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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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Patent
11 May 1990
TL;DR: In this article, a robotic surgical system with a multiple degree of freedom manipulator arm and a surgical tool is presented, where the manipulator is coupled to a controller for controllably positioning the surgical tool within a 3D coordinate system.
Abstract: A robotic surgical system (10) includes a multiple degree of freedom manipulator arm (14) having a surgical tool (22). The arm is coupled to a controller (24) for controllably positioning the surgical tool within a three dimensional coordinate system. The system further includes a safety monitoring processor (38) for determining the position of the surgical tool in the three dimensional coordinate system relative to a volumetric model. The volumetric model may be represented as a constructive solid geometry (CSG) tree data structure. The system further includes an optical tracking camera system (28, 32) disposed for imaging a region of space that includes at least a portion of the manipulator arm. An output of the camera system is coupled to the processor (38) that processes the volumetric model for determining if the surgical tool is positioned outside of the volumetric model. The system further includes a strain gage (40) for detecting slippage in three dimensions between an immobilized tissue, such as bone, and a reference point (44). The system also includes multiple and redundant safety features for suspending a motion of the surgical tool to prevent the tool from operating outside of the predetermined volume of space.

1,202 citations

Proceedings ArticleDOI
20 May 1996
TL;DR: A new formulation for coordinate system independent adaptation of arbitrary normal mutation distributions with zero mean enables the evolution strategy to adapt the correct scaling of a given problem and also ensures invariance with respect to any rotation of the fitness function (or the coordinate system).
Abstract: A new formulation for coordinate system independent adaptation of arbitrary normal mutation distributions with zero mean is presented. This enables the evolution strategy (ES) to adapt the correct scaling of a given problem and also ensures invariance with respect to any rotation of the fitness function (or the coordinate system). Especially rotation invariance, here resulting directly from the coordinate system independent adaptation of the mutation distribution, is an essential feature of the ES with regard to its general applicability to complex fitness functions. Compared to previous work on this subject, the introduced formulation facilitates an interpretation of the resulting mutation distribution, making sensible manipulation by the user possible (if desired). Furthermore it enables a more effective control of the overall mutation variance (expected step length).

1,119 citations

Journal ArticleDOI
TL;DR: In this paper, a closed-form solution to the least square problem for three or more points is presented, which requires the computation of the square root of a symmetric matrix, and the best scale is equal to the ratio of the root-mean-square deviations of the coordinates in the two systems from their respective centroids.
Abstract: Finding the relationship between two coordinate systems by using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. The solution has applications in stereophotogrammetry and in robotics. We present here a closed-form solution to the least-squares problem for three or more points. Currently, various empirical, graphical, and numerical iterative methods are in use. Derivation of a closed-form solution can be simplified by using unit quaternions to represent rotation, as was shown in an earlier paper [ J. Opt. Soc. Am. A4, 629 ( 1987)]. Since orthonormal matrices are used more widely to represent rotation, we now present a solution in which 3 × 3 matrices are used. Our method requires the computation of the square root of a symmetric matrix. We compare the new result with that obtained by an alternative method in which orthonormality is not directly enforced. In this other method a best-fit linear transformation is found, and then the nearest orthonormal matrix is chosen for the rotation. We note that the best translational offset is the difference between the centroid of the coordinates in one system and the rotated and scaled centroid of the coordinates in the other system. The best scale is equal to the ratio of the root-mean-square deviations of the coordinates in the two systems from their respective centroids. These exact results are to be preferred to approximate methods based on measurements of a few selected points.

1,101 citations

Proceedings ArticleDOI
J. S. Walther1
18 May 1971
TL;DR: This paper describes a single unified algorithm for the calculation of elementary functions including multiplication, division, sin, cos, tan, arctan, sinh, cosh, tanh, arCTanh, In, exp and square-root.
Abstract: This paper describes a single unified algorithm for the calculation of elementary functions including multiplication, division, sin, cos, tan, arctan, sinh, cosh, tanh, arctanh, In, exp and square-root The basis for the algorithm is coordinate rotation in a linear, circular, or hyperbolic coordinate system depending on which function is to be calculated The only operations required are shifting, adding, subtracting and the recall of prestored constants The limited domain of convergence of the algorithm is calculated, leading to a discussion of the modifications required to extend the domain for floating point calculations

1,044 citations

Journal ArticleDOI
01 May 1983
TL;DR: A new methodology is presented for measuring interfacial properties of liquids, such as surface tension and contact angles, by analyzing the shape of an axisymmetric liquid-fluid interface without use of apex coordinates.
Abstract: A general, yet user-oriented scheme is provided to determine liquid—fluid interfacial tensions and contact angles from the shapes of axisymmetric menisci, i.e., from sessile as well as pendant drops. The strategy employed is to construct an objective function which expresses the error between the physically observed and a theoretical Laplacian curve, i.e., a curve representing a solution of the Laplace equation of capillarity. This objective function is minimized numerically using the method of incremental loading in conjunction with the Newton—Raphson method. This strategy is necessary as the otherwise powerful Newton-Raphson method depends on a good initial approximation to the true curve. Incremental loading provides a scheme of approaching the solution from a remote situation. A spherical meniscus, i.e., the case of infinite interfacial tension, is chosen here as the simple, unloaded solution. The method is set up from the point of view of user convenience: Apart from local gravity and densities of liquid and fluid phases the only input information required to determine the liquid-fluid interfacial tension is information on meniscus shape, typically several coordinate points in a coordinate system the origin of which may be placed at will. Specifically it is not necessary to identify the apex of the drop profile, the drop width, or drop height. For determinations of contact angles, the vertical coordinate of the three-phase line needs to be specified. As an illustration, “synthetic” drops, simulating physical drop profiles, are investigated. Sessile drops are generated with the aid of the tables of Bashforth and Adams and pendant drops with the aid of the tables of Fordham. The results show that the technique, which is an absolute one independent of any tables, is fully functional. A computer program implementing the method may be purchased from the authors.

1,039 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023235
2022553
2021549
20201,365
20191,814
20181,569