论文标题
切点的能量和ROPELEGTH作为BIARC曲线上离散切点能量的γ-限制
Tangent-point energies and ropelength as Gamma-limit of discrete tangent-point energies on biarc curves
论文作者
论文摘要
使用BIARC曲线的插值，我们证明了$γ$ - 在$ C^1 $ - 学术中的连续截切点能量的离散分别切线能量以及ropelength功能中的连续截面能量。因此，离散的BIARC曲线几乎最小化会收敛到Ropelength的最小化器，并使连续的截切点能量的最小化。此外，从给定的$ c^{1,1} $ - 曲线$γ$中获取点数数据，我们建立了在BIARC曲线上评估的离散能量的收敛，将这些数据插入这些数据，与$γ$的连续切线均能，以及明显的融合利率。
Using interpolation with biarc curves we prove $Γ$-convergence of discretized tangent-point energies to the continuous tangent-point energies in the $C^1$-topology, as well as to the ropelength functional. As a consequence discrete almost minimizing biarc curves converge to ropelength minimizers, and to minimizers of the continuous tangent-point energies. In addition, taking point-tangent data from a given $C^{1,1}$-curve $γ$, we establish convergence of the discrete energies evaluated on biarc curves interpolating these data, to the continuous tangent-point energy of $γ$, together with an explicit convergence rate.
