Abstract
In this paper, we propose a 3D curve offset method, named directional offset, motivated from the observation of the needs in many engineering design practices such as flange of sheet metal parts. Since the normal vector of a 3D curve at a point is not unique, a 3D curve offset definition is about selecting the offset direction vector on the normal plane of the curve. In directional offset, the offset direction vector is chosen to be perpendicular to the user-specified projection direction vector as well as the curve tangent vector. Directional offset is a natural extension of planar curve offset, in the sense that they produce the same results when applied to planar curve. An overall procedure to compute a directional offset for a position-continuous NURBS curve is described with an emphasis on avoiding self-intersection loop.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Coquillart S, “Computing offsets of B-spline curves”, Computer-Aided Design, 1987, v19(6), pp.305–309.
Elber G, Lee I-K, Kim M-S, “Comparing Offset Curve Approximation Methods”, IEEE computer graphics and applications, 1997, v17(3), pp.62–71
Hoschek J, Wissel N, “Optimal approximate conversion of spline curves and spline approximation of offset curves”, Computer-Aided Design, 1988, v20(8), pp.475–483.
Hoschek J, “Spline approximation of offset curves”, Computer Aided Geometric Design, 1988, v5(1), pp.33–40
Kim D-S, “Hodograph Approach to a Geometric Characterization of Parametric Cubic Curves”, Computer Aided Design, 1993, v25(10), pp.644–654
Lipschultz M, Differential Geometry, 1969, McGraw Hill
Maekawa T, “An overview of offset curves and surfaces”, Computer-Aided Design, 1999, v31, pp.165–173
Park SC, Choi BK, “Uncut free pocketing tool-paths generation using pair-wise offset algorithm”, Computer-Aided Design, 2001, v33(10), pp.739–746
Park SC, Shin H, “Polygonal Chain Intersection”, Computers & Graphics, in press.
Pham B, “Offset approximation of uniform B-splines”, Computer-Aided Design, 1988, v20(8), pp.471–474
Pham B, “Offset curves and surfaces: a brief survey”, Computer-Aided Design, 1992, v24(4), pp.223–229
Piegl L, Tiller W, The NURBS book, 2nd ed, New York: Springer, 1997.
Peigl L, Tiller W, “Computing offsets of NURBS curves and surfaces”, Computer-Aided Design, 1999, v31(2), pp.147–156
Peternell M, Pottmann H, “A Laguerre geometric approach to rational offsets”, Computer Aided Geometric Design, 1998, v15, pp.223–249.
Shin H, Cho S, “Directional offset of a 3D curve”, Proceedings of 7th ACM Symposium on Solid Modeling and Applications (SM02), 2002, pp.329–335.
Tiller W, Hanson EG “Offsets of two-dimensional profiles”, IEEE Computer Graphics and Applications, 1984, v.4(9), pp.61.69
Wallner J, Sakkalis T, Maekawa T, Pottmann H, Yu G, “Self intersections of offset curves and surfaces”, Intl. Journal of Shape Modeling, 2001, v1, pp.1–22
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Shin, H., Yoo, S.K., Cho, S.K., Chung, W.H. (2003). Directional Offset of a Spatial Curve for Practical Engineering Design. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44842-X_72
Download citation
DOI: https://doi.org/10.1007/3-540-44842-X_72
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40156-8
Online ISBN: 978-3-540-44842-6
eBook Packages: Springer Book Archive