The generalised Cornu spiral and its application to span generation
Journal of Computational and Applied Mathematics - Special issue on computational methods in computer graphics
Sampling points on regular parametric curves with control of their distribution
Computer Aided Geometric Design
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Non-existence of rational arc length parameterizations for curves in Rn
Journal of Computational and Applied Mathematics
Smooth polynomial approximation of spiral arcs
Journal of Computational and Applied Mathematics
The best G1 cubic and G2 quartic Bézier approximations of circular arcs
Journal of Computational and Applied Mathematics
G3 quintic polynomial approximation for Generalised Cornu Spiral segments
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
In two recent papers Cripps et al. (2010) [3], and Cross and Cripps (2012) [2], quintic polynomial approximations of the generalized Cornu spirals have been studied by considering G^2 continuity and G^3 continuity at the end points respectively. The quintic curve is constructed so that the maximum curvature error is within the specified tolerance. In this paper, we provide corrections to the typing errors in Cross and Cripps (2012) [2], and propose a simpler and more efficient method for the G^2-constrained quintic polynomial approximation where the G^2 conditions are always satisfied by four free variables. Also, we introduce a new error measure of the maximum curvature error, which can greatly reduce the computational time when looking for the solution. Numerical experiments demonstrate the effectiveness of the new measure.