ARC-LENGTH ESTIMATIONS FOR QUADRATIC RATIONAL Bézier CURVES COINCIDING WITH ARC-LENGTH OF SPECIAL SHAPES

In this paper, we present arc-length estimations for quadratic rational Bézier curves using the length of polygon and distance between both end points. Our arc-length estimations coincide with the arc-length of the quadratic rational Bézier curve exactly when the weight w is 0, 1 and∞. We show that for all w > 0 our estimations are strictly increasing with respect to w. Moreover, we find the parameter μ∗ which makes our estimation coincide with the arc-length of the quadratic rational Bézier curve when it is a circular arc too. We also show that μ∗ has a special limit, which is used for optimal estimation. We present some numerical examples, and the numerical results illustrates that the estimation with the limit value of μ∗ is an optimal estimation.