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A priori Delaunayconformity
"... . This communication presents a method for redening a priori a eld of constraints represented in two dimensions by a set of edges, in three dimensions by a surface triangulation. The aim is to provide a resulting constraint, strongly Delaunayconforming, (i.e., that will be built by any Delaunay tri ..."
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Cited by 6 (0 self)
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. This communication presents a method for redening a priori a eld of constraints represented in two dimensions by a set of edges, in three dimensions by a surface triangulation. The aim is to provide a resulting constraint, strongly Delaunayconforming, (i.e., that will be built by any Delaunay
MAPS: Multiresolution Adaptive Parameterization of Surfaces
, 1998
"... We construct smooth parameterizations of irregular connectivity triangulations of arbitrary genus 2manifolds. Our algorithm uses hierarchical simplification to efficiently induce a parameterization of the original mesh over a base domain consisting of a small number of triangles. This initial param ..."
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Cited by 273 (13 self)
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We construct smooth parameterizations of irregular connectivity triangulations of arbitrary genus 2manifolds. Our algorithm uses hierarchical simplification to efficiently induce a parameterization of the original mesh over a base domain consisting of a small number of triangles. This initial parameterization is further improved through a hierarchical smoothing procedure based on Loop subdivision applied in the parameter domain. Our method supports both fully automatic and user constrained operations. In the latter, we accommodate point and edge constraints to force the align # wailee@cs.princeton.edu + wim@belllabs.com # ps@cs.caltech.edu cowsar@belllabs.com dpd@cs.princeton.edu ment of isoparameter lines with desired features. We show how to use the parameterization for fast, hierarchical subdivision connectivity remeshing with guaranteed error bounds. The remeshing algorithm constructs an adaptively subdivided mesh directly without first resorting to uniform subdivision followed by subsequent sparsification. It thus avoids the exponential cost of the latter. Our parameterizations are also useful for texture mapping and morphing applications, among others.
Numerical Conformal Mapping Using CrossRatios And Delaunay Triangulation
 SIAM J. Sci. Comput
"... We propose a new algorithm for computing the Riemann mapping of the unit disk to a polygon, also known as the SchwarzChristoffel transformation. The new algorithm, CRDT (for crossratios of the Delaunay triangulation), is based on crossratios of the prevertices, and also on crossratios of quadril ..."
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Cited by 33 (7 self)
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ratios of quadrilaterals in a Delaunay triangulation of the polygon. The CRDT algorithm produces an accurate representation of the Riemann mapping even in the presence of arbitrary long, thin regions in the polygon, unlike any previous conformal mapping algorithm. We believe that CRDT solves all difficulties with crowding
Stochastic Geometry and Wireless Networks, Volume
 II — Applications. Foundations and Trends in Networking. NoW Publishers
"... i Preface A wireless communication network can be viewed as a collection of nodes, located in some domain, which can in turn be transmitters or receivers (depending on the network considered, nodes may be mobile users, base stations in a cellular network, access points of a WiFi mesh etc.). At a giv ..."
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Cited by 257 (37 self)
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i Preface A wireless communication network can be viewed as a collection of nodes, located in some domain, which can in turn be transmitters or receivers (depending on the network considered, nodes may be mobile users, base stations in a cellular network, access points of a WiFi mesh etc.). At a given time, several nodes transmit simultaneously, each toward its own receiver. Each transmitter–receiver pair requires its own wireless link. The signal received from the link transmitter may be jammed by the signals received from the other transmitters. Even in the simplest model where the signal power radiated from a point decays in an isotropic way with Euclidean distance, the geometry of the locations of the nodes plays a key role since it determines the signal to interference and noise ratio (SINR) at each receiver and hence the possibility of establishing simultaneously this collection of links at a given bit rate. The interference seen by a receiver is the sum of the signal powers received from all transmitters, except its own transmitter. Stochastic geometry provides a natural way of defining and computing macroscopic properties of such networks, by averaging over all potential geometrical patterns for the nodes, in the same way as queuing theory provides response times or congestion, averaged over all potential arrival patterns within a given parametric class.
Adaptive Precision FloatingPoint Arithmetic and Fast Robust Geometric Predicates
 Discrete & Computational Geometry
, 1996
"... Exact computer arithmetic has a variety of uses including, but not limited to, the robust implementation of geometric algorithms. This report has three purposes. The first is to offer fast softwarelevel algorithms for exact addition and multiplication of arbitrary precision floatingpoint values. T ..."
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Cited by 172 (5 self)
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, and robust Delaunay triangulation using these tests. Timings of the implementations demonstrate their effectiveness. Supported in part by the Natural Sciences and Engineering Research Council of Canada under a 1967 Science and Engineering Scholarship and by the National Science Foundation under Grant CMS
landmarks: tools for evaluating a priori hypotheses
"... SUMMARY Identifying the modular components of a configuration of landmarks is an important task of morphometric analyses in evolutionary developmental biology. Modules are integrated internally by many interactions among their component parts, but are linked to one another only by few or weak intera ..."
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SUMMARY Identifying the modular components of a configuration of landmarks is an important task of morphometric analyses in evolutionary developmental biology. Modules are integrated internally by many interactions among their component parts, but are linked to one another only by few or weak interactions. Accordingly, traits within modules are tightly correlated with each other, but relatively independent of traits in other modules. Hypotheses concerning the boundaries of modules in a landmark configuration can therefore be tested by comparing the strength of covariation among alternative partitions of the configuration into subsets of landmarks. If a subdivision coincides with the true boundaries between modules, the correlations among subsets should be minimal. This article introduces Escoufier’s RV coefficient and the multiset RV coefficient as measures of the correlation between two or more subsets of landmarks. These measures can be compared between alternative partitions of the configuration into subsets. Because developmental interactions are tissue bound, it is sensible to require that modules should be spatially contiguous. I propose a criterion for spatial contiguity for sets of landmarks using an adjacency graph. The new methods are demonstrated with data on shape of the wing in Drosophila melanogaster and the mandible of the house mouse.
ObjectCentered Surface Reconstruction: Combining MultiImage Stereo and Shading
 International Journal of Computer Vision
, 1995
"... Our goal is to reconstruct both the shape and reflectance properties of surfaces from multiple images. We argue that an objectcentered representation is most appropriate for this purpose because it naturally accommodates multiple sources of data, multiple images (including motion sequences of a rig ..."
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Cited by 133 (20 self)
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Our goal is to reconstruct both the shape and reflectance properties of surfaces from multiple images. We argue that an objectcentered representation is most appropriate for this purpose because it naturally accommodates multiple sources of data, multiple images (including motion sequences of a rigid object), and selfocclusions. We then present a specific objectcentered reconstruction method and its implementation. The method begins with an initial estimate of surface shape provided, for example, by triangulating the result of conventional stereo. The surface shape and reflectance properties are then iteratively adjusted to minimize an objective function that combines information from multiple input images. The objective function is a weighted sum of stereo, shading, and smoothness components, where the weight varies over the surface. For example, the stereo component is weighted more strongly where the surface projects onto highly textured areas in the images, and less strongly othe...
The traveling salesman problem
, 1994
"... This paper presents a selfcontained introduction into algorithmic and computational aspects of the traveling salesman problem and of related problems, along with their theoretical prerequisites as seen from the point of view of an operations researcher who wants to solve practical problem instances ..."
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Cited by 130 (5 self)
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This paper presents a selfcontained introduction into algorithmic and computational aspects of the traveling salesman problem and of related problems, along with their theoretical prerequisites as seen from the point of view of an operations researcher who wants to solve practical problem instances. Extensive computational results are reported on most of the algorithms described. Optimal solutions are reported for instances with sizes up to several thousand nodes as well as heuristic solutions with provably very high quality for larger instances. This is a preliminary version of one of the chapters of the volume “Networks”
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