Visibility with One Reflection
Visibility with One Reflection
复制标题
一次反射的可见性
DOI：
10.1007/pl00009368
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发表时间：
1998
影响因子：
0.8
通讯作者：
D. Prasad
中科院分区：
文献类型：
--
作者：
B. Aronov;Alan R. Davis;T. Dey;S. P. Pal;D. Prasad
抽象的。我们通过考虑两种类型的反射，镜面反射和漫反射的可见性，在一个简单的多边形从源点S可见的多边形的概念。在镜面反射中，光线根据以下规则从多边形的边缘反射：入射角等于反射角。在漫反射中，光线从多边形的边缘向所有向内的方向反射。当最多允许一个反射时，描述了这两种反射下可见多边形的几个几何和组合性质。我们证明了镜面反射下的可见性多边形Vs（S）可能是非简单的，而漫反射下的可见性多边形Vd（S）总是简单的.我们给出了Vs（S）和Vd（S）的组合复杂度的一个Θ（n2）最坏情况界，并描述了构造集合的简单O（n2log2n）时间算法.
Abstract. We extend the concept of the polygon visible from a source point S in a simple polygon by considering visibility with two types of reflection, specular and diffuse. In specular reflection a light ray reflects from an edge of the polygon according to the rule: the angle of incidence equals the angle of reflection. In diffuse reflection a light ray reflects from an edge of the polygon in all inward directions. Several geometric and combinatorial properties of visibility polygons under these two types of reflection are described, when at most one reflection is permitted. We show that the visibility polygon Vs(S) under specular reflection may be nonsimple, while the visibility polygon Vd(S) under diffuse reflection is always simple. We present a Θ(n2) worst-case bound on the combinatorial complexity of both Vs(S) and Vd(S) and describe simple O(n2 log2 n) time algorithms for constructing the sets.