Abstract
The mean distance between a curve and its control polygon is bounded in terms of the norm of second order differences of the control points. We also analyze the distance of a rational curve to its control polygon and suggest a choice of the weight for obtaining rational curves much closer to its control polygon than Bézier curves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Carnicer, J.M., Floater, M.S., Peña, J.M.: The distance of a curve to its control polygon. Numerical methods of approximation theory and computer aided geometric design. RACSAM Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 96, 175–183 (2002)
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., Peña, J.M.: Monotonicity preserving representations. In: Laurent, P.J., Le Méhauté, A., Schumaker, L.L. (eds.) Curves and Surfaces in Geometric Design, pp. 83–90. AKPeters, Wellesley (1994)
Delgado, J., Peña, J.M.: Corner cutting systems. Computer Aided Geometric Design 22, 81–97 (2005)
Karavelas, M.I., Kaklis, P.D., Kostas, K.V.: Bounding the Distance between 2D Parametric Bézier Curves and their Control Polygon. Computing 72, 117–128 (2004)
Nairn, D., Peters, J., Lutterkort, D.: Sharp, quantitative bounds on the distance between a polynomial piece and its Bézier control polygon. Computer Aided Geometric Design 16, 613–631 (1999)
Reif, U.: Best bound on the approximation of polynomials and splines by their control structure. Computer Aided Geometric Design 17, 579–589 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Carnicer, J., Delgado, J. (2010). Mean Distance from a Curve to Its Control Polygon. In: Dæhlen, M., Floater, M., Lyche, T., Merrien, JL., Mørken, K., Schumaker, L.L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2008. Lecture Notes in Computer Science, vol 5862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11620-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-11620-9_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11619-3
Online ISBN: 978-3-642-11620-9
eBook Packages: Computer ScienceComputer Science (R0)