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# cart2sph

Transform Cartesian coordinates to spherical

## Syntax

[azimuth,elevation,r] = cart2sph(X,Y,Z)

## Description

[azimuth,elevation,r] = cart2sph(X,Y,Z) transforms Cartesian coordinates stored in corresponding elements of arrays X, Y, and Z into spherical coordinates. azimuth and elevation are angular displacements in radians. azimuth is the counterclockwise angle in the x-y plane measured from the positive x-axis. elevation is the elevation angle from the x-y plane. r is the distance from the origin to a point.

Arrays X, Y, and Z must be the same size (or any of them can be scalar).

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### Algorithms

The mapping from three-dimensional Cartesian coordinates to spherical coordinates is

```azimuth = atan2(y,x)
elevation = atan2(z,sqrt(x.^2 + y.^2))
r = sqrt(x.^2 + y.^2 + z.^2)```

The notation for spherical coordinates is not standard. For the cart2sph function, elevation is measured from the x-y plane. Notice that if elevation = 0, the point is in the x-y plane. If elevation = pi/2, then the point is on the positive z-axis.