Topic
Coordinate system
About: Coordinate system is a research topic. Over the lifetime, 22675 publications have been published within this topic receiving 269822 citations. The topic is also known as: system of coordinates.
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TL;DR: In this paper, a method for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of general multi-connected regions containing any number of arbitrarily shaped bodies is presented.
996 citations
TL;DR: In this article, the effect of anisotropic turbulence as diffusive transport along and across density surfaces was modeled by transforming the mixing tensor from a diagonal second-rank tensor in the isopycnal coordinate system to a tensor containing off-diagonal elements in the geopotential coordinate system.
Abstract: Current numerical models of oceanic circulation differentiate between the eddy diffusion and viscosity transport along the geopotential horizontal and vertical directions only. In order to model the effect of anisotropic turbulence as diffusive transport along and across density surfaces, the isopycnal mixing tensor has been transformed from a diagonal second-rank tensor in the isopycnal coordinate system to a tensor containing off-diagonal elements in the geopotential coordinate system.
993 citations
TL;DR: In this article, it is shown that a parameter L = f(B,I) can be defined which retains most of the desirable properties of I and has the additional property of organizing measurements along lines of force.
Abstract: Dipole representations of the earth's magnetic field have been found to have insufficient accuracy for the study of magnetically trapped particles. A coordinate system consisting of the magnitude of the magnetic field B, and the integral invariant I has been found to adequately organize, measurements made at different geographic locations. It is shown in the present paper, that a parameter L = f(B,I) can be defined which retains most of the desirable properties of I and which has the additional property of organizing measurements along lines of force. Since the parameter L is the analog of a physical distance in a dipole field (the equatorial radius of a magnetic shell), it is usually found to present fewer conceptual difficulties than the integral invariant I.
946 citations
TL;DR: This new approach to head modeling performed significantly better than a simple spherical shell approximation, especially in basal brain areas, including the temporal lobe, as compared to individually derived models.
883 citations
TL;DR: A roentgen stereophotogrammetric method for determination of positions of radiopaque markers in an object and how the degrees of freedom of the plate with control points, which are difficult to control at construction of the test cages, can be determined by specific calibration procedures is described.
Abstract: I have developed a roentgen stereophotogrammetric method for determination of positions of radiopaque markers in an object. The space coordinates are determined in a laboratory coordinate system, which is defined by markers in a test "cage". The markers in the test cage function as calibration points, and are roentgenographed on the same film(s) as the object. Calibration markers and object markers are exposed from two roentgen foci. The cage markers, are in their function, of two kinds, of which one (fiducial marks) is used for projective transformations of the image points to the laboratory coordinate system, while the other (control points) is used for determining the roentgen foci positions in the same coordinate system. After these calculations have been performed, the three-dimensional coordinates of object indicators are determined by crossing of lines between the roentgen foci and the transformed image points. The mathematical principles for the reconstruction of the bundles of rays from the roentgen foci at the moment of exposure are discussed in Chapter 2. Three constructions of test cages, Models 1A and 1B, and Model 2 are also discussed there. In Test Cage Model 1, the two exposures of the object are obtained on one film, but in Model 2 we expose on two films that are perpendicular to each other. The three cage models are, in turn, intended for high-accuracy determinations of lengths (Model 1A), general determinations of space coordinates, especially in larger objects (Model 1B), and high-accuracy determinations of space coordinates in medium-sized objects (Model 1B), and high-accuracy determinations of space coordinates in medium-sized objects (Model 1B). Note, that if the positions of the roentgen foci and the film are not altered, we can roentgenograph the calibration points separately on a film, and then, after removal of the test cage, roentgenograph the object on the same film. The calibration of the test cages is discussed in Chapter 3. To determine coordinates of markers in a plane is easy, if a rectangular coordinatograph is accessible, and we use the same instrument as for the measurements of the films, a Wild Autograph A8. Determination of the position in space of the plate with control points in relation to the plate with fiducial marks requires more consideration. We describe how the degrees of freedom of the plate with control points (translations in x- and y-directions, rotation angle phi about a z-axis), which are difficult to control at construction of the test cages, can be determined by specific calibration procedures.(ABSTRACT TRUNCATED AT 400 WORDS)
811 citations