Cross and Cripps [2] approximated the generalized Cornu spiral (GCS) with a G~3 quintic Bezier curves based on a curvature error measure, the curvatures by means of parameterized arc length. However, this measure computationally expensive. In order to overcome this problem, Lu [6] suggested another error measure which reduces both time and computation time. However, Cross and Cripps's error measure was still needed in order assess its approximation quality. In this paper we propose a new approach to compute the error measure by making a correspondence between the general parameter t and arc length parameter s. Numerical examples show that this error measure reduce both time and computations to certain extend, and preserves the approximation quality as obtained by Cross and Cripps.
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