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Topic: Polar coordinate system

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Coordinate system

Cartesian coordinate system

Curvilinear coordinates

Cartesian coordinates

Parabolic coordinates

Horizontal coordinate system

Azimuth

Point (spatial)

Generalized coordinates

Geographic coordinate system

Distance

Angle

Tuple

Longitude

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	Polar coordinate system - Wikipedia, the free encyclopedia
		The polar coordinate system is a two-dimensional coordinate system in which points are given by an angle and a distance from the pole, called the origin in the Cartesian coordinate system.
		The two polar coordinates r (the radial coordinate) and θ (the angular coordinate, polar angle, or azimuth angle, sometimes represented as φ or t) are defined in terms of Cartesian coordinates by
		The equation of a line or curve expressed in polar coordinates is known as a polar equation, and is usually written with r as a function of θ.
	en.wikipedia.org /wiki/Polar_coordinates (1058 words)

	Cartesian coordinate system - Wikipedia, the free encyclopedia
		In mathematics, the Cartesian coordinate system is used to uniquely determine each point in the plane through two numbers, usually called the x-coordinate and the y-coordinate of the point.
		Cartesian coordinate systems are also used in space (where three coordinates are used) and in higher dimensions.
		In analytic geometry the Cartesian coordinate system is the foundation for the algebraic manipulation of geometrical shapes.
	en.wikipedia.org /wiki/Cartesian_coordinate_system (1711 words)

	Coordinates (mathematics) - Wikipedia, the free encyclopedia
		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.
		The circular coordinate system, commonly referred to as the polar coordinate system, is a two-dimensional polar coordinate system, defined by an origin, O, and a semi-infinite line L leading from this point.
		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).
	en.wikipedia.org /wiki/Coordinates_(elementary_mathematics)#Spherical_coordinates (1233 words)

	Polar Coordinates
		The 2-D polar coordinate system involves the distance from the origin and an azimuth angle.
		The polar coordinates are useful in describing the human body motion since the essence of the human body motion is the joint motions.
		On the contrary, the Cartesian system normally used in biomechanics or motion analysis is a left-hand system.
	kwon3d.com /theory/crdsys/polar.html (408 words)

	Coordinate Systems, Vectors, Planes FAQ
		This is referred to as the "right-handed coordinate system" and is the system preferred by mathematicians.
		For example, using the Euclidean coordinate system to animate the movement of a multi-jointed robot arm, it is convenient to assign each joint separate local coordinate systems.
		In a virtual 3D environment, the position of an object is represented as a vector coordinate, the sloping surface as a plane equation and gravity is as a direction vector.
	www.j3d.org /matrix_faq/vectfaq_latest.html (5820 words)

	MATH 2422 #4: CYLINDRICAL AND SPHERICAL COORDINATES
		The coordinate surfaces for the rectangular coordinate system are the planes perpendicular to the coordinate axes, x = a, y = b, and z = c.
		The coordinate surfaces for the cylindrical coordinate system is: r = a (a cylinder),
		However, instead of the r coordinate, another polar coordinate system is drawn along the r-ray with the z axis as the polar axis.
	www-math.cudenver.edu /~rbyrne/online/s00/2422w4.htm (391 words)

	(WO/2001/004842) TEXTURE DESCRIPTION METHOD AND TEXTURE-BASED RETRIEVAL METHOD IN FREQUENCY DOMAIN (Site not responding. Last check: 2007-11-04)
		Polar coordinate system, in which similar images in various variations, such as different rotations or scales or pixel intensity, are retrieved by comparing a query texture descriptor with a data texture descriptor generated by the texture description method by taking account for such variations thereof.
		For this reason, a frequency layout of the Polar coordinate system for extracting the energy values and a frequency layout of the Polar coordinate system for extracting the energy deviation values are separately generated.
		The Polar coordinate frequency layout (transformed layout) is generated using the direction as a reference axis, and then the texture descriptor of Fig.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=01/04842.010118&ELEMENT_SET=DECL (5213 words)

	Polar Coordinates
		The polar coordinate system consists of a pole (a fixed point O) and a polar axis.
		Circles within polar coordinates are created with equations of the form r = a, r = a cosθ, and r = a sinθ.
		The area of a region (A), between values a and b of θ, in polar coordinates is calculated by affectively adding up small areas of rays (protruding from the pole) within the region you are calculating.
	people.bath.ac.uk /maf20/polarcoords.html (394 words)

	Department of Mathematics Education J.
		This investigation serves as introduction to the polar coordinate system and polar equations.
		Polar equations are based upon the polar coordinate system, which is constructed as follows.
		The polar axis is usually drawn horizontally and extending to the right (just as the posititve portion of the x-axis in the rectangular coordinate system).
	jwilson.coe.uga.edu /EMT668/EMAT6680.F99/Wise/writeup11/polar.htm (853 words)

	GIS Tips - Coordinate Systems Part 2
		In a cartesian coordinate system, a point in coordinate space (2D or 3D) is uniquely identified by the lines (2D) or the planes (3D) which intersect at that point.
		In polar, or spherical coordinate systems, a point is identified by the distance from the origin (also known as the pole of the coordinate system) and a direction; much like a surveyor notes the location of a new point with a distance and bearing from a previous point.
		Thus, in the polar coordinate case, points are identified by a distance and an angle.
	www.mentorsoftwareinc.com /CC/gistips/TIPS0199.HTM (1039 words)

	Polar Coordinates--AE
		The standard coordinate system specifies points by measuring the horizontal distance (x-axis) and the vertical distance (y-axis) from the origin.
		The polar coordinate system specifies points by measuring the length of a radius from the origin and its angle from the x-axis.
		For example, an x,y coordinate of 2,3 becomes a polar coordinate with a radius of 2 and a degree of 3.
	perso.wanadoo.es /lolota/web/c09af65.htm (204 words)

	ANALYTICAL GEOMETRY FOR STATICS
		Rectangular coordinates in 2-D: The location of a point in a two-dimensional plane can be represented by a pair of numbers representing the coordinates of the point in a rectangular coordinate system.
		In this case, the arrows on the coordinate axis indicate that points to the right of the origin O on the x-axis are positive and to the left are negative.
		In polar coordinates the equation of a circle is given by specifying the radial coordinate r to be constant.
	em-ntserver.unl.edu /Math/mathweb/analgeom/analsb97.html (819 words)

	1-1 Coordinate System (Site not responding. Last check: 2007-11-04)
		In case of raster data, image coordinates (i, j) with the pixel number in horizontal direction (column i or pixel i) and the line number in vertical direction (row j or line j) as shown in Figure 1.1 (c) are commonly used.
		In geodetic survey, a point is located with the azimuth (A) measured from the North and the distance D from a geodetic point as shown in Figure 1.2 (b).
		Three dimensional (3D) orthogonal coordinates are also used to locate points with the plane coordinates (x, y) and height or depth (z) as shown in Figure 1.3 (a) and (b).
	www.profc.udec.cl /~gabriel/tutoriales/giswb/vol2/cp1/cp1-1.htm (287 words)

	ipedia.com: Cartesian coordinate system Article (Site not responding. Last check: 2007-11-04)
		A three dimensional coordinate system is usually depicted using what is called the right-hand rule, and the system is called a right-handed coordinate system (see handedness).
		The three dimensional coordinate system is popular because it provides the physical dimensions of space, of height, width, and length, and this is often referred to as "the three dimensions".
		It may be interesting to note that some have indicated that the master artists of the Renaissance used a grid, in the form of a wire mesh, as a tool for breaking up the component parts of their subjects they painted--a trade secret.
	www.ipedia.com /cartesian_coordinate_system_1.html (987 words)

	NL96
		The polar coordinate system is a way to determine the location of a point on a plane given a known point and a known reference line.
		Typically, if we are drawing a polar coordinate system on a sheet of paper, the reference line is a vector which starts at the origin, and goes to the right.
		Plotting polar data is identical to plotting cartesian data, except that at some point during the routine, the data must be converted from polar coordinates to cartesian coordinates.
	babek.info /libertybasicfiles/lbnews/nl96/4.htm (3950 words)

	Polar coordinates
		From a polar equation to a cartesian equation
		Polar coordinates of a point P. In the plane we choose a fixed point O, and we call it the pole.
		The pole and the polar axis constitute the basis of the polar coordinate system.
	www.ping.be /~ping1339/polar.htm (3425 words)

	Lakes Environmental - ISCST3 User's Guide
		The ISC model uses either a polar or a Cartesian receptor network as specified by the user.
		In the polar coordinate system, the radial coordinate of the point (r, 2) is measured from the user-specified origin and the angular coordinate 2 is measured clockwise from the north.
		In the Cartesian coordinate system, the X axis is positive to the east of the user-specified origin and the Y axis is positive to the north.
	www.lakes-environmental.com /ISCVOL2/112.htm (284 words)

	Polar coordinates - Strabismus
		The only coordinate system for describing eye rotations that does not have these flaws is the polar coordinate system.
		In a polar coordinate system the position of the eye is also determined by two angles: One angle defines the direction of eye movement out of the primary position and a second angle defines the angle of eye movement out of the primary position.
		In this coordinate system, all tertiary positions of gaze are reached by simple rotation about a single axis.
	www.strabismus.nl /node/21 (425 words)

	RAXPOL
		Defines a local polar coordinate system where its limits are mapped into an area defined by the world coordinate system limits.
		In polar plots where the variations of R with T are small, these small variations can be "exaggerated" or "magnified", simply by setting the polar origin equal to the start radius (origin = radius_start).
		The argument rotation_angle is the angle measured counter-clockwise from the X-axis of the world coordinate system to the R-axis at T=0.
	www.uea.ac.uk /itcs/docs/unixwebdocs/help/fgl/raxpol.html (395 words)

	SparkNotes: Parametric Equations and Polar Coordinates: Polar Coordinates
		The polar coordinate system consists of a pole and a polar axis.
		The pole is a fixed point, and the polar axis is a directed ray whose endpoint is the pole.
		Every point in the plane of the polar axis can be specified according to two coordinates: r, the distance between the point and the pole, and θ, the angle between the polar axis and the ray containing the point whose endpoint is also the pole.
	www.sparknotes.com /math/precalc/parametricequationsandpolarcoordinates/section2.rhtml (304 words)

	Xah: Special Plane Curves: Coordinate System
		In polar coordinate system, a point is specified by its angle to a reference ray and distance from the Pole.
		In polar coordinate system, the plane is marked a point called Pole (also called Origin or Center).
		The bipolar system is sometimes used for curves that naturally have two special points, such as Conic Sections and Cassinian oval.
	xahlee.org /SpecialPlaneCurves_dir/CoordinateSystem_dir/coordinateSystem.html (1254 words)

	Calculus II (Math 2414) - Parametric Equations and Polar Coordinates - Polar Coordinates (Site not responding. Last check: 2007-11-04)
		In polar coordinates there is literally an infinite number of coordinates for a given point. For instance, the following four points are all coordinates for the same point.
		Next we should talk about the origin of the coordinate system. In polar coordinates the origin is often called the pole. Because aren’t actually moving away from the origin/pole we know that r=0. However, we can still rotate around the system by any angle we want and so the coordinates of the origin/pole are
		So, this is a circle of radius a centered at the origin. This is also one of the reasons why we might want to work in polar coordinates. The equation of a circle centered at the origin has a very nice equation, unlike the corresponding equation in Cartesian coordinates.
	tutorial.math.lamar.edu /AllBrowsers/2414/PolarCoordinates.asp (1530 words)

	polar coordinates - a definition from Whatis.com
		Polar coordinates provide a method of rendering graphs and indicating the positions of points on a two-dimensional (2D) surface.
		The polar coordinate system is employed in mathematics, physics, engineering, navigation, robotics, and other sciences.
		In the most common polar system, the reference ray points off toward the right, and angles are measured counterclockwise from it (illustration at left).
	whatis.techtarget.com /definition/0,,sid9_gci825449,00.html (309 words)

	2D Coordinate Systems
		In two dimensions, this system consists of a pair of lines on a flat surface or plane, that intersect at right angles.
		To be able to transform from Cartesian to polar coordinates and vice versa, we let the axis of the polar coordinate system coincide with the x-axis of the Cartesian coordinate system and the pole coincide with the origin.
		Cylindrical coordinates and spherical coordinates are two different extensions of polar coordinates to three dimensions.
	electron9.phys.utk.edu /vectors/2dcoordinates.htm (226 words)

	9. : 4665492 : Computer automated manufacturing process and system
		The coordinate information is input to the machine controller (16) which controls servos (20) and (22) in a polar coordinate system.
		An origination seed (32) is fixed at an origin of the coordinate system and the article (34) is built up around the origination seed (32).
		Other coordinate systems and apparatus for locating the mass particles at the coordinates of a three-d imensional article are disclosed so that the article may be built up in a number of coordinate systems, and controlled environments.XX Prev
	home.att.net /~rppat/museum/mp_9.htm (212 words)

	Coordinates elementary mathematics - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-04)
		Start the Coordinates elementary mathematics article or add a request for it.
		Look for Coordinates elementary mathematics in Wiktionary, our sister dictionary project.
		Look for Coordinates elementary mathematics in the Commons, our repository for free images, music, sound, and video.
	www.sciencedaily.com /encyclopedia/coordinates__elementary_mathematics_ (205 words)

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