Abstract
The rational de Casteljau algorithm for the evaluation of rational Bézier curves is extended to very general rational spaces. Many examples are included.
Similar content being viewed by others
References
Aumann, G.: Corner cutting curves and a new characterization of Bézier and B-spline curves. Comput. Aided Geom. Design 14, 449–474 (1997)
Carnicer, J.M., García-Esnaola, M., Peña, J.M.: Convexity of rational curves and total positivity. J. Comput. Appl. Math. 71, 365–382 (1996)
Carnicer, J.M., Mainar, E.: Factorizations of normalized totally positive systems. In: Laurent, P.J., Sablonnière, P., Schumaker, L.L. (eds.) Curve and Surface Design: Saint-Malo 1999, pp. 333–357. Academic Press, Boston (2000)
Carnicer, J.M., Peña, J.M.: Totally positive bases for shape preserving curve design and optimality of B-splines. Comput. Aided Geom. Design 11, 635–656 (1994)
Delgado, J., Peña, J.M.: Corner cutting systems. Comput. Aided Geom. Design 22, 81–97 (2005)
Farin, G.: Algorithms for rational Bézier curves. Comput. Aided Design 15, 73–77 (1983)
Farin, G.: Curves and surfaces for computer aided geometric design.A practical guide, 5th edn. Morgan-Kaufmann, New York (2002)
Mainar, E., Peña, J.M.: Error analysis of corner cutting algorithms. Numer. Algorithms 22, 41–52 (1999)
Mainar, E., Peña, J.M.: A general class of Bernstein-like bases. Comput. Math. Appl. 53, 1686–1703 (2007)
Shi-Min, H., Guo-Zhao, W., Tong-Guang, J.: Properties of two types of generalized Ball curves. Comput. Aided Geom. Design 28, 125–133 (1996)
Tien, H.L., Hansuebsai, D., Phien, H.N.: Rational Ball curves. Int. J. Math. Educ. Sci. Technol. 30, 243–257 (1999)
Author information
Authors and Affiliations
Corresponding author
Additional information
Partially supported by MTM2012-31544 Spanish Research Grant and by Gobierno de Aragón.
Rights and permissions
About this article
Cite this article
Mainar, E., Peña, J.M. Corner cutting evaluation algorithms for general rational curves. RACSAM 109, 117–123 (2015). https://doi.org/10.1007/s13398-014-0170-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13398-014-0170-x