Offset Approximation Along the Offset Direction for Planar Curve

This paper proposed a wholly new offset approximation method. Based on the improvement of the best rational Chebyshev approximation theory, approximating the offset curve along the offset direction is investigated, and the approximation error is also measured along the offset direction, which could reflect the real approximation effect. Experiments show that the proposed method has advantage of low complexity, high precision, and global error control.

[1]  Michael S. Floater.  An O(h2n) Hermite approximation for conic sections , 1997, Comput. Aided Geom. Des..

[2]  Josef Hoschek,et al.  Spline approximation of offset curves , 1988, Comput. Aided Geom. Des..

[3]  Farhad Arbab,et al.  An algorithm for generating NC tool paths for arbitrarily shaped pockets with islands , 1992, TOGS.

[4]  Wang Guo-jin,et al.  Rational offset approximation of rational Bézier curves , 2006 .

[5]  Gershon Elber,et al.  Planar curve offset based on circle approximation , 1996, Comput. Aided Des..

[6]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[7]  Hyun-Chul Kim,et al.  A new offset algorithm for closed 2D lines with Islands , 2006 .

[8]  Martin Held,et al.  On the Computational Geometry of Pocket Machining , 1991, Lecture Notes in Computer Science.

[9]  Hong-yan Zhao,et al.  Offset approximation based on reparameterizing the path of a moving point along the base circle , 2009 .

[10]  Les A. Piegl,et al.  Computing offsets of NURBS curves and surfaces , 1999, Comput. Aided Des..

[11]  Gershon Elber,et al.  Comparing Offset Curve Approximation Methods , 1997, IEEE Computer Graphics and Applications.

[12]  Young-Suk Shin,et al.  Approximation of circular arcs and offset curves by Bézier curves of high degree , 2004 .

[13]  Wayne Tiller,et al.  Offsets of Two-Dimensional Profiles , 1984, IEEE Computer Graphics and Applications.

[14]  Bahram Ravani,et al.  Offset Surface Generation and Contouring in Computer-Aided Design , 1987 .

[15]  Anthony Ralston,et al.  Mathematical Methods for Digital Computers , 1960 .

[16]  Nicholas M. Patrikalakis,et al.  Free-Form Plate Modeling Using Offset Surfaces , 1988 .

[17]  E. S. Cobb.  Design of sculptured surfaces using the b-spline representation , 1984 .