update packages

[CreaPhase.git] / octave_packages / m / general / pol2cart.m

diff --git a/octave_packages/m/general/pol2cart.m b/octave_packages/m/general/pol2cart.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{x}, @var{y}] =} pol2cart (@var{theta}, @var{r})
+## @deftypefnx {Function File} {[@var{x}, @var{y}, @var{z}] =} pol2cart (@var{theta}, @var{r}, @var{z})
+## @deftypefnx {Function File} {[@var{x}, @var{y}] =} pol2cart (@var{p})
+## @deftypefnx {Function File} {[@var{x}, @var{y}, @var{z}] =} pol2cart (@var{p})
+## @deftypefnx {Function File} {@var{C} =} pol2cart (@dots{})
+## Transform polar or cylindrical to Cartesian coordinates.
+##
+## @var{theta}, @var{r}, (and @var{z}) must be the same shape, or scalar.
+## @var{theta} describes the angle relative to the positive x-axis.
+## @var{r} is the distance to the z-axis (0, 0, z).
+## If called with a single matrix argument then each row of @var{p}
+## represents the polar/(cylindrical) coordinate (@var{x}, @var{y} (, @var{z})).
+##
+## If only a single return argument is requested then return a matrix
+## @var{C} where each row represents one Cartesian coordinate
+## (@var{x}, @var{y} (, @var{z})).
+## @seealso{cart2pol, sph2cart, cart2sph}
+## @end deftypefn
+
+## Author: Kai Habel <kai.habel@gmx.de>
+## Adapted-by: jwe
+
+function [x, y, z] = pol2cart (theta, r, z)
+
+  if (nargin < 1 || nargin > 3)
+    print_usage ();
+  endif
+
+  if (nargin == 1)
+    if (ismatrix (theta) && (columns (theta) == 2 || columns (theta) == 3))
+      if (columns (theta) == 3)
+        z = theta(:,3);
+      else
+        z = [];
+      endif
+      r = theta(:,2);
+      theta = theta(:,1);
+    else
+      error ("pol2car: matrix input must have 2 or 3 columns [THETA, R (, Z)]");
+    endif
+  elseif (nargin == 2)
+    if (! ((ismatrix (theta) && ismatrix (r))
+            && (size_equal (theta, r) || isscalar (theta) || isscalar (r))))
+      error ("pol2cart: arguments must be matrices of same size, or scalar");
+    endif
+  elseif (nargin == 3)
+    if (! ((ismatrix (theta) && ismatrix (r) && ismatrix (z))
+            && (size_equal (theta, r) || isscalar (theta) || isscalar (r))
+            && (size_equal (theta, z) || isscalar (theta) || isscalar (z))
+            && (size_equal (r, z) || isscalar (r) || isscalar (z))))
+      error ("pol2cart: arguments must be matrices of same size, or scalar");
+    endif
+  endif
+
+  x = r .* cos (theta);
+  y = r .* sin (theta);
+
+  if (nargout <= 1)
+    x  = [x, y, z];
+  endif
+
+endfunction
+
+%!test
+%! t = [0, 0.5, 1] * pi;
+%! r = 1;
+%! [x, y] = pol2cart (t, r);
+%! assert (x, [1, 0, -1], sqrt(eps));
+%! assert (y, [0, 1,  0], sqrt(eps));
+
+%!test
+%! t = [0, 1, 1] * pi/4;
+%! r = sqrt(2) * [0, 1, 2];
+%! [x, y] = pol2cart (t, r);
+%! assert (x, [0, 1, 2], sqrt(eps));
+%! assert (y, [0, 1, 2], sqrt(eps));
+
+%!test
+%! t = [0, 1, 1] * pi/4;
+%! r = sqrt(2) * [0, 1, 2];
+%! z = [0, 1, 2];
+%! [x, y, z2] = pol2cart (t, r, z);
+%! assert (x, [0, 1, 2], sqrt(eps));
+%! assert (y, [0, 1, 2], sqrt(eps));
+%! assert (z, z2);
+
+%!test
+%! t = 0;
+%! r = [0, 1, 2];
+%! z = [0, 1, 2];
+%! [x, y, z2] = pol2cart (t, r, z);
+%! assert (x, [0, 1, 2], sqrt(eps));
+%! assert (y, [0, 0, 0], sqrt(eps));
+%! assert (z, z2);
+
+%!test
+%! t = [1, 1, 1]*pi/4;
+%! r = 1;
+%! z = [0, 1, 2];
+%! [x, y, z2] = pol2cart (t, r, z);
+%! assert (x, [1, 1, 1] / sqrt(2), eps);
+%! assert (y, [1, 1, 1] / sqrt(2), eps);
+%! assert (z, z2);
+
+%!test
+%! t = 0;
+%! r = [1, 2, 3];
+%! z = 1;
+%! [x, y, z2] = pol2cart (t, r, z);
+%! assert (x, [1, 2, 3], eps);
+%! assert (y, [0, 0, 0] / sqrt(2), eps);
+%! assert (z, z2);
+
+%!test
+%! P = [0, 0; pi/4, sqrt(2); pi/4, 2*sqrt(2)];
+%! C = [0, 0; 1, 1; 2, 2];
+%! assert (pol2cart(P), C, sqrt(eps));
+
+%!test
+%! P = [0, 0, 0; pi/4, sqrt(2), 1; pi/4, 2*sqrt(2), 2];
+%! C = [0, 0, 0; 1, 1, 1; 2, 2, 2];
+%! assert (pol2cart(P), C, sqrt(eps));
+