### 17.8 Coordinate Transformations

[theta, r] = cart2pol (x, y)
[theta, r, z] = cart2pol (x, y, z)
[theta, r] = cart2pol (C)
[theta, r, z] = cart2pol (C)
P = cart2pol (…)

  Transform Cartesian coordinates to polar or cylindrical coordinates.

  The inputs x, y (, and z) must be the same shape, or scalar. If called with a single matrix argument then each row of C represents the Cartesian coordinate (x, y (, z)).

  theta describes the angle relative to the positive x-axis.

  r is the distance to the z-axis (0, 0, z).

  If only a single return argument is requested then return a matrix P where each row represents one polar/(cylindrical) coordinate (theta, phi (, z)).

  See also: pol2cart, cart2sph, sph2cart.

[x, y] = pol2cart (theta, r)
[x, y, z] = pol2cart (theta, r, z)
[x, y] = pol2cart (P)
[x, y, z] = pol2cart (P)
C = pol2cart (…)

  Transform polar or cylindrical coordinates to Cartesian coordinates.

  The inputs theta, r, (and z) must be the same shape, or scalar. If called with a single matrix argument then each row of P represents the polar/(cylindrical) coordinate (theta, r (, z)).

  theta describes the angle relative to the positive x-axis.

  r is the distance to the z-axis (0, 0, z).

  If only a single return argument is requested then return a matrix C where each row represents one Cartesian coordinate (x, y (, z)).

  See also: cart2pol, sph2cart, cart2sph.

[theta, phi, r] = cart2sph (x, y, z)
[theta, phi, r] = cart2sph (C)
S = cart2sph (…)

  Transform Cartesian coordinates to spherical coordinates.

  The inputs x, y, and z must be the same shape, or scalar. If called with a single matrix argument then each row of C represents the Cartesian coordinate (x, y, z).

  theta describes the angle relative to the positive x-axis.

  phi is the angle relative to the xy-plane.

  r is the distance to the origin (0, 0, 0).

  If only a single return argument is requested then return a matrix S where each row represents one spherical coordinate (theta, phi, r).

  See also: sph2cart, cart2pol, pol2cart.

[x, y, z] = sph2cart (theta, phi, r)
[x, y, z] = sph2cart (S)
C = sph2cart (…)

  Transform spherical coordinates to Cartesian coordinates.

  The inputs theta, phi, and r must be the same shape, or scalar. If called with a single matrix argument then each row of S represents the spherical coordinate (theta, phi, r).

  theta describes the angle relative to the positive x-axis.

  phi is the angle relative to the xy-plane.

  r is the distance to the origin (0, 0, 0).

  If only a single return argument is requested then return a matrix C where each row represents one Cartesian coordinate (x, y, z).

  See also: cart2sph, pol2cart, cart2pol.