منابع مشابه
Generalized polar varieties: geometry and algorithms
Let V be a closed algebraic subvariety of the n–dimensional projective space over the complex or real numbers and suppose that V is non–empty and equidimensional. The classic notion of a polar variety of V associated with a given linear subvariety of the ambient space of V was generalized and motivated in [2]. As particular instances of this notion of a generalized polar variety one reobtains t...
متن کاملA Simple Compact Fourth-Order PoissonSolver on Polar Geometry
We present a simple and efficient compact fourth-order Poisson solver in polar coordinates. This solver relies on the truncated Fourier series expansion, where the differential equations of the Fourier coefficients are solved by the compact fourthorder finite difference scheme. By shifting a grid a half mesh away from the origin and incorporating the symmetry constraint of Fourier coefficients,...
متن کاملThe geometry of hyperbolic lines in polar spaces
In this paper we consider partial linear spaces induced on the point set of a polar space, but with as lines the hyperbolic lines of this polar space. We give some geometric characterizations of these and related spaces. These results can be viewed as the geometric counterpart of the theory of k-transvection groups as developed by Timmesfeld and others.
متن کاملGeometry and construction of straight lines in log-polar images
This paper investigates, how straight lines are mapped to the non-Euclidean log-polar image plane and how their properties in logpolar coordinates can be used to perform two fundamental measurement operations: the construction of straight lines of given orientation angle and the measurement of distances along these lines. It is shown, how the two operations can be efficiently implemented for di...
متن کاملThe geometry of secants in embedded polar spaces
Consider a polar space S weakly embedded in a projective space P. A secant of S is the intersection of the point set of S with a line of P spanned by two non-collinear points of S. The geometry consisting of the points of S and as lines the secants is a so-called Delta space. In this paper we give a characterization of this and some related geometries.
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ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1960
ISSN: 1385-7258
DOI: 10.1016/s1385-7258(60)50028-x