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Section A

G2 blends of linear segments with cubics and Pythagorean-hodograph quintics

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Pages 1498-1511 | Received 07 Dec 2005, Accepted 25 Oct 2007, Published online: 22 Jul 2009

References

  • Farin , G. 1997 . Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide , 4 , San Diego, CA : Academic Press .
  • Farouki , R. T. , Manjunathaiah , J. and Yuan , G-F. 1999 . G codes for the specification of Pythagorean-hodograph tool paths and associated feedrate functions on open-architecture CNC machines . Int. J. Mach. Tools Manuf , 39 : 123 – 142 .
  • Farouki , R. T. and Neff , C. A. 1995 . Hermite interpolation by Pythagorean-hodograph quintics . Math. Computat , 64 : 1589 – 1609 .
  • Farouki , R. T. and Sakkalis , T. 1990 . Pythagorean hodographs . IBM J. Res. Dev , 34 : 736 – 752 .
  • Hoschek , J. and Lasser , D. 1993 . Fundamentals of Computer Aided Geometric Design , Wellesley, MA : A.K. Peters . (translated from German by L.L. Schumaker)
  • NURBS Interpolation . 2004 . Advanced techniques take out more cycle time . Competit. Mold Mak. , 3 ( 2 ) Available at http://www.moldmakermag.com/cgi-bin/frame it cover.pl?cover8.html (accessed 4 October 2004)
  • Smid , P. 2003 . CNC Programming Handbook , 2 , New York : Industrial Press Inc .
  • Unigraphics on NURBS . 2004 . Technical Articles . Makino , Available at http://www.makino.com/aerospace/structural components/technical articles (accessed 4 October 2004)
  • Walton , D. J. and Meek , D. S. 1998 . Planar G2 curve design with spiral segments . Comput. Aided Des. , 30 : 529 – 538 .
  • Walton , D. J. and Meek , D. S. 2001 . Curvature extrema of planar parametric polynomial cubic curves . J. Comput. Appl. Math. , 134 : 69 – 83 .
  • Walton , D. J. and Meek , D. S. 2004 . A generalisation of the Pythagorean hodograph quintic spiral . J. Comput. Appl. Math. , 172 : 271 – 287 .
  • Walton , D. J. , Meek , D. S. and Ali , J. M. 2003 . Planar G2 transition curves composed of cubic Bézier spiral segments . J. Comput. Appl. Math. , 157 : 453 – 476 .

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