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160
Threesomes, degenerates, and love triangles
 In Proc. 55th Annu. IEEE Sympos. Found. Comput. Sci. (FOCS
, 2014
"... The 3SUM problem is to decide, given a set of n real numbers, whether any three sum to zero. It is widely conjectured that a trivial Opn2qtime algorithm is optimal and over the years the consequences of this conjecture have been revealed. This 3SUM conjecture implies Ωpn2q lower bounds on numerous ..."
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Cited by 3 (1 self)
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problems in computational geometry and a variant of the conjecture implies strong lower bounds on triangle enumeration, dynamic graph algorithms, and string matching data structures. In this paper we refute the 3SUM conjecture. We prove that the decision tree complexity of 3SUM is Opn3{2?log nq and give
Euler’ triangle determination problem
 Forum Geom
, 2007
"... Abstract. We give a simple proof of Euler’s remarkable theorem that for a nondegenerate triangle, the set of points eligible to be the incenter is precisely the orthocentroidal disc, punctured at the ninepoint center. The problem is handled algebraically with complex coordinates. In particular, we ..."
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Abstract. We give a simple proof of Euler’s remarkable theorem that for a nondegenerate triangle, the set of points eligible to be the incenter is precisely the orthocentroidal disc, punctured at the ninepoint center. The problem is handled algebraically with complex coordinates. In particular
A Robust Procedure to Eliminate Degenerate Faces from Triangle Meshes
 VISION, MODELING AND VISUALIZATION (VMV01
, 2001
"... When using triangle meshes in numerical simulations or other sophisticated downstream applications, we have to guarantee that no degenerate faces are present since they have, e.g., no well defined normal vectors. In this paper we present a simple but effective algorithm to remove such artifacts from ..."
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Cited by 22 (1 self)
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When using triangle meshes in numerical simulations or other sophisticated downstream applications, we have to guarantee that no degenerate faces are present since they have, e.g., no well defined normal vectors. In this paper we present a simple but effective algorithm to remove such artifacts
Triangle Rasterization
, 2007
"... We will have α, β, γ ∈ [0, 1] if and only if x is in the triangle. Intuitively, a triangle consists of all weighted averages of its vertices. We call (α, β, γ) the barycentric coordinates of x. This is a nonorthogonal coordinate system for the plane. (Of course, none of this works if the triangle i ..."
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is degenerate, i.e. if the vertices lie along a common line.) 2 Rasterization Now suppose you want to draw a triangle with vertices pi = (xi, yi) , i ∈ {0, 1, 2} onto a canvas of discrete pixels. This is called triangle rasterization and can be accomplished in many ways; what follows is one conceptually simple
A Robust Procedure to Eliminate Degenerate Faces from Triangle Meshes
"... When using triangle meshes in numerical simulations or other sophisticated downstream applications, we have to guarantee that no degenerate faces are present since they have, e.g., no well defined normal vectors. In this paper we present a simple but effective algorithm to remove such artifacts from ..."
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When using triangle meshes in numerical simulations or other sophisticated downstream applications, we have to guarantee that no degenerate faces are present since they have, e.g., no well defined normal vectors. In this paper we present a simple but effective algorithm to remove such artifacts
Triangle inequalities in path metric spaces
 Geom. Topol
"... Abstract. We study sidelengths of triangles in path metric spaces. We prove that unless such a space X is bounded, or quasiisometric to R+ or to R, every triple of real numbers satisfying the strict triangle inequalities, is realized by the sidelengths of a triangle in X. We construct an example ..."
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of a complete path metric space quasiisometric to R 2 for which every degenerate triangle has one side which is shorter than a certain uniform constant. Given a metric space X define K3(X): = {(a, b, c) ∈ R 3 +: ∃ points x, y, z so that
A Simple and Efficient Triangle Strip Filtering Algorithm
"... A triangle strip is one of the standard rendering primitives used to reduce the amount of data transmitted to the graphics pipeline. In order to exploit such efficient triangulation data in levelofdetailbased rendering applications, realtime updating of triangle strips is required, and it can be ..."
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be done by repeating vertices. However, the number of degenerate triangles increases in strips as the mesh degrades to a coarser level. Such triangles only add overhead to the rendering task. In this paper, we propose a simple and efficient triangle strip filtering algorithm to convert a strip into a more
Handling Degenerate Cases in Exact Geodesic Computation On Triangle Meshes
 THE VISUAL COMPUTER
"... The computation of exact geodesics on triangle meshes is a widely used operation in computeraided design and computer graphics. Practical algorithms for computing such exact geodesics have been recently proposed by Surazhsky et al (2005). By applying these geometric algorithms to realworld data, ..."
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Cited by 13 (5 self)
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The computation of exact geodesics on triangle meshes is a widely used operation in computeraided design and computer graphics. Practical algorithms for computing such exact geodesics have been recently proposed by Surazhsky et al (2005). By applying these geometric algorithms to realworld data
ON LUCAS vTRIANGLES
, 1999
"... Let N = {0,1,2,...} and T = M \ {0}. Let A and B be fixed nonzero integers with (A,B) = l, and write A = A 24B. We will assume A^O, which excludes degenerate cases including \A \ = 2 and B = 1. Define {un}neN and {vn}neN as follows: u ..."
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Let N = {0,1,2,...} and T = M \ {0}. Let A and B be fixed nonzero integers with (A,B) = l, and write A = A 24B. We will assume A^O, which excludes degenerate cases including \A \ = 2 and B = 1. Define {un}neN and {vn}neN as follows: u
New specifications for exponential random graph models
, 2004
"... The most promising class of statistical models for expressing structural properties of social networks observed at one moment in time, is the class of Exponential Random Graph Models (ERGMs), also known as p ∗ models. The strong point of these models is that they can represent a variety of structura ..."
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Cited by 168 (27 self)
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to observed network data often has led to problems, however, which can be traced back to the fact that important parts of the parameter space correspond to nearly degenerate distributions, which may lead to convergence problems of estimation algorithms, and a poor fit to empirical data. This paper proposes
Results 1  10
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