Curve intersection using Be´zier clipping
Computer-Aided Design - Special Issue: Be´zier Techniques
Numerical analysis: an introduction
Numerical analysis: an introduction
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Computing roots of polynomials by quadratic clipping
Computer Aided Geometric Design
Computing intersections of planar spline curves using knot insertion
Computer Aided Geometric Design
Spiral fat arcs - Bounding regions with cubic convergence
Graphical Models
SMI 2012: Full Curve intersection using hybrid clipping
Computers and Graphics
A geometric strategy for computing intersections of two spatial parametric curves
The Visual Computer: International Journal of Computer Graphics
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In 1990 Sederberg et al. introduced Bezier clipping as a new method to determine the intersections of two Bezier curves in the plane. The method utilizes the convex hull property of Bezier curves. In experiments a quadratic convergence rate was observed at transversal intersections, the equivalent of simple roots of functions, but no formal proof for this has been provided. In this paper we formally prove the quadratic convergence rate. Bezier clipping bounds one of the curves by a region along a line. We also discuss the usefulness of arbitrary lines for creating these so called 'fat lines', leading to two general classes of fat lines which both give quadratic convergence.