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Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.4 P.593-595

http://doi.org/10.1631/jzus.2007.A0593


Vanishing torsion of parametric curves


Author(s):  JUHÁ,SZ Imre

Affiliation(s):  Department of Descriptive Geometry, University of Miskolc, Miskolc-Egyetemvá more

Corresponding email(s):   agtji@uni-miskolc.hu

Key Words:  Parametric curve, Torsion, Discriminant curve


JUHÁSZ Imre. Vanishing torsion of parametric curves[J]. Journal of Zhejiang University Science A, 2007, 8(4): 593-595.

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Abstract: 
We consider the class of parametric curves that can be represented by combination of control points and basis functions. A control point is let vary while the rest is held fixed. It’s shown that the locus of the moving control point that yields points of zero torsion is the osculating plane of the corresponding discriminant curve at its point of the same parameter value. The special case is studied when the basis functions sum to one.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Juhász, I., 2006. On the singularity of a class of parametric curves. Computer Aided Geometric Design, 23(2):146-156.

[2] Li, Y.M., Cripps, R.J., 1997. Identification of inflection points and cusps on rational curves. Computer Aided Geometric Design, 14(5):491-497.

[3] Manocha, D., Canny, J.F., 1992. Detecting cusps and inflection points in curves. Computer Aided Geometric Design, 9(1):1-24.

[4] Meek, D.S., Walton, D.J., 1990. Shape determination of planar uniform cubic B-spline segments. Computer-Aided Design, 22(7):434-441.

[5] Monterde, J., 2001. Singularities of rational Bézier curves. Computer Aided Geometric Design, 18(8):805-816.

[6] Sakai, M., 1999. Inflection points and singularities on planar rational cubic curve segments. Computer Aided Geometric Design, 16(3):149-156.

[7] Stone, M.C., DeRose, T.D., 1989. A geometric characterization of parametric cubic curves. ACM Transactions on Graphics, 8(3):147-163.

[8] Wang, C.Y., 1981. Shape classification of the parametric cubic curve and parametric B-spline cubic curve. Computer-Aided Design, 13(4):199-206.

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