We show that integral curvature energies on surfaces of the type $E_0(M) := \int_M f(x,n_M(x),D n_M(x))\,d\mathcal{H}^2(x)$ have discrete versions for triangular complexes, where the shape operator $D n_M$ is replaced by the piecewise gradient of a piecewise affine edge director field. We combine an ansatz-free asymptotic lower bound for any uniform approximation of a surface with triangular complexes and a recovery sequence consisting of any regular triangulation of the limit sequence and an almost optimal choice of edge director.
翻译:我们显示,$E_0(M) 类型表面的整体曲率 : =\int_M f(x,n_M(x),Dn_M(x)\,d\mathcal{H#2(x)$) 具有三角复合体的离散版本, 形状操作员$n_M$被一个小字形边边缘管理字段的平面梯度所取代。 我们将一个无炭色素的无亚麻药低端的表面与三角复合体和由限制序列的任何常规三角和边缘导师的近似最佳选择组成的恢复序列结合起来。