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# Topic: Coordinate rotation

###### In the News (Fri 31 Jul 15)

 Rotation (disambiguation) - Wikipedia, the free encyclopedia Generally, it is used to denote (in 3D) the rotation of movement of a rigid body in such a way that any given point of that body remains at a constant distance from some fixed line (in 2D: point). The retail practice of rotating stock (especially fresh produce/bread) to ensure the stock with the soonest sell by date is at the front of the shelf - meaning it will be sold first. In baseball pitching, the rotation is the group of starting pitchers for a team, and the order in which they pitch. en.wikipedia.org /wiki/Rotation_(disambiguation)   (297 words)

 Coordinates (elementary mathematics)   (Site not responding. Last check: 2007-11-05) The coordinates of a point are the components of a tuple of numbers used to represent the location of the point in the plane or space. The polar coordinate systems are coordinate systems in which a point is identified by a distance from some fixed feature in space and one or more subtended angles. In terms of the Cartesian coordinate system, one usually picks O to be the origin (0,0) and L to be the positive x-axis (the right half of the x-axis). hallencyclopedia.com /Coordinates_(elementary_mathematics)   (942 words)

 Encyclopedia: Coordinate rotation In linear algebra and geometry, a coordinate rotation is a type of transformation from one system of coordinates to another system of coordinates such that distance between any two points remains invariant under the transformation. On the other hand, the composition of a reflection and a rotation, or of a rotation and a reflection (composition is not commutative), will be equivalent to a reflection. Rotation matrices have a determinant of +1, and reflection matrices have a determinant of -1. www.nationmaster.com /encyclopedia/Coordinate-rotation   (395 words)

 Station Information - Coordinate rotation In linear algebra and geometry, a coordinate rotation is a transformation from one system of coordinates to another system of coordinates, such that distance between any two points remains invariant undr the transformation. It can also be described by means of quaternions (see quaternions and spatial rotation), an approach which is similar to the use of vector calculus. More generally, coordinate rotations are represented by orthogonal matrices. www.stationinformation.com /encyclopedia/c/co/coordinate_rotation.html   (345 words)

 Optimal Complex-Coordinate Rotation Method for the Calculation of Resonance States   (Site not responding. Last check: 2007-11-05) Complex-coordinate rotation method is useful for the calculation of resonance states encountered in atomic and molecular physics. In principle, as long as the hidden resonance pole is exposed by the complex-coordinate rotation, the actual angle of rotation used does not matter for exact calculation. The resulting optimal complex-coordinate rotation method, which has a wide range of applicability, is applied here to the Stark effect for illustration. flux.aps.org /meetings/BAPSMAY96/abs/S220015.html   (163 words)

 CSPICE Routines: EUL2M_C r is a rotation matrix representing the composition of the rotations defined by the input angle-axis pairs. The resulting matrix r may be thought of as a coordinate transformation; applying it to a vector yields the vector's coordinates in the rotated system. Viewing r as a coordinate transformation matrix, the basis that r transforms vectors to is created by rotating the original coordinate axes first by angle1 radians about the coordinate axis indexed by axis1, next by angle2 radians about the coordinate axis indexed by axis2, and finally by angle3 radians about coordinate axis indexed by axis3. www.gps.caltech.edu /~marsdata/cspice/eul2m_c.html   (985 words)

 The reserved FITS coordinate system keywords Axis Rotation: the rotation angle between the pixel axis and the physical coordinate axis in degrees. Rotation Matrix: the rotation (and skew) terms needed to convert from the pixel coordinate system to the physical coordinate system. Coordinate Rotation: the longitude and latitude in the native coordinate system of the standard system's north pole. heasarc.gsfc.nasa.gov /docs/heasarc/ofwg/docs/general/wcs_keywords/node6.html   (691 words)

 Projections and Coordinate Systems This section regards the simple case of rectangular coordinate systems in which x and y axes are perpendicular to eachother (orthagonal), and the units on each axis are the same and constant. Techniques for transformation of rectangular coordinate systems come into play when you have two maps that have been projected with the same method, or when the projection for one of the maps is unknown or irrelevant. Rotation of coordinate systems is simply illustrated as the pinning of the coordinate origin, and a radial motion of the axes while maintaining their orthagonal relationship. www.geog.ubc.ca /courses/geog516/notes/coordinates/Rect_CoordsLect.html   (1733 words)

 Rotations   (Site not responding. Last check: 2007-11-05) In the polar coordinate system however, the ordered pair is not represented by x or y but of r and angle originating from the origin or the pole, which is the center of the coordinate system. Now doing these rotations are pretty straightforward, all we have to do is smack the needed values on our 2d rotation equation for each axis and we're good to go. Which means for a full rotation on all the axes, do not directly put values until they are fully rotated on the axis that they are rotated. qbnz.com /pages/tutorials/relsoft/Chapter2   (1662 words)

 Matrix and Quaternion FAQ   (Site not responding. Last check: 2007-11-05) Rotation in X transforms Y and Z Rotation in Y transforms X and Z Rotation in Z transforms X and Y The argument to this goes as follows: Given a vertex V = (x,y,z), rotation angles (A,B and C) and translation (D,E,F). Negating the rotation angle is equivalent to generating the transpose of the matrix. Because the rotation axis is specifed as a unit direction vector, it may also be calculated through vector mathematics or from spherical coordinates ie (longitude/latitude). www.flipcode.com /documents/matrfaq.html   (7478 words)

 Coordinate rotation -   (Site not responding. Last check: 2007-11-05) In other words, a rotation is a type of isometry – note however that there are isometries other than rotations, such as translations, reflections, and glide reflections. In two dimensions, a counterclockwise rotation of the plane about the origin, where $\left(x,y\right)$ is mapped to $\left(x\text{'},y\text{'}\right)$, is given by the same formulas as a coordinate transformation with a clockwise rotation of the coordinate axes, resulting in a change of coordinates $\left(x,y\right)$ into $\left(x\text{'},y\text{'}\right)$: This rotation is similar to a two dimensional rotation, except that instead of x and y axes, there are $\mathbf\left\{u_\perp\right\}$ and $\mathbf\left\{v\right\} \times \mathbf\left\{u_\perp\right\}$ axes, both of which are perpendicular to v. www.grohol.com /psypsych/Coordinate_rotation   (993 words)

 Coordinate rotation digital computer processor (cordic processor) for vector rotations in carry-save architecture - ... A coordinate rotation digital computer processor for vector rotations, particularly for solving real-time processing of a vector of the vector components X.sub.0, Y.sub.0, by an angle Z.sub.0, where X.sub.0, Y.sub.0 and Z.sub.0 are each digital words having a plurality of data bits, said data bits having particular significances relative to one another, said processor comprising: The rotation of a vector is therefore realized by a plurality of identical stages that are composed only of adder/subtractor circuits, devices for realizing shift operations and a sign detection of Z.sub.i (sign (Z.sub.i)). Given a rotational angle Z.sub.o between +pi/2 and -pi/2 and an accuracy requirement of g=10.sup.-3, two additional bits for places preceding the decimal point are required, so that the input word width of the rotational angle amounts to 13 bits. www.freepatentsonline.com /5317753.html   (6627 words)

 OGIP/94-006 Note that this image representation is qualitatively different from the others in that the pixel coordinates are explicitly given in the table whereas in the first 2 cases the pixel coordinates are only implied by the location of the pixel within the array. Axis Rotation: the rotation angle between the pixel axis and the physical coordinate axis. Coordinate Rotation: the longitude in the native coordinate system of the standard system's north pole; default value = 180 degrees. heasarc.gsfc.nasa.gov /docs/heasarc/ofwg/docs/general/ogip_94_006/ogip_94_006.html   (2084 words)

 BASIC Stamp: CORDIC math   (Site not responding. Last check: 2007-11-05) The next rotation is (tan H = +/- 1/2) in the direction that rotates toward the given angle. The action taken in sequence is to rotate the coordinates in progressively smaller steps until the transformed x axis lines up with the point P, that is, the y coordinate finally is reduced to zero. In the calculation of the arctangent and length of the vector, it is the coordinate y that is minimized, while in the calculation of the sine and cosine, it is the difference between the given angle and the rotated angle that is minimized. www.emesystems.com /BS2mathC.htm   (3270 words)

 CS184 Lecture 6 summary   (Site not responding. Last check: 2007-11-05) So R is an explicit representation for a coordinate rotation, and vice versa. That follows because applying R to both the p and the coordinates [X' Y' Z'] moves the latter to normal coordinates [X Y Z], from which point the coordinates of p can be read off. A general 3D coordinate frame can be described by the directions of its axes X' Y' Z' and the position of its origin t. www.cs.berkeley.edu /~jfc/cs184f98/lec6/lec6.html   (398 words)

 Geographic Coordinate System Transformations One such application is the coordinate transformation introduced to enable the conversion of coordinates expressed in the North American Datum of 1927 (including the Clarke 1866 ellipsoid) to coordinates expressed in the new North American Datum of 1983 which takes the GRS 1980 ellipsoid. The sign convention is such that a positive rotation about an axis is defined as a clockwise rotation of the position vector when viewed from the origin of the Cartesian coordinate system in the positive direction of that axis; e.g. Because the coordinate differences are small and the coordinates in the source and target systems are very similar in magnitude, in reversible polynomial transformations it is possible to adopt the same coordinate values for the evaluation point in both source and target systems. www.posc.org /Epicentre.2_2/DataModel/ExamplesofUsage/eu_cs35.html   (5780 words)

 Rotation Given a rotation R and an orthonormal basis B, the matrix representation of R relative to B is a rotation matrix. For example, if M is the matrix that transforms vectors from J2000 coordinates to body equator and prime meridian coordinates, then the first row is the vector, expressed in J2000 coordinates, that points from the body center to the intersection of the prime meridian and body equator. The canonical form we've found shows why three-dimensional rotations are very much like two-dimensional rotations: The effect of a three-dimensional rotation on any vector is to rotate the component of that vector that is normal to the rotation axis, and leave the component parallel to the rotation axis fixed. www.gps.caltech.edu /~marsdata/req/rotation.html   (10322 words)

 [No title]   (Site not responding. Last check: 2007-11-05) Likewise, if your molecule has D2d symmetry, you will be given the option to rotate the coordinates of your molecule by 45 degrees in the XY plane, which generally should not be done unless GRABFF has the rotation matrix. The former refers to the set of coordinates generated by the Gxx Z-matrix input routine; the latter is obtained by a center-of-mass translation and principal moments of rotation transformation, and in most cases is identical to the default "master frame" coordinate system used in GAMESS. Therefore, if the rotation matrix is unknown, one has to use the Z-matrix coordinate system in GAMESS, which in turn generally means that one has to specify the molecular symmetry as C1. www.osc.edu /PET/CCM/software/tested/source/grabff/doc.html   (2508 words)

 Modern Physics:Math:Vectors - Wikibooks, collection of open-content textbooks The direction of a vector in two dimensions is generally represented by the counterclockwise angle of the vector relative to the x axis, as shown in figure 2. All that remains to be proven for equation (2.6) to hold in general is to show that it yields the same answer regardless of how the Cartesian coordinate system is oriented relative to the vectors. Since the laws of physics cannot depend on the choice of coordinate system being used, we insist that physical laws be expressed in terms of scalars and vectors, but not in terms of the components of vectors. en.wikibooks.org /wiki/Modern_Physics:Math:Vectors   (1161 words)

 Coordinate rotation for numerical control system - Patent 4370720 Multi-dimensional coordinate translation, rotation, and scaling for a machine control system provides translation, rotation, and scaling of coordinates such as for alignment, inch and metric, scaling, and expanded and contracted dimensions. Data can be entered in either absolute or incremental coordinates, G code selectable, with the capability to mix both coordinate schemes in the same block of commands. Position offset and axis rotation parameters are commanded either from the tape or with the manual data input (MDI) keyboard. www.freepatentsonline.com /4370720.html   (15749 words)

 CORDIC (COordinate Rotation DIgital Computer) CORDIC works by rotating the coordinate system through constant angles until the angle is reduced to zero. Let's start with some coordinates (X,Y) which we want to rotate by an angle 'a'. At each step, it also increments or decrements the X and Y coordinate register by the appropriate value (i.e. www.ee.ualberta.ca /courses/ee401/microboard/cordic_CCink.html   (815 words)

 SCATMECH: BRDF_Model The variable rotation is the rotation angle of the sample in radians about the surface normal. This variable stores the coordinate system for which the scattering is defined in the code. Near the surface normal, this coordinate system is close to the directions x and y, where x is a vector in the plane of incidence and the plane of the sample, and y is a vector perpendicular to the plane of incidence. physics.nist.gov /Divisions/Div844/facilities/scatmech/html/BRDF_Model.htm   (1186 words)

 Untitled Document   (Site not responding. Last check: 2007-11-05) CORDIC (COordinate Rotation DIgital Computer) algorithms are a family of iterative shift-add algorithms for computing a wide range of functions including certain trigonometric, hyperbolic, linear, and logarithmic functions. Trigonometric CORDIC algorithms were invented in 1956 as a digital solution for real-time navigation problems, and the theory was later extended to provide solutions to a broader class of functions. This presentation aims to introduce the main idea used in this family of algorithms with a mathematical formulation, and then show how it can be used to compute various functions. www.ee.bilkent.edu.tr /~eee591/abslevent.html   (105 words)

 Coordinate rotation   (Site not responding. Last check: 2007-11-05) In two dimensions, a counterclockwise coordinate rotation from a coordinate system Then z can be rotated counterclockwise by an angle θ by pre-multiplying it with Another way is to multiply by a matrix M, which will rotate by an angle www.sciencedaily.com /encyclopedia/coordinate_rotation   (638 words)

 Coordinate rotation   (Site not responding. Last check: 2007-11-05) Prior to calculating any fluxes and statistics, gen2 always rotates the two horizontal wind components into along-wind and cross-wind components based on the mean wind direction for the record. The record mean cross-wind component will be zero by definition. These estimates of wind speed are used in the third generation program in the bulk flux formula and in all calculations that require an estimate of mean wind speed. blg.oce.orst.edu /Software/2nd_and_3rdgen/node2.html   (152 words)

 Citations: Performance Degradation of Genetic Algorithms under Coordinate Rotation - Salomon (ResearchIndex)   (Site not responding. Last check: 2007-11-05) Previously, researchers have examined problems for which coordinate transformations were shown to provide measurable changes in the performances of EAs (e.g. The reason for this is that three of the five crossover methods used by GADO are rotation independent. A rotation induces epistasis, which describes a nonlinear interaction between the parameters with respect to the tness function. citeseer.ifi.unizh.ch /context/272952/0   (1087 words)

 U.S. Pregrant 20030227324 - COORDINATE ROTATION OF PRE-DISTORTION VECTOR IN FEEDFORWARD LINEARIZATION AMPLIFICATION ...   (Site not responding. Last check: 2007-11-05) An amplifier system (120, 820) for radio frequency signals comprises a phase and gain adjuster (122) which receives an input signal and a control vector (C) for producing a distortion-adjusted input signal. The composite control vector is applied to the phase and gain adjuster, thereby enabling the phase and gain adjuster to produce the distortion-adjusted input signal. In essence, the modified pre-distortion vector generator performs a vector multiplication (coordinate rotation) of a pre-distortion vector so that the resultant modified pre-distortion vector has a proper direction relative to the control vector. cxp.paterra.com /uspregrant20030227324.html   (258 words)

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