Showing papers on "Affine transformation published in 1985"
TL;DR: In this paper, a convex body is defined as a compact convex set with interior points in Euclidean n-dimensional space En and the affine surface area is defined for a restricted class of convex bodies.
Abstract: The purpose of this paper is to remove regularity assumptions on the class of convex bodies for which equality is obtained in three closely related affine extremal problems. These three problems are described in Sections 2, 3, and 4. The need to remove regularity assumptions was recently pointed out by Schneider [l5, p. 5521. Throughout this paper, a convex body is defined as a compact convex set with interior points in Euclidean n-dimensional space En. The oldest of these problems is called the a f h e isoperimetric problem and involves the afine surface area which is defined for a restricted class of convex bodies. Let K c En be a convex body whose surface aK is of class C2 and has positive Gaussian curvature C(u), where u is the outer normal to aK at the point of d K with Gaussian curvature G(u). The afine surface area A,(K) of K is defined by
177 citations
TL;DR: Theorem 3.1 in this paper generalizes that one previously given by Wang (1970) for affine non-linear systems, i.e., the scalar-input-scalar-output decoupling problem for square systems, with dynamic compensation.
Abstract: In this paper we tackle, for affine non-linear systems, the ‘Morgan Problem’, i.e. the scalar-input-scalar-output decoupling problem for square systems, with dynamic compensation. The result provided here (Theorem 3.1) generalizes that one previously given by Wang (1970) for linear systems.
173 citations
172 citations
TL;DR: In this paper, the authors define the Clifford and Weyl algebras as associative algebra with generators ai, a*, 1 < i < I, having, respectively, the anticommutation or commutation relations.
138 citations
TL;DR: A method is developed by which images resulting from orthogonal projection of rigid planar-patch objects arbitrarily oriented in three-dimensional (3-D) space may be used to form systems of linear equations which are solved for the affine transform relating the images.
Abstract: A method is developed by which images resulting from orthogonal projection of rigid planar-patch objects arbitrarily oriented in three-dimensional (3-D) space may be used to form systems of linear equations which are solved for the affine transform relating the images. The technique is applicable to complete images and to unlabeled feature sets derived from images, and with small modification may be used to transform images of unknown objects such that they represent images of those objects from a known orientation, for use in object identification. No knowledge of point correspondence between images is required. Theoretical development of the method and experimental results are presented. The method is shown to be computationally efficient, requiring O(N) multiplications and additions where, depending on the computation algorithm, N may equal the number of object or edge picture elements.
131 citations
01 Sep 1985
TL;DR: In this paper, the authors survey the potential method for blending implicit algebraic surfaces, summarizing and extending work previously reported, and give two paradigms by which to understand the method: the first paradigm views the blends as surfaces swept out by a family of space curves.
Abstract: We survey the potential method for blending implicit algebraic surfaces, summarizing and extending work previously reported. The method is capable of deriving blends for pairs of algebraic surfaces, and is guaranteed to produce blending surfaces of lowest possible degree for two quadrics in general position. We give two paradigms by which to understand the method. The first paradigm views the blends as surfaces swept out by a family of space curves. The second, more general paradigm considers the surfaces as result of deformation of a parameter space effected by substitution. The method has a general formulation based on projective parameter spaces, but is also the image under projective transformation of the simpler, affine formulation. The deformation by substitution paradigm is extended to blend blending surfaces at solid vertices without a degree penalty, under the assumption that the vertex valence has been reduced to three. It may also lead to a general solution for blending patches of algebraic surfaces that meet tangentially. A special case of this problem is solved and illustrated.
120 citations
119 citations
76 citations
Patent•
23 Sep 1985
TL;DR: In this article, the authors proposed a method to reduce the processing time by dividing an image into a plurality of sections and subjecting the thus-divided images to an image processing in a limited memory space.
Abstract: The present invention makes it possible to reduce the processing time by dividing an image, which is to be subjected to a processing, into a plurality of sections and subjecting the thus-divided images to an image processing in a limited memory space, especially, by making most effective use of the memory spaces of plural buffer memories to reduce the number of divisions of the original picture when a high-speed affine transformation is performed in the plural buffer memories.
73 citations
TL;DR: In this article, a local definition of zeros at infinity for affine nonlinear control systems is proposed, and a necessary and sufficient condition for the solvability of the general regular decoupling problem in terms of the zero at infinity is given.
Abstract: A definition of zeros at infinity for affine nonlinear control systems is proposed. The definition is local, which means that we exclude certain singularities. We argue the reasonableness of our definition by showing its relevance to the problem of nonlinear decoupling. In particular, we give a necessary and sufficient condition for the solvability of the general regular decoupling problem for affine systems in terms of the zeros at infinity.
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TL;DR: In this paper, a local definition of zeros at infinity for affine nonlinear control systems is proposed, and a necessary and sufficient condition for the solvability of the general regular decoupling problem in terms of the zero at infinity is given.
Abstract: A definition of zeros at infinity for affine nonlinear control systems is proposed. The definition is local, which means that we exclude certain singularities. We argue the reasonableness of our definition by showing its relevance to the problem of nonlinear decoupling. In particular, we give a necessary and sufficient condition for the solvability of the general regular decoupling problem for affine systems in terms of the zeros at infinity.
01 Jan 1985
TL;DR: In this paper, a function a(w) on an affine Weyl group of type An has been introduced, which is the analogue of the notion of left cell, which we call left V-cell.
Abstract: Recently, J. Y. Shi [4] determined the left cells (in the sense of [1]) of the affine Weyl group of type An; he has also obtained some partial results on the two-sided cells, which imply, in particular, that their number is at most equal to the number of partitions of n. In this paper we shall complete the results of Shi by proving the conjecture in [2,3.6] on the two-sided cells which implies in particular that the number of two-sided cells is exactly the number of partitions of n. The new ingredient in the proof is the function a(w) on an affine Weyl group which has been introduced in [3]. In the first three sections of this paper we shall recall the definition of a(w) and describe its connection with Gelfand-Kirillov dimension. In Section 4, we describe, following Vogan, an analogue of the notion of left cell, which we call left V-cell; in Section 5 we prove a finiteness theorem for the left V-cells of affine Weyl groups. Sections 6, 7 are concerned with affine Weyl groups of type An.
TL;DR: In this paper, a non-Markovian and multidimensional generalization of the Ito stochastic integral theory is proposed, and the variation δf of the pdf can be evaluated for a small change of support.
Abstract: Diffusion-type random functions are a first attempt at a non-Markovian and multidimensional generalization of the Ito stochastic integral theory. Within this framework, the variation δf of the pdf can be evaluated for a small change of support. These results are compared with the provisions of the usual approximate models. The conclusions are: the affine correction is false for the first order approximation, unless there is a linear factor. The isofactorial model is true for the first order, and in the multi-Gaussian case, almost correct for the second-order approximation. Counterexamples are given for the discontinuous case, and a more general model is suggested.
TL;DR: An infinite series of finite rank 3 geometries is obtained whose rank 2 residues are projective planes of order 2, and which possess a regular automorphism group isomorphic to SL3( p) or SU3(p) for some prime p.
TL;DR: In this article, a completely integrable nonlinear system with nontrivial spectral problem and the corresponding Backlund transformation is presented, and the affine geometric origin of the system is discussed briefly.
Patent•
12 Mar 1985
TL;DR: In this paper, a composition or a series of notes to be transposed are introduced with mathematical data into the memory (11) of a computer, a calculator (12) works out the data and a control unit (13) actuates an optical (4) or acoustical (3) output device.
Abstract: A composition or a series of notes to be transposed are introduced with mathematical data into the memory (11) of a computer (1). A calculator (12) works out the data and a control unit (13) actuates an optical (4) or acoustical (3) output device. All the series of notes received and calculated may be addressed by the computer to a memory (5) external to the computer.
TL;DR: In this paper, it was shown that an affine extension of a Prufer domain D with Noetherian spectrum is strongly affine over D if and only if there are only a finite number of intermediate rings.
TL;DR: A noetherian PI-ring which is affine over the center of the circle can be localized at every (finite or infinite) link connectivity component P, in the sense that the multiplicative set b (P ) satisfies the Ore condition and determines P.
TL;DR: In this article, the class of affine Barbilian spaces (P,L, φ,∥, ∥) has been characterized, up to isomorphisms, in successive stages adding geometrical axioms.
Abstract: In this paper we consider systems (P,L,φ,∥), where P is an arbitrary non-empty set, L a set of subsets of p and φ resp. ∥ a relation on PxP resp. LxL. In successive stages adding geometrical axioms, we characterize the class of those structures (P,L, φ,∥), which coincides — up to isomorphisms — with the class of all Affine Barbilian-Spaces.
TL;DR: In this paper, a nonlinear change of variables is required to transform a chemical reaction system model to a much simpler equation called the normal form, which retains all important local nonlinear features of the system.