Piecewise Bézier Curve Fitting by Multiobjective Simulated Annealing

The determination of an approximation curve from a given sequence of points is an important task in CAD. This work proposes an algorithm to determine a piecewise Bezier curve that approximates a sequence of points. It is used a multiobjective simulated annealing aiming at minimizing the discrepancy between the given sequence of points and the curve, the curve length and the absolute difference of the curve length and length of the given sequence of points. The discrepancy between the given sequence of points and the curve is determined by the sum of the distance between each point from the sequence and the approximation curve, and the distance from a point to the curve is determined by an enhanced method in which the curve is discretized.