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3D Visibility and the Partial Visibility Complex

机译:3D可见性和部分可见性复杂

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Visibility is an important topic in computer graphics, motion planning, and computational geometry. To deal with the increasing complexity of the scenes considered, some research has been performed in visibility processing in order to accelerate the visibility determination. Two of the most studied such structures are visibility graph and visibility complex. Visibility graph is a fundamental geometric structure which is used in many applications, including illumination and rendering, motion planning, pattern recognition, and sensor networks. While the concept of visibility graph is widely studied for 2D scenes, there is no acceptable equivalence of visibility graph for 3D space. Similarly, 3D visibility complex, proposed as an extension of visibility complex to 3D, is very complicated and cannot be used for visibility computations. In this paper, we propose a new model for defining the visibility relations in 3D. The main idea is to replace the role of lines and segments in 2D with planes and planar polygons in 3D. Moreover, we define two new structures, namely 3D visibility graph and partial visibility complex, which we believe is the natural way to extend the earlier models. We show how to compute these structures in acceptable times. We also use partial visibility complex to compute the view around a point in 3D in O((|V(q)|+n{sup}2) log n) time, where |V(q)| is the size of the view.
机译:可见性是计算机图形,运动规划和计算几何中的一个重要主题。为了处理所考虑的场景的越来越复杂,已经在可见性处理中进行了一些研究,以加速可见性确定。其中两个最多的这种结构是可见性图和可见性复合物。可见性图是一种基本的几何结构,用于许多应用中,包括照明和渲染,运动规划,模式识别和传感器网络。虽然可见性图表的概念被广泛研究了2D场景,但对于3D空间的可见性图表没有可接受的等价性。类似地,3D可见性复合物,提出作为3D的可见性复合物的延伸,非常复杂,不能用于可见性计算。在本文中,我们提出了一种确定三维能见度关系的新模型。主要思想是用3D中的平面和平面多边形取代线和段的角色和段的作用。此外,我们定义了两个新的结构,即3D可见性图和部分可见性复合体,我们认为是延长较早模型的自然方式。我们展示了如何在可接受的时间内计算这些结构。我们还使用部分可见性复合体来计算O中的3D的点周围的视图((| v(q)| + n {sup} 2)log n)时间,其中v(q)|是视图的大小。

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