3D Visibility and Partial Visibility Complex

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 0((|V(q)|+n²) log n) time, where |V(q)| is the size of the view.