Drawing an elliptical arc using polylines, quadratic or cubic Bézier curves
This paper presents algorithms to approximate an elliptical arc using line segments, quadratic or cubic Bézier curves, given a required accuracy. The algorithms are two-fold: the first part explains how too choose the control points and the second part explains how to compute the approximation error. A simple method to split the arc into sub-arcs in order to respect the required accuracy is also presented.
In addition to the on-line version, this document is available in LaTeX, PostScript and PDF formats in the downloads page, a Java class implementing the algorithms is also available.
Quick computation of the distance between a point and an ellipse
This paper presents an algorithm to quickly compute the distance between a point and an ellipse. The point can be inside, outside, or on the ellipse. The algorithms is efficient even with very degenerated ellipses (i.e. flat ellipses whose semi-minor axis isconsiderably smaller than the semi-major axis).
In addition to the on-line version, this document is available in LaTeX, PostScript and PDF formats in the downloads page, a Java class implementing the algorithm is also available.