Initial data for the construction of glass.

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 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.

光顺曲线（Fair curves）是视觉效果优美且无冗余设计特征的曲线。本文提出一种基于切向连续有理三次Said-Ball曲线（tangential continuous rational cubic Said-Ball curve，以下简称RCSBC）的曲线设计新方法。通过控制曲线的长度与曲率变化量即可生成光顺曲线。该曲线拥有充足的自由度，涵盖控制点与自由参数两类变量。通过选取不同的自由参数值，可得到一族形状可调的曲线。通过利用RCSBC端点处的连续性条件即可确定全部控制点。通过构建以拉伸能量与曲率变化能量为目标泛函的优化问题，可求解得到剩余自由参数（即基曲线的权重系数）的最优取值。本文通过多组数值算例验证了所提方法的有效性。最后，本文还展示了所提技术的两项实际应用场景。