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Practical Segment Intersection with Finite Precision Output
 Comput. Geom. Theory Appl
, 1993
"... This paper presents simple solutions to these problems and shows that they impose only a very modest performance penalty. Test data came from a data compression problem involving a map database. ..."
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Cited by 32 (0 self)
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This paper presents simple solutions to these problems and shows that they impose only a very modest performance penalty. Test data came from a data compression problem involving a map database.
Point Probe Decision Trees for Geometric Concept Classes
, 1993
"... A fundamental problem in modelbased computer vision is that of identifying to which of a given set of concept classes of geometric models an observed model belongs. Considering a "probe" to be an oracle that tells whether or not the observed model is present at a given point in an image, we study t ..."
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Cited by 7 (5 self)
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A fundamental problem in modelbased computer vision is that of identifying to which of a given set of concept classes of geometric models an observed model belongs. Considering a "probe" to be an oracle that tells whether or not the observed model is present at a given point in an image, we study the problem of computing efficient strategies ("decision trees") for probing an image, with the goal to minimize the number of probes necessary (in the worst case) to determine in which class the observed model belongs. We prove a hardness result and give strategies that obtain decision trees whose height is within a log factor of optimal. These results grew out of discussions that began in a series of workshops on Geometric Probing in Computer Vision, sponsored by the Center for Night Vision and ElectroOptics, Fort Belvoir, Virginia, and monitored by the U.S. Army Research Office. The views, opinions, and/or findings contained in this report are those of the authors and should not be con...
On the Complexity of Some Geometric Intersection Problems
 Journal of Computing and Information
, 1995
"... : A classification of polygons is proposed together with a new class of connected polygons, called ordinary polygons. Ordinary polygons include simple polygons possibly with holes. The determination of the intersection of a line segment and an ordinary polygon with N edges requires\Omega\Gamma N lo ..."
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: A classification of polygons is proposed together with a new class of connected polygons, called ordinary polygons. Ordinary polygons include simple polygons possibly with holes. The determination of the intersection of a line segment and an ordinary polygon with N edges requires\Omega\Gamma N log N) time in the worst case. A lineartime algorithm is given, however, if a planar subdivision of the polygon in trapezoids is allowed as a preprocessing. As the minimal trapezoidal subdivision of an ordinary polygon is NPcomplete, we propose a subdivision that, although not minimal, has at most 3N vertices and 5N edges, and can be computed in optimal \Theta(N log N) time in the worst case. The intersection of an Medge ordinary polygon with an Nedge ordinary polygon can be obtained in \Theta(M log M + MN + N log N) time, which is also worstcase optimal. Applications to worstcase optimal clipping and scanconversion algorithms and efficient hiddenline and hiddensurface algorithms th...
On the Computational Requirements of Virtual Reality Systems
, 1997
"... The computational requirements of highquality, realtime rendering exceeds the limits of generally available computing power. However illumination effects, except shadows, are less noticeable on moving pictures. Shadows can be produced with the same techniques used for visibility computations, ther ..."
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The computational requirements of highquality, realtime rendering exceeds the limits of generally available computing power. However illumination effects, except shadows, are less noticeable on moving pictures. Shadows can be produced with the same techniques used for visibility computations, therefore the basic requirements of realtime rendering are transformations, preselection of the part of the scene to be displayed and visibility computations. Transformations scale well, ie, their time requirement grows linearly with the input size. Preselection, if implemented by the traditional way of polygon clipping, has a growing rate of N log N in the worst case, where N is the total number of edges in the scene. Visibility computations, exhibiting a quadratic growing rate, are the bottleneck from a theoretical point of view. Three approaches are discussed to speed up visibility computations: (i) reducing the expected running time to O(N log N ) (ii) using approximation algorithms with ...
A Geometric Framework for Computer Graphics Addressing Modeling, Visibility, and Shadows
, 1999
"... The main question this dissertation addresses is the following: Is it possible to design a computer graphics API such that modeling primitives, computing visibility, and generating shadows from point, linear, and area light sources can be conveniently and concisely expressed? The thesis answers this ..."
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The main question this dissertation addresses is the following: Is it possible to design a computer graphics API such that modeling primitives, computing visibility, and generating shadows from point, linear, and area light sources can be conveniently and concisely expressed? The thesis answers this question in the affirmative by describing a framework for geometric computing in computer graphics. The classes in the layered system constituting the framework are described using the UML notation and each algorithm presented is encapsulated in a member method of a class in the hierarchy. We identify a number of abstractions for object–space graphics such as transparent visibility and opaque visibility. These abstractions are somewhat harder to implement than standard rasterized abstractions as they rely on graphs and planar maps. Nevertheless, these notions prove to be fundamental in this work on object–space graphics and also appear to be fundamental for computer graphics in general. We propose that clients of a graphics API such as the one presented here should be relieved from the onus of computing shadows and we show that the computation of shadows can be automated and encapsulated in the framework. We address illumination under a point, a linear,