Algorithm for Tool Path Offsetting Based on NURBS Surface


Article Preview

This paper presents an algorithm for tool path offsetting based on NURBS surface. First the progenitor free surface is fitted with a bi-cubic NURBS surface and the unit normal vectors of the NURBS surface is computed precisely, then the offset surface can be obtained by offsetting the NURBS surface in the normal vector direction with the required distance. Considerable extra computational time can be saved, especially when they are to be offset by several times. As the method successfully computes the unit normal vector of the progenitors, the offset error of this method is zero. The method can also be generalized to other degree NURBS surface, and it can improve the machining accuracy of the surface.



Advanced Materials Research (Volumes 945-949)

Edited by:

Jingtao Han, Zhengyi Jiang and Xianghua Liu




Y. Yue, "Algorithm for Tool Path Offsetting Based on NURBS Surface", Advanced Materials Research, Vols. 945-949, pp. 111-114, 2014

Online since:

June 2014





* - Corresponding Author

[1] Klass R. An offset spline approximation for plane cubic splines. Computer Aided Design vol. 15(1983), p.297.


[2] Lee I K, Kim M S, Elber G. Planar curve offset progenitord on circle approximation. Computer Aided Design vol. 28(1996), p.617.


[3] Elber G Lee. Comparing offset curve approximation methods. IEEE Computer Graphics and Its Applications vol. 5(1997), p.62.

[4] Pottmann H. Rational curves and surfaces with rational offsets. Computer Aided Geometric Design vol. 12(1995), p.175.


[5] Pham B. Offset curves and surfaces: a brief survey. Computer-Aided Design vol. 24(1992), p.223.


[6] Maekawa T. An overview of offset curves and surfaces. Computer-Aided Design vol. 31(1999), p.165.

[7] Hwan Pyo Moon. Equivolumetric offset surfaces. Computer Aided Geometric Design vol. 1(2009), p.17.


[8] J. -L. Shih and S. -H. Frank Chuang. One-sided offset approximation of freeform curves for interference-free NURBS machining. Computer-Aided Design vol. 40(2008), p.931.


[9] Zhu Xinxiong. Modeling technology for curve and surface. Science Press, Beijing 2000. (in Chinese).