Abstract
We present a method for computing the domain, where a control point is free to move so that the corresponding spatial curve is regular and of constant sign of torsion along a subinterval of its parametric domain of definition. The approach encompasses all curve representations that adopt the control-point paradigm and is illustrated for a spatial Bézier curve.
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Bruce, J.W., Giblin, P.J.: Curves and Singularities. Cambridge University Press, Cambridge (1988)
Costa, S.I.R.: On closed twisted curves. Proceedings of the American Mathematical Society 109, 205–214 (1990)
Costa, S.I.R., Romero-Fuster, M.C.: Nowhere vanishing torsion closed curves always hide twice. Geometriae Dedicata 66, 1–17 (1997)
Dooner, D.B.: Introducing radius of torsure and cylindroid of torsure. Journal of Robotic Systems 20, 429–436 (2003)
Farin, G.: Class A Bézier Curves. CAGD 23, 573–581 (2006)
Grégoire, M., Schömer, E.: Interactive simulation of one dimensional flexible parts. In: SPM 2006, ACM Symposium on Solid and Physical Modeling, Cardiff, Wales, UK, June 2006, pp. 95–103 (2006)
Juhász, I.: On the singularity of a class of parametric curves. CAGD 23, 146–156 (2006)
Kong, V.P., Ong, B.H.: Shape preserving F 3 curve interpolation. CAGD 19, 239–256 (2002)
Li, S.Z.: Similarity invariants for 3D space curve matching. In: Proceedings of the First Asian Conference on Computer Vision, Osaka, Japan, November 1993, pp. 454–457 (1993)
Mokhtarian, F.: A theory of multiscale, torsion-based shape represenation for space curves. Computer Vision and Image Understanding 68, 1–17 (1997)
Moll, M., Kavraki, L.E.: Path planning for variable resolution minimal-energy curves of constant length. In: Proceedings of the 2005 IEEE International Conference on Robotics and Automation, Barcelona, Spain, April 2005, pp. 2130–2135 (2005)
Nuño-Balesteros, J.J., Romero-Fuster, M.C.: A four vertex theorem for strictly convex space curves. Journal of Geometry 46, 119–126 (1993)
Pogorelov, A.: Geometry. MIR Publishers, Moscow (1987)
Rao, P.V.M., Bodas, M., Dhande, S.G.: Shape matching of planar and spatial curves for part inspection. Computer-Aided Design & Applications 3, 289–296 (2006)
Struik, D.J.: Lectures on Classical Differential Geometry, 2nd edn. Addison-Wesley Publishing Company, INC., Reading (1961)
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© 2008 Springer-Verlag Berlin Heidelberg
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Karousos, E.I., Ginnis, A.I., Kaklis, P.D. (2008). Controlling Torsion Sign. In: Chen, F., Jüttler, B. (eds) Advances in Geometric Modeling and Processing. GMP 2008. Lecture Notes in Computer Science, vol 4975. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79246-8_7
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DOI: https://doi.org/10.1007/978-3-540-79246-8_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79245-1
Online ISBN: 978-3-540-79246-8
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