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Geometric Objects and Cohomology Operations
 Proc. of the 5th Workshop on Computer Algebra in Scientific Computing
, 2002
"... Cohomology operations (including the cohomology ring) of a geometric object are finer algebraic invariants than the homology of it. In the literature, there exist various algorithms for computing the homology groups of simplicial complexes ([Mun84], [DE95,ELZ00], [DG98]), but concerning the algorith ..."
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Cited by 4 (4 self)
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Cohomology operations (including the cohomology ring) of a geometric object are finer algebraic invariants than the homology of it. In the literature, there exist various algorithms for computing the homology groups of simplicial complexes ([Mun84], [DE95,ELZ00], [DG98]), but concerning
Arrangements of Geometric Objects
 in Handbook of Discrete and Combinatorial Mathematics
"... INTRODUCTION A wide range of applied fields (Statistics, Computer Graphics, Robotics, Geographical Databases) depend on solutions to geometric problems: polygon intersection, visibility computations, range searching, shortest paths among obstacles, just to name a few. These problems typically start ..."
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in the field of Computational Geometry. In this section we will restrict our attention to the most studied and best understood arrangements of geometric objects: points, lines and hyperplanes. Introducing the concepts relies on linear algebra. The combinatorial properties we are interested in belong however
On Approximation in Spaces of Geometric Objects
 Mathematics of Surfaces IX
, 2000
"... this paper, we will restrict the class of developable surfaces we are working with: We only consider surfaces whose family of tangent planes is of the form U(t) = (u 0 (t); u 1 (t); u 2 (t); 1) () z = u 0 (t) + u 1 (t)x + u 2 (t)y: (17) 10 Helmut Pottmann and Martin Peternell For NURBS surfaces th ..."
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Cited by 4 (1 self)
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this paper, we will restrict the class of developable surfaces we are working with: We only consider surfaces whose family of tangent planes is of the form U(t) = (u 0 (t); u 1 (t); u 2 (t); 1) () z = u 0 (t) + u 1 (t)x + u 2 (t)y: (17) 10 Helmut Pottmann and Martin Peternell For NURBS surfaces this is equivalent to the choice of control planes U i = (u 0;i , u 1;i , u 2;i , u 3;i ) such that always u 3;i = 1. This means that for all possible planes U we no longer allow to choose an arbitrary coordinate quadruple describing U , but we restrict ourselves to the unique one whose last coordinate equals 1. This is not possible if the last coordinate is zero, so we have to exclude all surfaces with tangent planes parallel to the zaxis. In most cases this requirement is easily fullled by choosing an appropriate coordinate system
State of the Union (of Geometric Objects)
 CONTEMPORARY MATHEMATICS
"... Let C be a set of geometric objects in R d. The combinatorial complexity of the union of C is the total number of faces of all dimensions on its boundary. We survey the known upper bounds on the complexity of the union of n geometric objects satisfying various natural conditions. These bounds play ..."
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Cited by 11 (7 self)
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Let C be a set of geometric objects in R d. The combinatorial complexity of the union of C is the total number of faces of all dimensions on its boundary. We survey the known upper bounds on the complexity of the union of n geometric objects satisfying various natural conditions. These bounds
SIMPLIFICATION, ESTIMATION AND CLASSIFICATION OF GEOMETRIC OBJECTS
, 2004
"... The main focus of this thesis is on the analysis, via simplification, estimation and classification, of discrete geometric objects using methods from discrete and combinatorial geometry. Geometric objects are ubiquitous in computing today, with uses in areas from GIS to structural molecular biology ..."
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Cited by 1 (1 self)
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The main focus of this thesis is on the analysis, via simplification, estimation and classification, of discrete geometric objects using methods from discrete and combinatorial geometry. Geometric objects are ubiquitous in computing today, with uses in areas from GIS to structural molecular
ON HOMOGENITY AND TRANSITIVITY OF FIELDS OF GEOMETRIC OBJECTS
"... ABSTRACT. If a is a field of geometric objects on a manifold M then we can associate with it a principal subbundle of Hr (M). We show that (infinitesimal) homogenity and (iñfinitesi mal) transitivity of this subbundle are equivalent to some int_e gral conditions for the Lie eauations generated by a. ..."
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ABSTRACT. If a is a field of geometric objects on a manifold M then we can associate with it a principal subbundle of Hr (M). We show that (infinitesimal) homogenity and (iñfinitesi mal) transitivity of this subbundle are equivalent to some int_e gral conditions for the Lie eauations generated by a
Results 1  10
of
484,500