A second-order algorithm for curve orthogonal projection onto parametric surface

References

• Alexa , M. and Adamson , A. On normals and projection operators for surfaces defined by point sets . Proceedings of Eurographics Symposium on Point-based Graphics . Zurich, Switzerland.
   Google Scholar
• Azariadis , P. N. and Sapidis , N. S. 2005 . Drawing curves onto a cloud of points for point-based modelling . Comput. Aided Design , 37 : 109 – 122 .
   Web of Science ®Google Scholar
• Besl , P. J. and McKay , N. D. 1992 . A method for registration of 3-D shapes . IEEE Trans. Pattern Anal. Mach. Intell , 14 : 239 – 256 .
   Web of Science ®Google Scholar
• Chen , X. D. , Su , H. , Yong , J. H. , Paul , J. C. and Sun , J. G. 2007 . A counterexample on point inversion and projection for NURBS curve . Comput. Aided Geom. D , 24 : 302
   Google Scholar
• Chen , X. D. , Yong , J. H. , Wang , G. Z. , Paulet , J. C. and Xu , G. 2008 . Computing the minimum distance between a point and a NURBS curve . Comput. Aided Design , 40 : 1051 – 1054 .
   Web of Science ®Google Scholar
• Du , M. C. and Liu , Y. S. 2008 . An extension on robust directed projection of points onto point clouds . Comput. Aided Design , 40 : 537 – 553 .
   Google Scholar
• Dyllong , E. and Luther , W. Distance calculation between a point and a NURBS surface . Proceedings of the 4th International Conference on Curves and Surfaces . Saint-Malo.
   Google Scholar
• Hu , S. M. and Wallner , J. 2005 . A second order algorithm for orthogonal projection onto curves and surfaces . Comput. Aided Geom. D , 22 : 251 – 260 .
   Web of Science ®Google Scholar
• Limaiem , A. and Trochu , F. 1995 . Geometric algorithms for the intersection of curves and surfaces . Comput. Graphics , 19 : 391 – 403 .
   Web of Science ®Google Scholar
• Liu , Y. S. , Paul , J. C. , Yong , J. H. , Yu , P. Q. , Zhang , H. , Sun , J. G. and Ramani , K. 2006 . Automatic least-squares projection of points onto point clouds with applications in reverse engineering . Comput. Aided Design , 38 : 1251 – 1263 .
   Web of Science ®Google Scholar
• Liu , X. M. , Yang , L. , Yong , J. H. , Gu , H. J. and Sun , J. G . 2009 . A torus patch approximation approach for point projection on surfaces . Comput. Aided Geom. D , 26 : 593 – 598 .
   Web of Science ®Google Scholar
• Ma , Y. L. and Hewitt , W. T. 2003 . Point inversion and projection for NURBS curve and surface: Control polygon approach . Comput. Aided Geom. D , 20 : 79 – 99 .
   Web of Science ®Google Scholar
• Mortenson , M. E. 1985 . Geometric Modeling , New York : John Wiley & Sons .
   Google Scholar
• Pegna , J. and Wolter , F. E. 1996 . Surface curve design by orthogonal projection of space curves onto free-form surfaces . J. Mech. Design , 118 : 45 – 52 .
   Google Scholar
• Piegl , L. A. and Tiller , W. 1997 . The NURBS Book , Berlin : Springer-Verlag . Heidelberg, New York
   Google Scholar
• Piegl , L. A. and Tiller , W. 2001 . Parameterization for surface fitting in reverse engineering . Comput. Aided Design , 33 : 593 – 603 .
   Web of Science ®Google Scholar
• Selimovic , I. 2006 . Improved algorithms for the projection of points on NURBS curves and surfaces . Comput. Aided Geom. D , 23 : 439 – 445 .
   Web of Science ®Google Scholar
• Wang , X. P. , Zhang , W. Z. , Zhou , L. S. and Zhang , L. Y. 2010 . Constructing G1 continuous curve on a free-form surface with normal projection . Int. J. Comput. Math , 87 : 2291 – 2302 .
   Web of Science ®Google Scholar
• Wang , X. P. , Wei , W. and Zhang , W. Z. 2010 . Projecting curves onto free-form surfaces . Int. J. Comput. Appl. Technol , 37 : 153 – 159 .
   Google Scholar
• Wang , X. P. , Meng , Y. Q. , Wang , Z. G. and Zhang , L. Y. 2010 . Constructing up to G2 continuous curve on freeform surface . Vis. Comput , 26 : 813 – 822 .
   Google Scholar
• Zhou , J. M. , Sherbrooke , E. C. and Patrikalakis , N. 1993 . Computation of stationary points of distance functions . Eng. Comput , 9 : 231 – 246 .
   Web of Science ®Google Scholar