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ε-Guarantee of a covering of 2D domains using random-looking curves

机译：使用随机看似曲线的2D域覆盖的ε-保证

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The problem of covering a given 2D convex domain D with a C-1 random-looking curve C is considered. C within D is said to cover D up to epsilon 0 if all points of D are within epsilon distance of C. This problem has applications, for example, in manufacturing, 3D printing, automated spray-painting, polishing, and also in devising a (pseudo) random patrol-path that will visit (i.e. cover) all of D using a sensor of epsilon distance span. Our distance bound approach enumerates the complete set of local distance extrema, enumeration that is used to provide a tight bound on the covering distance. This involves computing bi/tri-normals, or circles tangent to C at two/three different points, etc. A constructive algorithm is then proposed to iteratively refine and modify C until C covers a given convex domain D and examples are given to illustrate the effectiveness of our algorithm. (C) 2017 Elsevier Inc. All rights reserved.
机译：考虑了用C-1随机外观曲线C覆盖给定的2D凸域D的问题。如果D的所有点都在C的epsilon距离之内，则D内的C可以覆盖D直到epsilon>0。此问题在制造，3D打印，自动喷涂，抛光以及设计中都有应用一个（伪）随机巡逻路径，它将使用epsilon距离跨度的传感器访问（即覆盖）所有D。我们的距离限制方法枚举了局部距离极值的完整集合，该枚举用于提供覆盖距离的紧密边界。这涉及计算双/三法线，或在两个/三个不同点处与C相切的圆，等等。然后，提出了一种构造算法来迭代地细化和修改C，直到C覆盖给定的凸域D，并给出了示例来说明我们算法的有效性。 （C）2017 Elsevier Inc.保留所有权利。

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