A rational cubic trigonometric approximation scheme of the generalized Cornu spirals

Abstract

The G2 and G1-approximation schemes are introduced to approximate the popular generalized Cornu spirals with the help of the parametric rational cubic trigonometric Bézier curves. The G2-approximation scheme has two free parameters whereas G1-approximation scheme has four free parameters. To approximate the generalized Cornu spirals, the values of these free parameters are optimized by the minimization of the maximum relative curvature error of approximation. By comparing the relative curvature errors of approximation schemes, the developed approximation schemes are found less erroneous and more efficient than the existing GCS approximation schemes.