One of the most important problems in computer graphics is the classification of all objects in a scene as either being at least partially visible or totally invisible. The issue of rapidly identifying entirely invisible objects is of importance in any rendering system, but it is especially crucial when interactive frame update rates are desired. In an ideal rendering system it would be possibl...

We first consider the set of faces of the complex representing rays issued from a given object. We define an order on these faces and show, once the visibility complex is computed, how to visit all of them with no additional data structure in optimal time O(kf ), where kf is the number of faces visited. Then we show how to use this walk to perform a topological sweep of the vertices incident to...

In this paper we explore some novel aspects of visibility for stationary and moving points inside a simple polygon P . We provide a mechanism for expressing the visibility polygon from a point as the disjoint union of logarithmically many canonical pieces using a quadratic-space data structure. This allows us to report visibility polygons in time proportional to their size, but without the cubi...

A bar visibility representation of a graph G is a collection of horizontal bars in the plane corresponding to the vertices of G such that two vertices are adjacent if and only if the corresponding bars can be joined by an unobstructed vertical line segment. In a bar k-visibility graph, two vertices are adjacent if and only if the corresponding bars can be joined by a vertical line segment that ...

This paper presents a new technique for determining a small set of views that allow the observation and acquisition of the surfaces of the objects present in a target scene through a range sensor that moves over a sphere containing that scene. No a priori knowledge about the shape of those objects is assumed. Instead of applying costly visibility analysis techniques from the beginning as in mos...

Given a set of n disjoint line segments in the plane, the segment visibility graph is the graph whose 2n vertices correspond to the endpoints of the line segments and whose edges connect every pair of vertices whose corresponding endpoints can see each other. In this paper we characterize and provide a polynomial time recognition algorithm for planar segment visibility graphs. Actually, we char...

This thesis is concerned with simple agents that move from vertex to vertex along straight lines inside a simple polygon with the goal of reconstructing the visibility graph. The visibility graph has a node for each vertex of the polygon with an edge between two nodes if the corresponding vertices see each other, i.e., if they can be connected by a straight line inside the polygon. While at a v...

The paper considers representations of unions and products of trees as rectangle-visibility graphs (abbreviated RVGs), i.e., graphs whose vertices are rectangles in the plane, with adjacency determined by horizontal and vertical visibility. Our main results are that the union of any tree (or forest) with a depth-1 tree is an RVG, and that the union of two depth-2 trees and the union of a depth-...

We present optimal parallel algorithms that run in O p n time on a p n pn mesh connected computer for a number of fundamental problems concerning proximity and vis ibility in a simple polygon These include computing shortest paths shortest path trees shortest path partitions all farthest neighbors the visibility polygon of a point the weak visibility polygon of an edge and the ray shooting problem