Results 291 to 300 of about 144,513 (307)
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1965
Publisher Summary The group of similarity transformations of the plane is a subgroup of a group of more general transformations that preserve collinearity and parallelism but not, in general, the lengths of segments and the sizes of angles or areas. These transformations are called affine transformations.
A.S. Parkhomenko, P.S. Modenov
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Publisher Summary The group of similarity transformations of the plane is a subgroup of a group of more general transformations that preserve collinearity and parallelism but not, in general, the lengths of segments and the sizes of angles or areas. These transformations are called affine transformations.
A.S. Parkhomenko, P.S. Modenov
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Affine Transformational Optics
Frontiers in Optics 2011/Laser Science XXVII, 2011We describe a class of devices whose refractive index distribution results from an affine transformation over piece–wise uniform space, including theoretical analysis and experimental realizations using anisotropic materials and surface nanopatterning.
Handong Sun +7 more
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Realization of fractal affine transformation
Journal of Shanghai University (English Edition), 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lin Yi-xia, Xu Jing
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Affine transformations and the geometry of superspace
Journal of Mathematical Physics, 1981A graded Cartan-type connection is devised on a bundle of graded affine frames over superspace. The relation of the gauged graded affine group to the geometry of superspace is discussed in the context of bundle reduction to simulate spontaneous symmetry breakdown. A complex quaternionic calculus is used to simplify the algebraic analysis.
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2016
The name, which goes back to Mobius and Leonhard Euler, implies that, in such a transformation, infinitely distant points correspond again to infinitely distant points, so that, in a sense, the “ends” of space are preserved. In fact, the formulas show at once that x´, y´, z´ become infinite with x, y, z.
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The name, which goes back to Mobius and Leonhard Euler, implies that, in such a transformation, infinitely distant points correspond again to infinitely distant points, so that, in a sense, the “ends” of space are preserved. In fact, the formulas show at once that x´, y´, z´ become infinite with x, y, z.
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Affine and Projective Transformations
2010In addition to isometries, there are two kinds of mappings that preserve lines: affine (Section 3.1) and projective (Section 3.2) transformations. Affine transformations f of \({\mathbb{R}}^{n}\) have the following property: If l is a line then f(l) is also a line, and if l ∥ k then f(l) ∥ f(k). A line in \({\mathbb{R}}^{n}\) means a set of the form {r
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Affine Transformations in Affine Differential Geometry
Results in Mathematics, 1989openaire +2 more sources
Affine and Projective Transformations (Affinities and Projectivities)
1973Abe Shenitzer, I. M. Yaglom
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