×

C-curves: An extension of cubic curves. (English) Zbl 0900.68405

Summary: A linearly parametrized set of curves, named C-curves, is suggested with basis sin t, cos t, t, and 1. C-curves are an extension of cubic curves, they depend on a parameter \(\alpha >0\), and their limiting case for \(\alpha \rightarrow 0\) is a cubic curve. They can deal with free form curves and surfaces, and provide exact reproduction of circles and cylinders. So, they could be used to unify the representation and processing of both free and normal form curves and surfaces in engineering.

MSC:

68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
41A15 Spline approximation
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bézier, P., Mathematical and practical possibilities of UNISURF, Computer Aided Geometric Design, 127-152 (1975)
[2] Boehm, W., Inserting new knots into B-spline curves, Computer-Aided Design, 12, 99-102 (1980)
[3] Coons, S. A., Surfaces for computer aided design of space forms, MIT Project MAC-TR-41 (1967)
[4] Farin, G., (Curves and Surfaces for Computer Aided Geometric Design (1988), Academic Press), 1-273 · Zbl 0694.68004
[5] Gordan, W. J.; Riesenfeld, R. F., B-spline curves and surfaces, Computer Aided Geometric Design, 95-126 (1974)
[6] Koch, P. E.; Lyche, T., Exponential B-splines in tension, (Chui, C. K.; Schumaker, L. L.; Ward, J. D., Approximation Theory VI (1989), Academic Press: Academic Press New York), 361-364 · Zbl 0754.41006
[7] Koch, P. E.; Lyche, T., Construction of exponential tension B-splines of arbitrary order, (Laurent, P. J.; Le Méhauté, A.; Schumaker, L. L.; Ward, J. D., Curves and Surfaces (1991), Academic Press: Academic Press New York), 225-258 · Zbl 0736.41013
[8] Piegl, L.; Tiller, W., Curve and surface constructions using rational B-splines, Computer-Aided Design, 19, 487-498 (1987) · Zbl 0655.65012
[9] Schumaker, L. L., Spline Functions: Basic Theory, ((1981), Wiley: Wiley Boston, MA), 363-499 · Zbl 0187.37703
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.