Fair curve designing by Said-Ball curve - Sana Zafar; Maria Hussain (PLoS ONE, 2025)
Fair curves are visually alluring curves and are free of unnecessary design features. A new curve designing method is introduced using the tangential continuous rational cubic Said-Ball curve. Fair curves are achieved by controlling its length and variation in curvature. It has enough degrees of freedom (control points and free parameters). A family of curves can be obtained for different choices for the values of free parameters. The control points are fixed by employing the G1 continuity conditions at the end points of the RCSBC. The optimal values of the remaining free parameters that are the weights of the underlying curve are obtained by constructing the optimization problems with stretch energy and curvature variation energy as the objective functionals. Different numerical examples are constructed to consolidate the effectiveness of the presented methods. Finally, two applications of the proposed techniques is also presented in the end.