منابع مشابه
Point Configurations and Coxeter Operads
The minimal blow-ups of simplicial Coxeter complexes are natural generalizations of the real moduli space of Riemann spheres. They inherit a tiling by the graph-associahedra convex polytopes. We obtain explicit configuration space models for the classical infinite families of finite and affine Weyl groups using particles on lines and circles. A Fulton-MacPherson compactification of these spaces...
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We present an algorithm that verifies if two unlabeled configurations of N points in Rd are or are not an orthogonal transformation of one another, and if applicable, explicitly compute that transformation. We also give a formula for the orthogonal transformation in the case of noisy measurements. AMS subject classification: 65F15, 65F35, 65G99.
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The study of combinatorial properties of finite point configurations is a vast area of research in geometry, whose origins go back at least to the ancient Greeks. Since it includes virtually all problems starting with “consider a set of n points in space,” space limitations impose the necessity of making choices. As a result, we will restrict our attention to Euclidean spaces and will discuss p...
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We consider the problem of translating a given pattern set B of size m, and matching every point of B to some point of a larger ground set A of size n in an injective way, minimizing the sum of the squared distances between matched points. We show that when B can only be translated along a line, there can be at most m(n − m) + 1 different matchings as B moves along the line, and hence the optim...
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For most algorithms dealing with sets of points in the plane, the only relevant information carried by the input is the combinatorial configuration of the points: the orientation of each triple of points in the set (clockwise, counterclockwise, or collinear). This information is called the order type of the point set. In the dual, realizable order types and abstract order types are combinatoria...
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ژورنال
عنوان ژورنال: Manuscripta Mathematica
سال: 2014
ISSN: 0025-2611,1432-1785
DOI: 10.1007/s00229-014-0692-8