title: A rational cubic trigonometric approximation scheme of the generalized Cornu spirals.
abstract: The [Formula: see text] and [Formula: see text]-approximation schemes are introduced to approximate the popular generalized Cornu spirals with the help of the parametric rational cubic trigonometric Bézier curves. The [Formula: see text]-approximation scheme has two free parameters whereas [Formula: see text]-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.
authors.affiliation: Department of Mathematics, University of the Punjab, Lahore, Pakistan.
authors.forename: Hira
authors.initials: H
authors.lastname: Mahmood
authors.affiliation: Lahore College for Women University, Lahore, Pakistan.
authors.forename: Maria
authors.initials: M
authors.lastname: Hussain
authors.affiliation: Department of Mathematics, University of the Punjab, Lahore, Pakistan.
authors.forename: Malik Zawwar
authors.initials: MZ
authors.lastname: Hussain
keywords: G1-approximation; G2-approximation; Generalized Cornu spirals; Rational cubic trigonometric Bézier curve; Relative curvature error