Conventions
Several different conventions exist for representing the three coordinates, and for the order in which they should be written. The use of (r, θ, φ) to denote, respectively, radial distance, inclination (or elevation), and azimuth, is common practice in physics, and is specified by ISO standard 31-11.
However, some authors (including mathematicians) use φ for inclination (or elevation) and θ for azimuth, which "provides a logical extension of the usual polar coordinates notation". Some authors may also list the azimuth before the inclination (or elevation), and/or use ρ instead of r for radial distance. Some combinations of these choices result in a left-handed coordinate system. The standard convention (r, θ, φ) conflicts with the usual notation for the two-dimensional polar coordinates, where θ is often used for the azimuth. It may also conflict with the notation used for three-dimensional cylindrical coordinates.
The angles are typically measured in degrees (°) or radians (rad), where 360° = 2π rad. Degrees are most common in geography, astronomy, and engineering, whereas radians are commonly used in mathematics and theoretical physics. The unit for radial distance is usually determined by the context.
When the system is used for physical three-space, it is customary to use positive sign for azimuth angles that are measured in the counter-clockwise sense from the reference direction on the reference plane, as seen from the zenith side of the plane. This convention is used, in particular, for geographical coordinates, where the "zenith" direction is north and positive azimuth (longitude) angles are measured eastwards from some prime meridian.
| coordinates | corresponding local geographical directions |
right/left-handed |
|---|---|---|
| right | ||
| right | ||
| left | ||
| Note: easting, northing, upwardness . Local azimuth angle would be measured, e.g., counter-clockwise from to in the case of . | ||
Read more about this topic: Spherical Coordinate System, Definition
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