space curves)에 대한 낫 제거 실험을 통해 제안된 기법의 효율성과 우수성을 입증한다.

Keywords

References

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