## What is coordinate geometry?

Coordinate geometry (COGO) is a method of inserting surveying or engineering data into geographic information system (GIS), computer-aided design (CAD), or mapping software. These data can be collected on the proposed construction site using standard surveying techniques and instrumentation or may be taken from existing maps, engineering plans, drawings, or records. Data gathered on the site includes coordinates of points, bearings, and distances between points. The data are noticed and noted through conventional surveying procedures, like a traverse or layout measurement series and it can be either digital or non-digital. The maps and plans are inclusive of boundaries, divisions, and other components, and these features are shown with coordinate values, the lengths, offset distance, and bearings between them.

## Types of coordinate

Coordinate is defined as a number set used in pinpointing the location of a mark on any line, or on the surface or plane, e.g., latitudes and longitudes are coordinates on the surface of the Earth. Linear or angular quantities are the ones to select the particular point’s position related to the reference given. The two main types of coordinates used in surveying are polar coordinates and rectangular coordinates. Each of them is further divided into plane coordinates, spherical coordinates, and space coordinates.

### Assumed plane coordinates

A local plane-coordinate system is built at the surveyor’s convenience. Assumption of the reference axes takes place for all coordinates to be in the 1^{st} quadrant and the Y-axis will be the true, magnetic north direction.

#### Astronomic coordinates

The position of a point is defined by quantities on the geoid with reference to the planes of the celestial equator and a certain celestial meridian.

#### Cartesian coordinates

The position of a point is defined by quantities on the geoid with reference to the planes of the celestial equator and certain celestial meridian.

#### Geocentric coordinates

They determine the place of the point with respect to the Earth’s center. Terrestrial or geocentric coordinates may either be Cartesian (x, y, z) or spherical (latitude, longitude, and radial distance) in nature.

#### Geodetic coordinates (Geographic coordinates)

The latitude and longitude locate the position of the point with respect to the reference ellipsoid on the Earth’s surface.

#### Grid coordinates

The two distances, the normal distance to the point from Y-axis (x-coordinate or abscissa) and the normal distance to the point from X-axis (y-coordinates or ordinate) will secure the point’s location on the particular grid. All survey computations can be created by the equations and procedures of plane surveying.

#### Military coordinates

The usage of fire-control coordinates by the US Army was based on a polyconic projection.

### Plane rectangular coordinates

The normal distances of a point form a pair of axes intersecting at 90° angles. The plane rectangular coordinates are generally computed from data that are in the polar coordinates. Azimuth or bearing from the previous point on a tangent plane and the procedure utilized is based on plane geometry and trigonometry.

#### Polar coordinates

The direction and interval from a central point of reference to a defined point are a polar coordinate and the angle between the secured line to the preferred direction and the radius vector is the vectorial angle. To compute the geodetic positions, they are related to azimuths and the extent from familiar locations.

#### Rectangular coordinates

The reference axes intersect at right angles to each other.

### Spherical coordinates

A coordinate system recognizes a point on the sphere or ellipsoid by the means of its angular distances from a primary great circle and a reference of the secondary great circle, as longitude and latitude.

#### State plane coordinates

The east-west limited dimension zones and indefinite north-south extent zones have the transverse Mercator projection. It acts as the base for the state coordinate system and the state plane coordinates that are exclusively used for compiling field survey data.

#### Universal Polar Stereographic coordinates

The Universal Polar Stereographic (UPS) grid includes two polar stereographic projections, one for the north polar area and the other for the south polar area. The false northing and false easting are both at the range of 2,000,000 m.

## The Universal Transverse Mercator (UTM) coordinates

The following specifications of The Universal Transverse Mercator (UTM) grid:

- The longitude of the origin is the central meridian of every zone.
- The scale factor at the central meridian is 0.9996.
- The zones are bounded by meridians whose longitudes are multiples of 6° east or west of the Greenwich meridian.
- On large-scale maps, an overlay of 25 miles roughly on either side of the junction is given for surveyors and firing.

It is a reference system for locating points that traverse in space or on a specific surface with the help of distances or angles and in relation to the proposed axes, planes, or surfaces. The origin of coordinates is the place from which the computation of the components of the coordinate system proceeds.

## Coordinate system

Three usual types of reference systems that are used in surveying and mapping are:

**Plane-polar**: The points in a plane are marked by distance from a particular point along the direction of the ray with respect to a certain baseline.**Rectangular**: The points are determined by linear distances from two axes perpendicular to each other or from three planes that are mutually perpendicular to one another. Many special plane-rectangular coordinate systems have been produced for certain areas.**Spherical**: The points on a spherical or ellipsoidal surface are located by the angles between a normal or radius through the point.

Examples of coordinate systems involve geographic, astronomic, and azimuth-altitude systems.

The process to project the geographic coordinate system on a plane by a mathematical modification to lay over a rectangular grid on the plane projection. The most regular projections include the Lambert conformal conic and the transverse Mercator and over the transverse Mercator projector, another nearly same type projection-type was generated for the global usage in 6° longitudinal width zones called the Universal Transverse Mercator (UTM).

## Curvilinear coordinate system

The coordinate system in which at least one of the geometric components used for reference is curved. Coordinates are defined by the convergence or intersection of curved lines or surfaces rather than by convergence or intersection of only straight lines or planes.

### State plane coordinate system (SPCS)

It comprises 124 geographic zones or coordinate systems developed for selected regions of the United States. Each state has one or more than one state plane zone and its boundaries normally follow the county lines.

## Context and applications

The topic is studied in courses such as:

- Bachelors of Technology (Civil Engineering)
- Bachelors of Technology (Remote Sensing)
- Masters of Technology (Geospatial Systems Engineering)

## Practice problems

Q 1. In which type of coordinates does the point identify and derive by calculation of its distance from every axis parallel to the other axis?

- State plane coordinates
- Cartesian coordinates
- Boundary coordinates
- Measurement coordinates

Correct Option: b

Explanation: In cartesian coordinates, the point is identified and derived by the calculation of its distance from every axis that is parallel to the other axis. The position of a point is defined by quantities on the geoid with reference to the planes of the celestial equator and certain celestial meridian.

Q 2. From which form of data does plane rectangular coordinates calculate?

- Polar coordinates
- Measurement coordinates
- Azimuth coordinates
- Rectangular coordinates

Correct Option: a

Explanation: Plane rectangular coordinates are calculated from the polar coordinates form of data and the normal distances of a point form a pair of axes intersecting at 90° angles.

Q 3. What is the full form of UTM?

- Universal Traverse Mercator
- Universal Transport Mercator
- Universal Transverse Mercator
- United Transverse Mercator

Correct Option: c

Explanation: The full form of UTM is Universal Transverse Mercator. It is a reference system for locating points that traverse in space or on a specific surface with the help of distances or angles and in relation to the proposed axes, planes, or surfaces.

Q 4. What is the scale factor at the central meridian of UTM?

- 0.9993
- 0.9994
- 0.9995
- 0.9996

Correct Option: d

Explanation: The scale factor specification at the central meridian of the Universal Transverse Mercator (UTM) grid is 0.9996. The longitude of the origin is the central meridian of every zone and the zones are bounded by meridians whose longitudes are multiples of 6° east or west of the Greenwich meridian.

Q 5. Which coordinate system comprises 124 geographic zones for selected regions of the U.S.?

- Curvilinear coordinate system
- State plane coordinate system
- All of these
- None of these

Correct Option: b

Explanation: State plane coordinate system comprises 124 geographic zones for selected regions of the U.S. and each state has one or more than one state plane zone and its boundaries normally follow the county lines.

## Related Concepts

- SPC (Statistical Process Control)
- Defense Mapping Agency
- Traverse survey
- Surveyor's evaluations

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