Curvature continuous cubic algebraic splines

Marco Paluszny; Richard R. Patterson

doi:10.1117/12.131732

1 November 1992 Curvature continuous cubic algebraic splines

Marco Paluszny, Richard R. Patterson

Proceedings Volume 1830, Curves and Surfaces in Computer Vision and Graphics III; (1992) https://doi.org/10.1117/12.131732
Event: Applications in Optical Science and Engineering, 1992, Boston, MA, United States

Abstract

It is shown how to construct G2-continuous spline with arcs of cubics. Each arc is a piece of the oval of a cubic and it is controlled locally by a triangle tangent to the arc at both endpoints. Formulas for mixed interpolation of further points and tangents are given in terms of geometrically meaningful shape parameters. It is shown that under certain restrictions, the numerical values of the curvatures may be prescribed at the joints. Some new shape handles are developed for the local control of each arc of the spline. Intersection problems are easily handled. The main advantage of algebraic splines is that they are completely parametrization free.

Citation Download Citation

Marco Paluszny and Richard R. Patterson "Curvature continuous cubic algebraic splines", Proc. SPIE 1830, Curves and Surfaces in Computer Vision and Graphics III, (1 November 1992); https://doi.org/10.1117/12.131732

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