update packages

[CreaPhase.git] / octave_packages / m / general / cart2sph.m

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+## Copyright (C) 2000-2012 Kai Habel
+##
+## This file is part of Octave.
+##
+## Octave is free software; you can redistribute it and/or modify it
+## under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or (at
+## your option) any later version.
+##
+## Octave is distributed in the hope that it will be useful, but
+## WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+## General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with Octave; see the file COPYING.  If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn  {Function File} {[@var{theta}, @var{phi}, @var{r}] =} cart2sph (@var{x}, @var{y}, @var{z})
+## @deftypefnx {Function File} {[@var{theta}, @var{phi}, @var{r}] =} cart2sph (@var{C})
+## @deftypefnx {Function File} {@var{S} =} cart2sph (@dots{})
+## Transform Cartesian to spherical coordinates.
+##
+## @var{theta} describes the angle relative to the positive x-axis.
+## @var{phi} is the angle relative to the xy-plane.
+## @var{r} is the distance to the origin @w{(0, 0, 0)}.
+## @var{x}, @var{y}, and @var{z} must be the same shape, or scalar.
+## If called with a single matrix argument then each row of @var{c}
+## represents the Cartesian coordinate (@var{x}, @var{y}, @var{z}).
+##
+## If only a single return argument is requested then return a matrix
+## @var{s} where each row represents one spherical coordinate
+## (@var{theta}, @var{phi}, @var{r}).
+## @seealso{sph2cart, cart2pol, pol2cart}
+## @end deftypefn
+
+## Author: Kai Habel <kai.habel@gmx.de>
+## Adapted-by: jwe
+
+function [theta, phi, r] = cart2sph (x, y, z)
+
+  if (nargin != 1 && nargin != 3)
+    print_usage ();
+  endif
+
+  if (nargin == 1)
+    if (ismatrix (x) && columns (x) == 3)
+      z = x(:,3);
+      y = x(:,2);
+      x = x(:,1);
+    else
+      error ("cart2sph: matrix input must have 3 columns [X, Y, Z]");
+    endif
+  elseif (nargin == 3)
+    if (! ((ismatrix (x) && ismatrix (y) && ismatrix (z))
+            && (size_equal (x, y) || isscalar (x) || isscalar (y))
+            && (size_equal (x, z) || isscalar (x) || isscalar (z))
+            && (size_equal (y, z) || isscalar (y) || isscalar (z))))
+      error ("cart2sph: X, Y, Z must be matrices of the same size, or scalar");
+    endif
+  endif
+
+  theta = atan2 (y, x);
+  phi = atan2 (z, sqrt (x .^ 2 + y .^ 2));
+  r = sqrt (x .^ 2 + y .^ 2 + z .^ 2);
+
+  if (nargout <= 1)
+    theta = [theta, phi, r];
+  endif
+
+endfunction
+
+%!test
+%! x = [0, 1, 2];
+%! y = [0, 1, 2];
+%! z = [0, 1, 2];
+%! [t, p, r] = cart2sph (x, y, z);
+%! assert (t, [0, pi/4, pi/4], eps);
+%! assert (p, [0, 1, 1]*atan(sqrt(0.5)), eps);
+%! assert (r, [0, 1, 2]*sqrt(3), eps);
+
+%!test
+%! x = 0;
+%! y = [0, 1, 2];
+%! z = [0, 1, 2];
+%! [t, p, r] = cart2sph (x, y, z);
+%! assert (t, [0, 1, 1] * pi/2, eps);
+%! assert (p, [0, 1, 1] * pi/4, eps);
+%! assert (r, [0, 1, 2] * sqrt(2), eps);
+
+%!test
+%! x = [0, 1, 2];
+%! y = 0;
+%! z = [0, 1, 2];
+%! [t, p, r] = cart2sph (x, y, z);
+%! assert (t, [0, 0, 0]);
+%! assert (p, [0, 1, 1] * pi/4);
+%! assert (r, [0, 1, 2] * sqrt(2));
+
+%!test
+%! x = [0, 1, 2];
+%! y = [0, 1, 2];
+%! z = 0;
+%! [t, p, r] = cart2sph (x, y, z);
+%! assert (t, [0, 1, 1] * pi/4);
+%! assert (p, [0, 0, 0]);
+%! assert (r, [0, 1, 2] * sqrt(2));
+
+%!test
+%! C = [0, 0, 0; 1, 0, 1; 2, 0, 2];
+%! S = [0, 0, 0; 0, pi/4, sqrt(2); 0, pi/4, 2*sqrt(2)];
+%! assert (cart2sph(C), S, eps);