Sherif Ghali

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Consider a viewpoint moving amongst a set of non– intersecting line segments in the plane. We would like to compute efficiently the set of segments visible at successive positions along the viewpoint trajectory. This problem can be solved in either the off–line or the on–line setting. The latter case, in which the updates of the viewpoint are known only as(More)
Given a set of polyhedra and a polygon in E3, the –aspect graph is a partition of the faces of the polyhedra into regions such that the area of that is visible from each region has the same structure or “aspect.” We present an output-sensitive algorithm to compute the –aspect graph. In computer graphics, this problem arises in rendering images of polyhedral(More)
This paper describes a fast, practical algorithm to compute the shadow boundaries in a polyhedral scene illuminated by a polygonal light source. The shadow boundaries divide the faces of the scene into regions such that the structure or “aspect” of the visible area of the light source is constant within each region. The paper also describes a(More)
Consider the following problem: A viewpoint moves amongst a set of line segments in the plane and it is desired to maintain the sequence of lines visible from the viewpoint at every increment in its position. The sequence of visible lines is identical for most increments in the position of the viewpoint. It is diierent only when the viewpoint crosses a(More)
We introduce a novel representation for visibility in three dimensions and describe an efficient algorithm to construct it. The data structure is a spherical map that consists of a doubly–connected edge list embedded on the surface of a sphere. Each face of the spherical map is labeled with the polygon visible in the corresponding cone. We demonstrate that(More)
This paper presents a treatment of first–order discontinuities (D1) that arise in discontinuitymeshes. An algorithm is described that, given a planar D1 discontinuity surface in a polyhedral scene, computes the corresponding discontinuity curves on the faces of the scene. A method is described to efficiently update the backprojection across a D1(More)
Computer graphics is ostensibly based on projective geometry. The graphics pipeline—the sequence of functions applied to 3D geometric primitives to determine a 2D image—is described in the graphics literature as taking the primitives from Euclidean to projective space, and then back to Euclidean space. This is a weak foundation for computer graphics. An(More)