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Practical segment intersection with finite precision output
 Computer Geom. Theory Appl
, 1999
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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, ..."
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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...
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,
The spherical visibility map
 Comput. Aided Des
, 2007
"... 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 pol ..."
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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 the algorithm is efficient and robust by showing statistics of its time and space requirements for handling several classes of input. 1
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 ...
Visibility Computation on Reconfigurable Meshes
, 1995
"... Visibility problems are investigated using reconfigurable meshes. A set of algorithms are proposed on the architecture for visibility computation in two and three dimensions. We show that visibility of a total of n disjoint edges in the plane can be computed in O(1) time on an n \Theta n mesh. The ..."
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Visibility problems are investigated using reconfigurable meshes. A set of algorithms are proposed on the architecture for visibility computation in two and three dimensions. We show that visibility of a total of n disjoint edges in the plane can be computed in O(1) time on an n \Theta n mesh. The result is optimal in the word model of VLSI. For the case that the edges are not disjoint, the problem is shown to be solvable in O(1) time by using a mesh of slightly larger size or in slightly more time on an n \Theta n mesh. We also present hidden line and surface elimination algorithms that run on an n \Theta n \Theta n mesh for a set of disjoint triangles in 3space containing a total of n vertices in O(1) time and O(k) time, respectively, where 0 k ! n is an inputdependent constant. Keywords. visibility, hidden line and surface elimination, reconfigurable meshes, parallel algorithms. 1 Introduction The visibility problem has been extensively studied in the literature in computer ...
Balancing Runtime Space and Time Complexity in Synthetic Database Driven Hand Posture Reconstruction Systems
"... Abstract—Hand posture reconstruction systems based on large databases of synthetically rendered images of a 3D hand model offer a simple and flexible means of exploiting domain knowledge to provide training data. Such systems may also be applied to other domains in the posture reconstruction field b ..."
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Abstract—Hand posture reconstruction systems based on large databases of synthetically rendered images of a 3D hand model offer a simple and flexible means of exploiting domain knowledge to provide training data. Such systems may also be applied to other domains in the posture reconstruction field by changing the model under consideration. Typically, the index structures used to answer similarity queries at runtime explicitly contain the prerendered feature data. However, the combinatorial explosion resulting from the multiple degrees of freedom available to the human hand severely limits the complexity of feature data that may be embedded into the index structure. The system presented in this paper exploits realtime objectspace rendering techniques to rebalance the preprocessing and runtime workloads such that the space complexity of the database relative to the number of degrees of freedom is greatly reduced. A prototype of the database subsystem is implemented and its properties investigated to obtain insight into its scaling behaviour. I.