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An Implicit Surface Polygonizer
 Graphics Gems IV
, 1994
"... Introduction Some shapes are more readily defined by implicit, rather than parametric, techniques. For example, consider a sphere centered at C with radius r. It can be described parametrically as {P}, where: (P x , P y , P z ) = (C x , C y , C z )+(r cosb cosa, r cosb sina, r sinb), a (0, 2p), b ..."
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Cited by 142 (0 self)
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(p/2, p/2). The implicit definition for the same sphere is more compact: (P x C x ) 2 +(P y C y ) 2 +(P z C z ) 2<F1
On Compatible Triangulations of Simple Polygons
 Computational Geometry: Theory and Applications
, 1993
"... It is well known that, given two simple nsided polygons, it may not be possible to triangulate the two polygons in a compatible fashion, if one's choice of triangulation vertices is restricted to polygon corners. Is it always possible to produce compatible triangulations if additional vertices ..."
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Cited by 48 (3 self)
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, we also show that creating compatible triangulations requires a quadratic number of extra vertices in the worst case. 1 The Problem Given two simple polygons P 1 and P 2 , each with n vertices, it is not always possible to find compatible triangulations of the two polygons. In other words, there may
Searching for Mobile Intruders in a Polygonal Region by a Group of Mobile Searchers
 SIAM JOURNAL ON COMPUTING
"... The problem of searching for mobile intruders in a polygonal region by mobile searchers is considered. A searcher can move continuously inside a polygon holding a flashlight that emits a single ray of light whose direction can be changed continuously. The visibility of a searcher at any time instant ..."
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Cited by 156 (3 self)
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+ blog 3 rc, and ps(P ) 2 + dlog 2 ge. These upper bounds are tight or almost tight in the worst case, since we show that for any natural number s 2, there is a polygon P such that ps(P ) = log 3 (n + 1) = log 3 (2r + 3) = 1 + log 3 (2g \Gamma 1) = s.
Improved Localization of Cortical Activity by Combining EEG and MEG with MRI Cortical Surface Reconstruction: A Linear Approach
 J. Cogn. Neurosci
, 1993
"... We describe a comprehensive linear approach to the prob lem of imaging brain activity with high temporal as well as spatial resolution based on combining EEG and MEG data with anatomical constraints derived from MRI images. The "inverse problem" of estimating the distribution of dipole st ..."
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Cited by 263 (19 self)
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formulation. ;m explicit polygonal model of the cortical manifold is first constructed :,s follows: (1) slice data in three onhogon;,l pJ:,ncs of section (needleshaped voxels) are combined with a linear aleblurring technique to make a single high.resolution 3D image (cubic voxels), (2) the image
Dissections of polygons into convex polygons
"... Abstract In the paper we present purely combinatorial conditions that allow us to recognize the topological equivalence (or nonequivalence) of two given dissections. Using a computer program based on this result, we are able to generate a set which contains all topologically nonequivalent dissect ..."
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equivalent dissections of a p0gon into convex pigons, i = 1, ..., n, where n, p0, ..., pn are integers such that n ≥ 2, pi ≥ 3. By analyzing generated structures, we are able to find all (up to similarity) dissections of a given type. Since the number of topologically nonequivalent dissections is huge even
Rotational Polygon Overlap Minimization
 Computational Geometry: Theory and Applications
, 1997
"... An effective and fast algorithm is given for rotational overlap minimization: given an overlapping layout of polygons P1 ; P2 ; P3 ; : : : ; Pk in a container polygon C, translate and rotate the polygons to a layout that minimizes an overlap measure. A (local) overlap minimum has the property that ..."
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Cited by 5 (1 self)
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An effective and fast algorithm is given for rotational overlap minimization: given an overlapping layout of polygons P1 ; P2 ; P3 ; : : : ; Pk in a container polygon C, translate and rotate the polygons to a layout that minimizes an overlap measure. A (local) overlap minimum has the property
deformations of polygons
 Proc. Annual Symposium on Computational Geometry
, 1989
"... We consider a discrete version of the WhitneyGraustein theorem concerning regular equivalence of closed curves. Two regular polygons P and P’, i.e. polygons without overlapping adjacent edges, are called regularly equivalent if there is a continuous oneparameter family Pa, 0 5 s 5 1, of regular po ..."
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Cited by 5 (0 self)
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We consider a discrete version of the WhitneyGraustein theorem concerning regular equivalence of closed curves. Two regular polygons P and P’, i.e. polygons without overlapping adjacent edges, are called regularly equivalent if there is a continuous oneparameter family Pa, 0 5 s 5 1, of regular
Rotational Polygon Overlap Minimization and Compaction
 Computational Geometry: Theory and Applications
, 1998
"... An effective and fast algorithm is given for rotational overlap minimization: given an overlapping layout of polygons P 1 ,P 2 ,P 3 ,...,P k in a container polygon Q, translate and rotate the polygons to diminish their overlap to a local minimum. A (local) overlap minimum has the property that any p ..."
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Cited by 9 (2 self)
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An effective and fast algorithm is given for rotational overlap minimization: given an overlapping layout of polygons P 1 ,P 2 ,P 3 ,...,P k in a container polygon Q, translate and rotate the polygons to diminish their overlap to a local minimum. A (local) overlap minimum has the property that any
On The Moduli Space Of Polygons In The Euclidean Plane
 Journal of Differential Geometry
, 1994
"... . We study the topology of moduli spaces of polygons with fixed side lengths in the Euclidean plane. We establish a duality between the spaces of marked Euclidean polygons with fixed side lengths and marked convex Euclidean polygons with prescribed angles. 1. We consider the space P n of all polygon ..."
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Cited by 69 (7 self)
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. We study the topology of moduli spaces of polygons with fixed side lengths in the Euclidean plane. We establish a duality between the spaces of marked Euclidean polygons with fixed side lengths and marked convex Euclidean polygons with prescribed angles. 1. We consider the space P n of all
Tiling a Polygon with Rectangles
 Proc. 33rd Symp. Foundations of Computer Science
, 1992
"... We study the problem of tiling a simple polygon of surface n with rectangles of given types (tiles). We present a linear time algorithm for deciding if a polygon can be tiled with 1 \Theta m and k \Theta 1 tiles (and giving a tiling when it exists), and a quadratic algorithm for the same problem whe ..."
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Cited by 35 (4 self)
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We study the problem of tiling a simple polygon of surface n with rectangles of given types (tiles). We present a linear time algorithm for deciding if a polygon can be tiled with 1 \Theta m and k \Theta 1 tiles (and giving a tiling when it exists), and a quadratic algorithm for the same problem
Results 1  10
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743