ARC-LENGTH ESTIMATIONS FOR QUADRATIC RATIONAL B´ezier CURVES COINCIDING WITH ARC-LENGTH OF SPECIAL SHAPES

Abstract

In this paper, we present arc-length estimations for quadratic rational B´ezier 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 B´ezier 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 B´ezier 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.