Bounding the distance between 2D parametric Bézier curves and their control polygon

Authors:
M. I. Karavelas;P. D. Kaklis;K. V. Kostas
Affiliations:
University of Notre Dame, Dept. Computer Science and Engineering, Notre Dame, IN;National Technical University of Athens, Dept. Naval Arch. & Mar. Eng., Greece;National Technical University of Athens, Dept. Naval Arch. & Mar. Eng., Greece
Venue:
Computing - Geometric modelling dagstuhl 2002
Year:
2004

Citing 3
Cited 6

Davenport-Schinzel sequences and their geometric applications

Davenport-Schinzel sequences and their geometric applications
Sharp, quantitative bounds on the distance between a polynomial piece and its Bézier control polygon

Computer Aided Geometric Design - Special issue dedicated to Paul de Faget de Casteljau
Best bounds on the approximation of polynomials and splines by their control structure

Computer Aided Geometric Design

Estimating error bounds for binary subdivision curves/surfaces

Journal of Computational and Applied Mathematics
A simple and efficient approximation of a Bézier piece by its cutdown polygon

Computer Aided Geometric Design
Consolidated sharp bounds for Bézier curve approximation with cutdown polygon and corner cutting polygon

Computer Aided Geometric Design
Tight numerical bounds for digital terrain modeling by interpolatory subdivision schemes

Mathematics and Computers in Simulation
Mean distance from a curve to its control polygon

MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Efficient piecewise linear approximation of bézier curves with improved sharp error bound

GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Employing the techniques presented by Nairn, Peters and Lutterkort in [1], sharp bounds are firstly derived for the distance between a planar parametric Bézier curve and a parameterization of its control polygon based on the Greville abscissae. Several of the norms appearing in these bounds are orientation dependent. We next present algorithms for finding the optimal orientation angle for which two of these norms become minimal. The use of these bounds and algorithms for constructing polygonal envelopes of planar polynomial curves, is illustrated for an open and a closed composite Bézier curve.