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In geometry, the polar angle may be 2D polar angle, the angular coordinate of a two-dimensional polar coordinate system; 3D polar angle, ...
The reference point (analogous to the origin of a Cartesian coordinate system) is called the pole, and the ray from the pole in the reference direction is the polar axis. The distance from the pole is called the radial coordinate, radial distance or simply radius, and the angle is called the angular coordinate, polar angle, or azimuth. [1]
Even with these restrictions, if the polar angle (inclination) is 0° or 180°—elevation is −90° or +90°—then the azimuth angle is arbitrary; and if r is zero, both azimuth and polar angles are arbitrary. To define the coordinates as unique, the user can assert the convention that (in these cases) the arbitrary coordinates are set to zero.
The log-polar coordinate system represents a point in the plane by the logarithm of the distance from the origin and an angle measured from a reference line intersecting the origin. Plücker coordinates are a way of representing lines in 3D Euclidean space using a six-tuple of numbers as homogeneous coordinates .
That is, convert polar coordinates to Cartesian coordinates. Then compute the arithmetic mean of these points. The resulting point will lie within the unit disk but generally not on the unit circle. Convert that point back to polar coordinates. The angle is a reasonable mean of the input angles. The resulting radius will be 1 if all angles are ...
The geocentric latitude θ is the complement of the polar angle or colatitude θ′ in conventional spherical polar coordinates in which the coordinates of a point are P(r,θ′,λ) where r is the distance of P from the centre O, θ′ is the angle between the radius vector and the polar axis and λ is longitude.
In polar coordinates, the polar tangential angle is defined as the angle between the tangent line to the curve at the given point and ray from the origin to the point. [6] If ψ denotes the polar tangential angle, then ψ = φ − θ, where φ is as above and θ is, as usual, the polar angle.
In a spherical coordinate system, a colatitude is the complementary angle of a given latitude, i.e. the difference between a right angle and the latitude. [1] In geography, Southern latitudes are defined to be negative, and as a result the colatitude is a non-negative quantity, ranging from zero at the North pole to 180° at the South pole.