214
Views
2
CrossRef citations to date
0
Altmetric
Section B

G2 curve design with planar quadratic rational Bézier spiral segments

&
Pages 325-340 | Received 12 Dec 2011, Accepted 25 Jul 2012, Published online: 03 Sep 2012

References

  • Baass , K. G. 1984 . The use of clothoid templates in highway design . Transp. Forum , 1 : 47 – 52 .
  • Farin , G. 1997 . Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide , 4 , San Diego , CA : Academic Press .
  • Fleury , S. , Soures , P. , Laumond , J.-P. and Chatila , R. 1995 . Primitives for smoothing mobile robot trajectories . IEEE Trans. Robot. Autom. , 11 : 441 – 448 . (doi:10.1109/70.388788)
  • Frey , W. H. and Field , D. A. 2000 . Designing Bézier conic sections with monotone curvature . Comput. Aided Geom. Design , 17 : 457 – 483 . (doi:10.1016/S0167-8396(00)00011-X)
  • Hartman , R. 1957 . The highway spiral for combining curves of different radii . Trans. Amer. Soc. Civil Eng. , 22 : 389 – 409 .
  • Higashi , M. , Kaneko , K. and Hosaka , M. 1988 . “ Generation of high quality curve and surface with smoothly varying curvature ” . In Eurographics’88, Nice, France , Edited by: Duce , D. A. and Jancene , P. 79 – 92 . Amsterdam : Elsevier Science Publishers B.V .
  • Levien , R. and Séquin , C. H. 2009 . Interpolating splines: Which is the fairest of them all? . Comput.-Aided Des. Appl. , 6 : 91 – 102 .
  • Li , Z. , Ma , L. , Meek , D. , Tan , W. , Mao , Z. and Zhao , M. 2006 . “ Curvature monotony condition for rational quadratic B-spline curves ” . In ICCSA 2006, LNCS 3980M , Edited by: Gavrilova , M. L. , Gervasi , O. , Kumar , V. , Tan , C. J.K. , Taniar , D. , Laganá , A. , Mun , Y. and Choo , H. 1118 – 1126 . Berlin : Springer-Verlag .
  • Mineur , Y. , Lichah , T. , Castelain , J. M. and Giaume , H. 1998 . A shape controlled fitting method for Bézier curves . Comput. Aided Geom. Design , 15 : 879 – 891 . (doi:10.1016/S0167-8396(98)00025-9)
  • Piegl , L. and Tiller , W. 1997 . The NURBS Book , 2 , New York : Springer-Verlag .
  • Piegl , L. A. , Rajab , K. , Smarodzinava , V. and Valavanis , K. P. 2009 . Using a biarc filter to compute curvature extremes of NURBS curves . Eng. Comput. , 25 : 379 – 387 . (doi:10.1007/s00366-009-0131-8)
  • Walton , D. J. and Meek , D. S. 1996 . A triangular G 1 patch from boundary curves . Comput.-Aided Des. , 28 : 113 – 23 . (doi:10.1016/0010-4485(95)00046-1)
  • Walton , D. J. and Meek , D. S. 1996 . A planar cubic Bézier spiral . J. Comput. Appl. Math. , 72 : 85 – 100 . (doi:10.1016/0377-0427(95)00246-4)
  • Walton , D. J. and Meek , D. S. 1998 . G 2 curves composed of planar cubic and Pythagorean hodograph quintic spirals . Comput. Aided Geom. Design , 15 : 547 – 566 . (doi:10.1016/S0167-8396(97)00028-9)
  • Walton , D. J. and Meek , D. S. 1998 . Planar G 2 curve design with spiral segments . Comput.-Aided Des. , 30 : 529 – 538 . (doi:10.1016/S0010-4485(98)00007-4)
  • Walton , D. J. and Meek , D. S. 2009 . G 2 blends of linear segments with cubics and Pythagorean-hodograph quintics . Int. J. Comput. Math. , 86 : 1498 – 1511 . (doi:10.1080/00207160701828157)
  • Walton , D. J. and Meek , D. S. 2010 . “ Cubic Bézier spiral segments for planar G 2 curve design ” . In Proceedings of the 7th International Conference on Computer Graphics, Virtual Reality, Visualisation and Interaction in Africa (Afrigraph 2010), Franschoek, South Africa , Edited by: Gain , J. E. and Marais , P. 21 – 25 . New York : ACM, (Association for Computing Machinery, Inc .
  • Walton , D. J. and Meek , D. S. 2010 . G 2 Hermite interpolation with circular precision . Comput.-Aided Des. , 42 : 749 – 758 . (doi:10.1016/j.cad.2010.04.004)
  • Walton , D. J. and Meek , D. S. 2012 . A further generalisation of the planar cubic Bézier spiral . J. Comput. Appl. Math. , 236 : 2869 – 2882 . (doi:10.1016/j.cam.2012.01.024)
  • Walton , D. J. , Meek , D. S. and Ali , J. M. 2003 . Planar G 2 transition curves composed of cubic Bézier spiral segments . J. Comput. Appl. Math. , 157 : 453 – 476 . (doi:10.1016/S0377-0427(03)00435-7)

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.