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## Copyright (C) 2000-2020 The Octave Project Developers
##
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## distribution or .
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## Octave is free software: you can redistribute it and/or modify it
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## -*- texinfo -*-
## @deftypefn {} {[@var{theta}, @var{r}] =} cart2pol (@var{x}, @var{y})
## @deftypefnx {} {[@var{theta}, @var{r}, @var{z}] =} cart2pol (@var{x}, @var{y}, @var{z})
## @deftypefnx {} {[@var{theta}, @var{r}] =} cart2pol (@var{C})
## @deftypefnx {} {[@var{theta}, @var{r}, @var{z}] =} cart2pol (@var{C})
##
## Transform Cartesian coordinates to polar or cylindrical coordinates.
##
## The inputs @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 pair (@var{x}, @var{y}) or triplet
## (@var{x}, @var{y}, @var{z}).
##
## The outputs @var{theta}, @var{r} (, and @var{z}) will match the shape of the
## inputs. For a matrix input @var{C} 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
## $$ \theta = \arctan \left ( \frac {y} {x} \right ) $$
## $$ r = \sqrt{x^2 + y^2} $$
## $$ z = z $$
## @end tex
## @ifnottex
##
## @example
## @var{theta} = arctan (@var{y} / @var{x})
## @var{r} = sqrt (@var{x}^2 + @var{y}^2)
## @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{pol2cart, cart2sph, sph2cart}
## @end deftypefn
function [theta, r, z] = cart2pol (x, y, z = [])
if (nargin < 1 || nargin > 3)
print_usage ();
endif
if (nargin == 1)
if (! (isnumeric (x) && ismatrix (x)))
error ("cart2pol: matrix input must be 2D numeric array");
endif
if isvector (x)
elsize = numel (x);
if (elsize == 2 || elsize == 3)
if (elsize == 3)
z = x(3);
endif
y = x(2);
x = x(1);
else
error ("cart2pol: matrix input must be a 2 or 3 element vector or a 2 or 3 column array");
endif
else
cols_x = columns(x);
if (cols_x == 2 || cols_x == 3)
if (cols_x == 3)
z = x(:,3);
endif
y = x(:,2);
x = x(:,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 (x) || ! isnumeric (y))
error ("cart2pol: X, Y must be numeric arrays or scalars");
endif
[err, x, y] = common_size (x, y);
if (err)
error ("cart2pol: X, Y must be the same size or scalars");
endif
elseif (nargin == 3)
if (! isnumeric (x) || ! isnumeric (y) || ! isnumeric (z))
error ("cart2pol: X, Y, Z must be numeric arrays or scalars");
endif
[err, x, y, z] = common_size (x, y, z);
if (err)
error ("cart2pol: X, Y, Z must be the same size or scalars");
endif
endif
theta = atan2 (y, x);
r = sqrt (x .^ 2 + y .^ 2);
endfunction
%!test
%! x = [0, 1, 2];
%! y = 0;
%! [t, r] = cart2pol (x, y);
%! assert (t, [0, 0, 0]);
%! assert (r, x);
%!test
%! x = [0, 1, 2];
%! y = [0, 1, 2];
%! [t, r] = cart2pol (x, y);
%! assert (t, [0, pi/4, pi/4], eps);
%! assert (r, sqrt (2)*[0, 1, 2], eps);
%!test
%! x = [0, 1, 2]';
%! y = [0, 1, 2]';
%! [t, r] = cart2pol (x, y);
%! assert (t, [0; pi/4; pi/4], eps);
%! assert (r, sqrt (2)*[0; 1; 2], eps);
%!test
%! x = [0, 1, 2];
%! y = [0, 1, 2];
%! z = [0, 1, 2];
%! [t, r, z2] = cart2pol (x, y, z);
%! assert (t, [0, pi/4, pi/4], sqrt (eps));
%! assert (r, sqrt (2)*[0, 1, 2], sqrt (eps));
%! assert (z2, z);
%!test
%! x = [0, 1, 2];
%! y = 0;
%! z = 0;
%! [t, r, z2] = cart2pol (x, y, z);
%! assert (t, [0, 0, 0], eps);
%! assert (r, x, eps);
%! assert (z2, [0, 0, 0]);
%!test
%! x = 0;
%! y = [0, 1, 2];
%! z = 0;
%! [t, r, z2] = cart2pol (x, y, z);
%! assert (t, [0, 1, 1]*pi/2, eps);
%! assert (r, y, eps);
%! assert (z2, [0, 0, 0]);
%!test
%! x = 0;
%! y = 0;
%! z = [0, 1, 2];
%! [t, r, z2] = cart2pol (x, y, z);
%! assert (t, [0, 0, 0]);
%! assert (r, [0, 0, 0]);
%! assert (z2, z);
%!test
%! C = [0, 0; 1, 1; 2, 2];
%! [t, r] = cart2pol (C);
%! assert (t, [0; 1; 1]*pi/4, eps);
%! assert (r, [0; 1; 2]*sqrt(2), eps);
%!test
%! C = [0, 0, 0; 1, 1, 1; 2, 2, 2];
%! [t, r, z] = cart2pol (C);
%! assert (t, [0; 1; 1]*pi/4, eps);
%! assert (r, [0; 1; 2]*sqrt(2), eps);
%! assert (z, [0; 1; 2]);
%!test
%! C = [0, 0, 0; 1, 1, 1; 2, 2, 2;1, 1, 1];
%! [t, r, z] = cart2pol (C);
%! assert (t, [0; 1; 1; 1]*pi/4, eps);
%! assert (r, [0; 1; 2; 1]*sqrt(2), eps);
%! assert (z, [0; 1; 2; 1]);
%!test
%! x = zeros (1, 1, 1, 2);
%! x(1, 1, 1, 2) = sqrt (2);
%! y = x;
%! [t, r] = cart2pol (x, y);
%! T = zeros (1, 1, 1, 2);
%! T(1, 1, 1, 2) = pi/4;
%! R = zeros (1, 1, 1, 2);
%! R(1, 1, 1, 2) = 2;
%! assert (t, T, eps);
%! assert (r, R, eps);
%!test
%! [x, y, Z] = meshgrid ([0, 1], [0, 1], [0, 1]);
%! [t, r, z] = cart2pol (x, y, Z);
%! T(:, :, 1) = [0, 0; pi/2, pi/4];
%! T(:, :, 2) = T(:, :, 1);
%! R = sqrt (x.^2 + y.^2);
%! assert (t, T, eps);
%! assert (r, R, eps);
%! assert (z, Z);
## Test input validation
%!error cart2pol ()
%!error cart2pol (1,2,3,4)
%!error cart2pol ({1,2,3})
%!error cart2pol (ones (3,3,2))
%!error cart2pol ([1])
%!error cart2pol ([1,2,3,4])
%!error cart2pol ({1,2,3}, [1,2,3])
%!error cart2pol ([1,2,3], {1,2,3})
%!error cart2pol (ones (3,3,3), ones (3,2,3))
%!error cart2pol ([1; 1], [2, 2])
%!error cart2pol ([1; 1], [2, 2], [3, 3])
%!error cart2pol ({1,2,3}, [1,2,3], [1,2,3])
%!error cart2pol ([1,2,3], {1,2,3}, [1,2,3])
%!error cart2pol ([1,2,3], [1,2,3], {1,2,3})
%!error cart2pol (ones (3,3,3), 1, ones (3,2,3))
%!error cart2pol (ones (3,3,3), ones (3,2,3), 1)