An improved Hoschek intrinsic parametrization

Smoothing a set of points pi with a B-spline curve is an usual CAGD application, which remains an open problem due to the choice of the parameter values. J. Hoschek proposed one of the first iterative solution called intrinsic parametrization. This idea has been improved several times by introducing different parameter corrections. This paper deals with a new improvement of Hoschek's method providing better results with a higher speed of convergence. Examples are proposed and compared with the different approaches.

[1]  Michel Bercovier,et al.  Curve and surface fitting and design by optimal control methods , 2001, Comput. Aided Des..

[2]  Josef Hoschek,et al.  Intrinsic parametrization for approximation , 1988, Comput. Aided Geom. Des..

[3]  Eric Saux,et al.  Data reduction of polygonal curves using B-splines , 1999, Comput. Aided Des..

[4]  D. F. Rogers.  Constrained B-spline curve and surface fitting , 1989 .

[5]  Michel Bercovier,et al.  Spline Curve Approximation and Design by Optimal Control Over the Knots , 2004, Computing.

[6]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[7]  B. V. Shah,et al.  Integer and Nonlinear Programming , 1971 .

[8]  Josef Hoschek,et al.  Global reparametrization for curve approximation , 1998, Comput. Aided Geom. Des..

[9]  Panagiotis D. Kaklis,et al.  Advanced Course on FAIRSHAPE , 2012, Vieweg+Teubner Verlag.

[10]  E. T. Y. Lee,et al.  Choosing nodes in parametric curve interpolation , 1989 .

[11]  Josef Hoschek,et al.  Spline conversion for trimmed rational Bézier- and B-spline surfaces , 1990, Comput. Aided Des..

[12]  Gregory M. Nielson,et al.  Knot selection for parametric spline interpolation , 1989 .

[13]  Caiming Zhang,et al.  A method for determining knots in parametric curve interpolation , 1998, Comput. Aided Geom. Des..

[14]  Josef Hoschek,et al.  Optimal approximate conversion of spline surfaces , 1989, Comput. Aided Geom. Des..

[15]  Ulrich Dietz.  B-Spline Approximation with Energy Constraints , 1996, Advanced Course on FAIRSHAPE.

[16]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[17]  Tom Lyche,et al.  Mathematical methods in computer aided geometric design , 1989 .

[18]  M. Al-Baali.  Descent Property and Global Convergence of the Fletcher—Reeves Method with Inexact Line Search , 1985 .

[19]  Joachim Rix,et al.  Modelling and graphics in science and technology , 1996 .