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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})
## 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 pair (@var{theta}, @var{r}) or
## triplet (@var{theta}, @var{r}, @var{z}).
##
## The outputs @var{x}, @var{y} (, and @var{z}) will match the shape of the
## inputs. For a matrix input @var{P} the outputs will be column vectors with
## rows corresponding to the rows of the input matrix.
##
## @var{theta} describes the angle relative to the positive x-axis
## measured in the xy-plane.
##
## @var{r} is the distance to the z-axis @w{(0, 0, z)}.
##
## If present, @var{z} is unchanged by the transformation.
##
## The coordinate transformation is computed using:
##
## @tex
## $$ x = r \cos \theta $$
## $$ y = r \sin \theta $$
## $$ z = z $$
## @end tex
## @ifnottex
##
## @example
## @var{x} = @var{r} * cos (@var{theta})
## @var{y} = @var{r} * sin (@var{theta})
## @var{z} = @var{z}
## @end example
##
## @end ifnottex
## Note: To improve Matlab compatibility, this function no longer returns a
## full coordinate matrix when called with a single return argument.
## @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)))
error ("cart2pol: matrix input must be 2D numeric array");
endif
if isvector (theta)
elsize = numel (theta);
if (elsize == 2 || elsize == 3)
if (elsize == 3)
z = theta(3);
endif
r = theta(2);
theta = theta(1);
else
error ("cart2pol: matrix input must be a 2 or 3 element vector or a 2 or 3 column array");
endif
else
cols_theta = columns(theta);
if (cols_theta == 2 || cols_theta == 3)
if (cols_theta == 3)
z = theta(:,3);
endif
r = theta(:,2);
theta = theta(:,1);
else
error ("cart2pol: matrix input must be a 2 or 3 element vector or a 2 or 3 column array");
endif
endif
elseif (nargin == 2)
if (! isnumeric (theta) || ! isnumeric (r))
error ("pol2cart: THETA, R must be numeric arrays or scalars");
endif
[err, theta, r] = common_size (theta, r);
if (err)
error ("pol2cart: THETA, R must be the same size or scalars");
endif
elseif (nargin == 3)
if (! isnumeric (theta) || ! isnumeric (r) || ! isnumeric (z))
error ("pol2cart: THETA, R, Z must be numeric arrays or scalars");
endif
[err, theta, r, z] = common_size (theta, r, z);
if (err)
error ("pol2cart: THETA, R, Z must be the same size or scalars");
endif
endif
x = r .* cos (theta);
y = r .* sin (theta);
endfunction
%!test
%! t = [0, 0.5, 1] * pi;
%! r = 1;
%! [x, y] = pol2cart (t, r);
%! assert (x, [1, 0, -1], eps);
%! assert (y, [0, 1, 0], eps);
%!test
%! t = [0, 1, 1] * pi/4;
%! r = sqrt (2) * [0, 1, 2];
%! [x, y] = pol2cart (t, r);
%! assert (x, [0, 1, 2], 2*eps);
%! assert (y, [0, 1, 2], 2*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], 2*eps);
%! assert (y, [0, 1, 2], 2*eps);
%! assert (z2, z);
%!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], 2*eps);
%! assert (y, [0; 1; 2], 2*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], eps);
%! assert (y, [0, 0, 0], 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)];
%! [x, y] = pol2cart(P);
%! assert (x, [0; 1; 2], 2*eps);
%! assert (y, [0; 1; 2], 2*eps);
%!test
%! P = [0, 0, 0; pi/4, sqrt(2), 1; pi/4, 2*sqrt(2), 2];
%! [x, y, z] = pol2cart(P);
%! assert (x, [0; 1; 2], 2*eps);
%! assert (y, [0; 1; 2], 2*eps);
%! assert (z, P(:,3), 2*eps);
%!test
%! P = [0, 0, 0; pi/4, sqrt(2), 1; pi/4, 2*sqrt(2), 2; 0, 0, 0];
%! [x, y, z] = pol2cart(P);
%! assert (x, [0; 1; 2; 0], 2*eps);
%! assert (y, [0; 1; 2; 0], 2*eps);
%! assert (z, P(:,3), 2*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 pol2cart ({1,2,3})
%!error pol2cart (ones (3,3,2))
%!error pol2cart ([1])
%!error pol2cart ([1,2,3,4])
%!error pol2cart ({1,2,3}, [1,2,3])
%!error pol2cart ([1,2,3], {1,2,3})
%!error pol2cart (ones (3,3,3), ones (3,2,3))
%!error pol2cart ([1; 1], [2, 2])
%!error pol2cart ([1; 1], [2, 2], [3, 3])
%!error pol2cart ({1,2,3}, [1,2,3], [1,2,3])
%!error pol2cart ([1,2,3], {1,2,3}, [1,2,3])
%!error pol2cart ([1,2,3], [1,2,3], {1,2,3})
%!error pol2cart (ones (3,3,3), 1, ones (3,2,3))
%!error pol2cart (ones (3,3,3), ones (3,2,3), 1)