Abstract
The G^{2} and G^{1} -approximation schemes are introduced to approximate the popular generalized Cornu spirals with the help of the parametric rational cubic trigonometric Bézier curves. The G^{2} -approximation scheme has two free parameters whereas G^{1} -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.
Highlights
Monotonicity of curvature is a desirable feature in numerical curve and surface drawing applications e.g. in designing of robotic trajectories (Yang and Choi 2013), roads (Habib and Sakai 2007) and car bodies (Simon and Isik 1991)
This void has been filled by constructing a parametric rational cubic trigonometric Bézier curve (RCTBC) approximation of the generalized Cornu spirals such that it has a monotonic curvature profile within a specified tolerance
The tolerances for the relative curvature error of the developed approximation schemes of GCS are determined by using non-rational cubic trigonometric Bézier curve
Summary
Monotonicity of curvature is a desirable feature in numerical curve and surface drawing applications e.g. in designing of robotic trajectories (Yang and Choi 2013), roads (Habib and Sakai 2007) and car bodies (Simon and Isik 1991). The tolerances for the relative curvature error of the developed approximation schemes of GCS are determined by using non-rational cubic trigonometric Bézier curve.
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