Co-ordinate System
Coordinates are numbers which describe the location of points in a plane or in space. For example, the height above sea level is a coordinate which is useful for describing points near the surface of the earth. A coordinate system, in a plane or in space, is a systematic method of assigning a pair or a triple of numbers to each point in the plane or in space (respectively) which describe its position uniquely. For example, the triple consisting of latitude, longitude and altitude (height above sea level) define a coordinate system near to the surface of the earth.
Coordinates may be defined in more general contexts. For example, if one is not interested in height, then latitude and longitude form a coordinate system on the surface of the earth, which is (approximately) a sphere. Coordinates such as these are also important in astronomy for describing the location of objects in the (night) sky.
In mathematics and its applications, a coordinate system is a system for assigning an n-tuple of numbers or scalars to each point in an n-dimensional space. This concept is part of the theory of manifolds. "Scalars" in many cases means real numbers, but, depending on context, can mean complex numbers or elements of some other commutative ring. For complicated spaces, it is often not possible to provide one consistent coordinate system for the entire space. In this case, a collection of coordinate systems, called charts, are put together to form an atlas covering the whole space. A simple example (which motivates the terminology) is the surface of the earth.
Although a specific coordinate system is useful for numerical calculations in a given space, the space itself is considered to exist independently of any particular choice of coordinates. From this point of view, a coordinate on a space is simply a function from the space (or a subset of the space) to the scalars. When the space has additional structure, one restricts attention to the functions which are compatible with this structure. Examples include:
Continuous functions on topological spaces;
Smooth functions on smooth manifolds;
Measurable functions on measure spaces;
Rational functions on algebraic varieties;
Linear functional on vector spaces.
In informal usage, coordinate systems can have singularities: these are points where one or more of the coordinates is not well-defined. For example, the origin in the polar coordinate system (r,θ) on the plane is singular, because although the radial coordinate has a well-defined value (r = 0) at the origin, θ can be any angle, and so is not a well-defined function at the origin.
Some coordinate systems are the following:
The Cartesian coordinate system (also called the "rectangular coordinate system"), which, for three-dimensional flat space, uses three numbers representing distances.
The polar coordinate systems:
Circular coordinate system (commonly referred to as the polar coordinate system) represents a point in the plane by an angle and a distance from the origin.
Cylindrical coordinate system represents a point in space by an angle, a distance from the origin and a height.
Spherical coordinate system represents a point in space with two angles and a distance from the origin.
Relative coordinate system is to specify a distance in Cad Overlay.
Geographical coordinate system
Absolute coordinate system
The Cartesian coordinate system - The Cartesian coordinate system (also called rectangular coordinate system) is used to determine each point uniquely in a plane through two numbers, usually called the x-coordinate or abscissa and the y-coordinate or ordinate of the point. To define the coordinates, two perpendicular directed lines (the x-axis, and the y-axis), are specified, as well as the unit length, which is marked off on the two axes. Cartesian coordinate systems are also used in space (where three coordinates are used) and in higher dimensions.
Illustration of the Cartesian coordinate system. Four points are marked: (2, 3) in green, (−3, 1) in red, (−1.5, −2.5) in blue and (0, 0), the origin, in purple.
A Cartesian coordinate system in two dimensions is commonly defined by two axes, at right angles to each other, forming a plane (a xy-plane). The horizontal axis is normally labeled x, and the vertical axis is normally labeled y. There are four quadrants. In the 1st quadrant x & y both are positive, in the 2nd quadrant x is –ve & y is +ve, in the 3rd quadrant x & y both are –ve and in the 4th quadrant x is +ve and y is –ve. The crossing point of x and y is called Origin and the quadrant of origin is (0, 0).
Three dimensional Cartesian coordinate system with y-axis pointing away from the observer.
The three dimensional Cartesian coordinate system provides the three physical dimensions of space — length, width, and height. The three Cartesian axes defining the system are perpendicular to each other. The relevant coordinates are of the form (x, y, z). The x-, y-, and z-coordinates of a point can also be taken as the distances from the yz-plane, xz-plane, and xy-plane respectively. The xy-, yz-, and xz-planes divide the three-dimensional space into eight subdivisions known as octants, similar to the quadrants of 2D space. While conventions have been established for the labeling of the four quadrants of the x-y plane, only the first octant of three dimensional spaces is labeled. It contains all of the points whose x, y, and z coordinates are positive.
The z-coordinate is also called applicate.
The polar coordinate systems – The form of this system is r < Ө. In this form r represents the distance of the point from origin in the direction of ‘Ө’ angle. Angles are always measured in counter clockwise direction an in the unit of degree. It can also be measured in clockwise direction by giving a ‘-’ sign (-30). Here -30 represent 330 degree angle. A point is 4 < 30, means the point is situated on 4 units from the origin at the direction of 30 degree angle.
Circular coordinate system (commonly referred to as the polar coordinate system) represents a point in the plane by an angle and a distance from the origin.
Cylindrical coordinate system represents a point in space by an angle, a distance from the origin and a height.
Spherical coordinate system represents a point in space with two angles and a distance from the origin.
Relative coordinate system – To specify a distance in Cad Overlay, one can use relative coordinate system; either relative Cartesian or relative polar coordinate. The forms of this system are @x,y and @r<Ө respectively. The (@) symbol tells Cad Overlay that the displacement will measure with reference to the previous point rather than to the origin.
Example: If your last point was at 12,8 (see FIGURE below), you can type @11,7 and AutoCAD will locate an entity or point 11 along the x axis and 7 along the y axis from the 12,8 point.
Geographical coordinate system - Geography and cartography utilize various geographic coordinate systems to map positions on the 3-dimensional globe to a 2-dimensional document. The Global Positioning System uses the WGS84 coordinate system. The Universal Transverse Mercator (UTM) and Universal Polar Stereographic (UPS) coordinate systems both use a metric-based cartesian grid laid out on a conformally projected surface to locate positions on the surface of the Earth. The UTM system is not a single map projection but a series of map projections, one for each of sixty zones. The UPS system is used for the Polar Regions, which are not covered by the UTM system. During medieval times, the stereographic coordinate system was used for navigation purposes. The stereographic coordinate system was superseded by the latitude-longitude system, and more recently, the Global Positioning System. Although no longer used in navigation, the stereographic coordinate system is still used in modern times to describe crystallographic orientations in the field of materials science.
Absolute coordinate system - Absolute Coordinates uses the Cartesian System to specify a position in the X, Y, and (if needed) Z axes to locate a point from the 0-X, 0-Y, and 0-Z (0,0,0) point. To locate a point using the Absolute Coordinate system, type the X-value, Y-value, and, if needed, the Z-value separated by commas (with no spaces). Example: If you type 12,8 for a position, AutoCAD will locate an entity or part of an entity 12 along the X-axis and 8 along the Y-axis.