Search results for "Convex polygon"
showing 2 items of 2 documents
Optimal Guard Placement Problem Under L-Visibility
2006
Two points a and b in the presence of polygonal obstacles are L-visible if the length of the shortest path avoiding obstacles is no more than L. For a given convex polygon Q, Gewali et al [4]. addressed the guard placement problem on the exterior boundary that will cover the maximum area exterior to the polygon under L-visibility. They proposed a linear time algorithm for some given value of L. When the length L is greater than half of the perimeter, they declared that problem as open. Here we address that open problem and present an algorithm whose time complexity is linear in number of vertices of the polygon.
Shape identification in inverse medium scattering problems with a single far-field pattern
2016
Consider time-harmonic acoustic scattering from a bounded penetrable obstacle $D\subset {\mathbb R}^N$ embedded in a homogeneous background medium. The index of refraction characterizing the material inside $D$ is supposed to be Holder continuous near the corners. If $D\subset {\mathbb R}^2$ is a convex polygon, we prove that its shape and location can be uniquely determined by the far-field pattern incited by a single incident wave at a fixed frequency. In dimensions $N \geq 3$, the uniqueness applies to penetrable scatterers of rectangular type with additional assumptions on the smoothness of the contrast. Our arguments are motivated by recent studies on the absence of nonscattering waven…