Hierarchical Techniques for Visibility Computations

Visibility computation is crucial for computer graphics from its very beginning. The first visibility algorithms aimed to determine visible lines or surfaces in a synthesized image of a 3D scene. Nowadays there is a plethora of visibility algorithms for various applications. The thesis proposes a taxonomy of visibility problems based on the dimension of the problem-relevant line set, i.e. set of lines forming the domain of the visibility problem. The taxonomy helps to identify relationships between visibility problems from various application areas by grouping together problems of similar complexity. The thesis presents a general concept of a visibility algorithm suitable for solution of several classes of visibility problems. The concept is based on three main ideas: an approximate occlusion sweep, an occlusion tree, and hierarchical visibility tests. The central idea of the concept is the occlusion tree representing an aggregated occlusion map by means of a hierarchical subdivision in line space. The thesis presents several applications of the concept. The major focus is placed on visibility culling algorithms for real-time rendering acceleration. First, we describe an algorithm for real-time visibility culling. The algorithm is used to accelerate rendering of large densely occluded scenes. It improves previous results by efficiently performing occluder fusion in real-time. We propose several techniques exploiting temporal and spatial coherence applicable to most existing hierarchical visibility culling methods. Second, we propose an algorithm for computing visibility maps in polygonal scenes. The algorithm provides a comprehensive description of the topology of the given view of the scene. We discuss an application of the algorithm to discontinuity meshing. Third, the proposed concept is applied to computation of from-region visibility in 2D scenes. We present and evaluate an exact analytic algorithm for computing a potentially visible set for a polygonal region in the plane. Fourth, we propose two algorithms for computing from-region visibility in 212D scenes. Both algorithms are targeted at visibility preprocessing for walkthroughs of outdoor urban scenes. The methods are compared with another recent technique. Finally, we describe an exact analytic algorithm for computing from-region visibility in 3D scenes suitable for various applications. The algorithm uses Plücker coordinates and maintains a hierarchical subdivision of 5D space. We discuss its application to visibility preprocessing, occluder synthesis and discontinuity meshing.