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## -*- texinfo -*-
## @deftypefn  {} {[@var{x}, @var{y}] =} pol2cart (@var{theta}, @var{r})
## @deftypefnx {} {[@var{x}, @var{y}, @var{z}] =} pol2cart (@var{theta}, @var{r}, @var{z})
## @deftypefnx {} {[@var{x}, @var{y}] =} pol2cart (@var{P})
## @deftypefnx {} {[@var{x}, @var{y}, @var{z}] =} pol2cart (@var{P})
## @deftypefnx {} {@var{C} =} pol2cart (@dots{})
## Transform polar or cylindrical coordinates to Cartesian coordinates.
##
## The inputs @var{theta}, @var{r}, (and @var{z}) must be the same shape, or
## scalar.  If called with a single matrix argument then each row of @var{P}
## represents the polar/(cylindrical) coordinate (@var{theta}, @var{r}
## (, @var{z})).
##
## @var{theta} describes the angle relative to the positive x-axis.
##
## @var{r} is the distance to the z-axis (0, 0, 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

function [x, y, z] = pol2cart (theta, r, z = [])

  if (nargin < 1 || nargin > 3)
    print_usage ();
  endif

  if (nargin == 1)
    if (! (isnumeric (theta) && ismatrix (theta)
           && (columns (theta) == 2 || columns (theta) == 3)))
      error ("pol2cart: matrix input must have 2 or 3 columns [THETA, R (, Z)]");
    endif
    if (columns (theta) == 3)
      z = theta(:,3);
    endif
    r = theta(:,2);
    theta = theta(:,1);
  elseif (nargin == 2)
    if (! isnumeric (theta) || ! isnumeric (r))
      error ("pol2cart: THETA, R must be numeric arrays of the same size, or scalar");
    endif
    [err, theta, r] = common_size (theta, r);
    if (err)
      error ("pol2cart: THETA, R must be numeric arrays of the same size, or scalar");
    endif
  elseif (nargin == 3)
    if (! isnumeric (theta) || ! isnumeric (r) || ! isnumeric (z))
      error ("pol2cart: THETA, R, Z must be numeric arrays of the same size, or scalar");
    endif
    [err, theta, r, z] = common_size (theta, r, z);
    if (err)
      error ("pol2cart: THETA, R, Z must be numeric arrays of the same size, or scalar");
    endif
  endif

  x = r .* cos (theta);
  y = r .* sin (theta);

  if (nargout <= 1)
    if (isempty (z))
      x = [x(:), y(:)];
    else
      x = [x(:), y(:), z(:)];
    endif
  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];
%! C = pol2cart (t, r);
%! assert (C(:,1), [0; 1; 2], sqrt (eps));
%! assert (C(:,2), [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 (z2, z);

%!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 (z2, z);

%!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 (z2, z);

%!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 (z2, [1, 1, 1]);

%!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));

%!test
%! r = ones (1, 1, 1, 2);
%! r(1, 1, 1, 2) = 2;
%! t = pi/2 * r;
%! [x, y] = pol2cart (t, r);
%! X = zeros (1, 1, 1, 2);
%! X(1, 1, 1, 2) = -2;
%! Y = zeros (1, 1, 1, 2);
%! Y(1, 1, 1, 1) = 1;
%! assert (x, X, 2*eps);
%! assert (y, Y, 2*eps);

%!test
%! [t, r, Z] = meshgrid ([0, pi/2], [1, 2], [0, 1]);
%! [x, y, z] = pol2cart (t, r, Z);
%! X = zeros(2, 2, 2);
%! X(:, 1, 1) = [1; 2];
%! X(:, 1, 2) = [1; 2];
%! Y = zeros(2, 2, 2);
%! Y(:, 2, 1) = [1; 2];
%! Y(:, 2, 2) = [1; 2];
%! assert (x, X, eps);
%! assert (y, Y, eps);
%! assert (z, Z);

## Test input validation
%!error pol2cart ()
%!error pol2cart (1,2,3,4)
%!error <matrix input must have 2 or 3 columns> pol2cart ({1,2,3})
%!error <matrix input must have 2 or 3 columns> pol2cart (ones (3,3,2))
%!error <matrix input must have 2 or 3 columns> pol2cart ([1])
%!error <matrix input must have 2 or 3 columns> pol2cart ([1,2,3,4])
%!error <numeric arrays of the same size> pol2cart ({1,2,3}, [1,2,3])
%!error <numeric arrays of the same size> pol2cart ([1,2,3], {1,2,3})
%!error <numeric arrays of the same size> pol2cart (ones (3,3,3), ones (3,2,3))
%!error <numeric arrays of the same size> pol2cart ({1,2,3}, [1,2,3], [1,2,3])
%!error <numeric arrays of the same size> pol2cart ([1,2,3], {1,2,3}, [1,2,3])
%!error <numeric arrays of the same size> pol2cart ([1,2,3], [1,2,3], {1,2,3})
%!error <numeric arrays of the same size> pol2cart (ones (3,3,3), 1, ones (3,2,3))
%!error <numeric arrays of the same size> pol2cart (ones (3,3,3), ones (3,2,3), 1)