Journal of the Korean Society for Precision Engineering (한국정밀공학회지)

Korean Society for Precision Engineering (한국정밀공학회)
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An Investigation on the Computing Offsets of Free form Curve using the Biarc Approximation Method

이중원호 근사법을 이용한 자유형상곡선의 오프셋 계산에 관한 연구

  • 유동진 (대진대학교 컴퓨터응용기계설계공학과)
  • Published : 2005.08.01
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Abstract

In this study a general method for computing offsets of free form curves is presented. In the method arbitrary free form curve is approximated with point series considering required tolerance. The point series are offset precisely using the normal vectors computed at each point and loop removal is carried out by the newly suggested algorithm. The resulting offset points are transformed to lines and arcs using the biarc approximation method. Tangent vectors for approximation of discrete points data are calculated by traditional local interpolation scheme. In order to show the validity and generality of the proposed method , various of offsettings are carried our for the base curves with complex shapes.

Keywords

References

  1. Tiller, W. and Hanson, E.G., 'Offsets of twodimensional profiles,' IEEE Computer Graphics and Application, Vol. 4, pp. 61-69, 1984 https://doi.org/10.1109/MCG.1984.275995
  2. Hoschek, J. and Wissel, N., 'Optimal approximate conversion of spline curves and spline approximation of offset curves,' Computer Aided Design, Vol. 20, pp. 475-483, 1988 https://doi.org/10.1016/0010-4485(88)90006-1
  3. Hoschek, J., 'Spline approximation of offset curves,' Computer Aided Geometric Design, Vol. 5, pp. 33-40, 1988 https://doi.org/10.1016/0167-8396(88)90018-0
  4. Coquillart, S., 'Computing offsets of B-spline curves,' Computer Aided Design, Vol. 19, pp. 305-309, 1987 https://doi.org/10.1016/0010-4485(87)90284-3
  5. Pham, B., 'Offset approximation of uniform B-splines,' Computer Aided Design, Vol. 20, pp. 471-474, 1988 https://doi.org/10.1016/0010-4485(88)90005-X
  6. Meek, D.S. and Walton, D.J., 'Offset curves of clothoidal splines,' Computer Aided Design, Vol. 22, pp. 199-201, 1990 https://doi.org/10.1016/0010-4485(90)90048-H
  7. Sederberg, T.W. and Buehler, D.B., 'Offset of polynomial Bezier curves : Hermite approximation with error bounds,' Mathematical methods in computer aided geometric design II. San Diego, CA : Academic Press, pp. 549-558, 1992
  8. Wolter, F.E and Tuohy, S.T., 'Approximation of high-degree and procedural curves,' Engineering with Computers, Vol. 8, pp. 61-80, 1992 https://doi.org/10.1007/BF01200103
  9. Piegl, L. and Tiller, W., 'Computing offsets of NURBS curves and surfaces,' Computer Aided Design, Vol. 31, pp. 147-156, 1999 https://doi.org/10.1016/S0010-4485(98)00066-9
  10. Faux, I.D. and Pratt, M.J., 'Computational geometry for design and manufacture, John Wiley & Sons, 1981
  11. Piegl, L. and Tiller, W., 'Data approximation using biarcs,' Engineering with Computers, Vol. 18, pp. 59-65, 2002 https://doi.org/10.1007/s003660200005