ZenithalEquidistantProjection

class sofia_redux.scan.coordinate_systems.projection.zenithal_equidistant_projection.ZenithalEquidistantProjection

Bases: ZenithalProjection

Initialize a zenithal equidistant projection.

A useful property of the zenithal equidistant projection is that all points are at proportionally correct distances from the center point, and all points are at the correct azimuth from the center point. All meridians are straight lines and distances from the pole are all correct.

The forward projection is given by:

x = (pi/2 - theta)sin(phi) y = -(theta - pi/2)cos(phi)

with cot(theta) evaluating to zero at theta=90 degrees, and the inverse transform (deprojection) is given by:

phi = arctan(x, -y) theta = pi/2 - sqrt(x^2 + y^2)

Methods Summary

get_fits_id()	Return the FITS ID for the projection.
get_full_name()	Return the full name of the projection.
r(theta)	Return the radius of a point from the center of the projection.
theta_of_r(r)	Return theta (latitude) given a radius from the central point.

Methods Documentation

classmethod get_fits_id()

Return the FITS ID for the projection.

Returns:

str

classmethod get_full_name()

Return the full name of the projection.

Returns:

str

classmethod r(theta)

Return the radius of a point from the center of the projection.

For the zenithal equidistant projection, the radius of a point from the center of the projection, given the latitude (theta) is:

r = pi/2 - theta

Parameters:

thetafloat or numpy.ndarray or units.Quantity

The latitude angle.

Returns:

valueunits.Quantity

The distance of the point from the central point.

classmethod theta_of_r(r)

Return theta (latitude) given a radius from the central point.

For the zenithal equidistant projection, the latitude (theta) of a point at a distance r from the center of the projection is given as:

theta = pi/2 - r

Parameters:

rfloat or numpy.ndarray or units.Quantity

The distance of the point from the central point.

Returns:

thetaunits.Quantity

The latitude angle.