The Length of Bézier Curves
Jens Gravesen, Mathematical Institute Technical University of Denmark Lyngby, Denmark
Introduction
It is an often-used fact that the control polygon of a Bézier curve approximates the curve and that repeated subdivision produces a sequence of control polygons that converge to the curve (Farin 1988). The length of these control polygons converges to the arc length of the Bézier curve, and with the use of a certain convex combination of the length of the control polygon and the length of the chord between the endpoints of the segments, the convergence becomes much faster. This gem derives and implements an adaptive method for the calculation of the arc length based on this result. Previously, Gaussian quadrature ...
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