Beacon attraction, or simply attraction, is a movement system whereby a point moves in a free space so as to always locally minimize its Euclidean distance to an activated beacon (also a point). This results in the point moving directly towards the beacon when it can, and otherwise sliding along the edge of an obstacle or being stuck (unable to move). When the point can reach the activated beacon by this method, we say that the beacon attracts the point. In this paper, we study attraction-convex polygons, which are those where every point in the polygon attracts every other point. We find that these polygons are a subclass of weakly externally visible polygons, which are those where every point on the boundary is visible from some point arbitrarily distant (or at infinity on the projective plane). We propose a new class of polygons called normally visible, and show that this is exactly the class of attraction-convex polygons. This alternative characterization of attraction-convex polygons leads to a simple linear-time attraction-convex polygon recognition algorithm. We also give a Helly-type characterization of inverse-attraction star-shaped polygons.

信标吸引，或简称为吸引，是一种移动系统，点在自由空间中移动，从而始终将其到激活信标（也是点）的欧几里德距离最小化。这会导致该点尽可能地直接移向信标，否则会沿着障碍物的边缘滑动或被卡住（无法移动）。当点可以通过这种方法到达激活的信标时，我们说信标吸引了该点。在本文中，我们研究了吸引凸多边形，即多边形中每个点都吸引其他所有点的多边形。我们发现这些多边形是外部可见的弱子类多边形，即从任意距离的某个点（或在投影平面上为无穷大）可以看到边界上每个点的多边形。我们提出了一种称为“通常可见”的新多边形类别，并证明这正是吸引凸多边形的类别。吸引-凸多边形的这种替代特征导致一种简单的线性时间吸引-凸多边形识别算法。我们还给出了反吸引星形多边形的Helly型特征。