论文标题
离散的曲率和交叉比率的扭转
Discrete Curvature and Torsion from Cross-Ratios
论文作者
论文摘要
由多边形的莫比乌斯不变细分方案的动机，我们研究了一个离散曲线的曲率概念，在我们的所有关键定义中，交叉比例都起着重要作用。使用特定的Möbius不变的点插入规则，可与经典的四点旋转相媲美，我们沿离散曲线构造圆圈。渐近分析表明，随着采样密度的增加，在采样曲线上定义的这些圆圈会收敛到光滑的曲率圆圈。我们使用交叉比例表达了空间曲线的离散扭转，这不是Möbius不变的概念，并以类似于曲率的方式显示了其渐近行为。
Motivated by a Möbius invariant subdivision scheme for polygons, we study a curvature notion for discrete curves where the cross-ratio plays an important role in all our key definitions. Using a particular Möbius invariant point-insertion-rule, comparable to the classical four-point-scheme, we construct circles along discrete curves. Asymptotic analysis shows that these circles defined on a sampled curve converge to the smooth curvature circles as the sampling density increases. We express our discrete torsion for space curves, which is not a Möbius invariant notion, using the cross-ratio and show its asymptotic behavior in analogy to the curvature.
