×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
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., (), 1-273
[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, (), 361-364 · Zbl 0754.41006
[7] Koch, P.E.; Lyche, T., Construction of exponential tension B-splines of arbitrary order, (), 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, (), 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.