Shortest Inspection Curves for the Sphere
Shortest Inspection Curves for the Sphere
复制标题
球体最短检测曲线
DOI：
--
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
V. A. Zalgaller
中科院分区：
文献类型：
--
作者：
V. A. Zalgaller
ℝ3 中超出单位球体 S 的最短曲线 C 的形式是什么，使得沿着 C 我们可以从外部看到 S 的所有点？如果我们要求 C 在 S 上有一个（或两个）端点，那么 C 的形式将如何变化？后一个问题的解决方案也回答了以下问题。你处于距边界面 P 单位距离的半空间中，但你不知道 P 在哪里。沿着 C 一定会到达 P 的最短空间曲线 C 是什么？几何参数表明，应根据几个参数在某些类别中寻找所需的曲线。计算机辅助分析产生了同类中最好的曲线。其他一些问题也可以用类似的方法解决。参考书目：4个标题。
What is the form of the shortest curve C going outside the unit sphere S in ℝ3 such that passing along C we can see all points of S from outside? How will the form of C change if we require that C has one (or both) of its endpoints on S? A solution to the latter problem also answers the following question. You are in a half-space at a unit distance from the boundary plane P, but you do not know where P is. What is the shortest space curve C such that going along C you will certainly come to P? Geometric arguments suggest that the required curves should be looked for in certain classes depending on several parameters. A computer-aided analysis yields the best curves in the classes. Some other questions are solved in a similar way. Bibliography: 4 titles.