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changeset 8533:fb1b87ea4af9

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Permit scalars when transforming coordinates.
author Ben Abbott <bpabbott@mac.com>
date Sat, 17 Jan 2009 17:32:11 -0500
parents 4d884a016846
children 0eb83938c8bc
files scripts/ChangeLog scripts/general/cart2pol.m scripts/general/cart2sph.m scripts/general/pol2cart.m scripts/general/sph2cart.m
diffstat 5 files changed, 231 insertions(+), 42 deletions(-) [+]
line wrap: on
line diff
--- a/scripts/ChangeLog
+++ b/scripts/ChangeLog
@@ -1,3 +1,8 @@
+2009-01-17 Ben Abbott <bpabbott@mac.com>
+
+	* general/cart2sph.m, cart2pol.m, sph2cart.m pol2cart.m:
+	Permit scalars when transforming coordinates.
+
 2009-01-17  Steven Verstoep <isgoed@hotmail.com>
 
 	* plot/__quiver__.m: __quiver__.m: Fix auto-size of (x,y) coord.
--- a/scripts/general/cart2pol.m
+++ b/scripts/general/cart2pol.m
@@ -20,7 +20,7 @@
 ## @deftypefn {Function File} {[@var{theta}, @var{r}] =} cart2pol (@var{x}, @var{y})
 ## @deftypefnx {Function File} {[@var{theta}, @var{r}, @var{z}] =} cart2pol (@var{x}, @var{y}, @var{z})
 ## Transform cartesian to polar or cylindrical coordinates.
-## @var{x}, @var{y} (and @var{z}) must be of same shape.
+## @var{x}, @var{y} (and @var{z}) must be of same shape, or scalar.
 ## @var{theta} describes the angle relative to the x-axis.
 ## @var{r} is the distance to the z-axis (0, 0, z).
 ## @seealso{pol2cart, cart2sph, sph2cart}
@@ -29,7 +29,7 @@
 ## Author: Kai Habel <kai.habel@gmx.de>
 ## Adapted-by: jwe
 
-function [Theta, R, Z] = cart2pol (X, Y, Z)
+function [theta, r, z] = cart2pol (x, y, z)
 
   if (nargin < 2 || nargin > 3)
     error ("cart2pol: number of arguments must be 2 or 3");
@@ -39,13 +39,67 @@
     error ("cart2pol: number of output arguments must not be greater than number of input arguments");
   endif
 
-  if (! (ismatrix (X) && ismatrix (Y))
-      || ! size_equal (X, Y)
-      || (nargin == 3 && ! (size_equal (X, Z) && ismatrix (Z))))
-    error ("cart2pol: arguments must be matrices of same size");
+  if ((ismatrix (x) && ismatrix (y) && (nargin == 2 || ismatrix (z)))
+      && (size_equal (x, y) || isscalar (x) || isscalar (y))
+      && (nargin == 2 || size_equal (x, z) || isscalar (x) || isscalar (z))
+      && (nargin == 2 || size_equal (y, z) || isscalar (y) || isscalar (z)))
+  
+    theta = atan2 (y, x);
+    r = sqrt (x .^ 2 + y .^ 2);
+
+  else
+    error ("cart2pol: arguments must be matrices of same size, or scalar");
   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], sqrt(eps));
+%! assert (r, sqrt(2)*[0, 1, 2], sqrt(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 (z, z2);
 
-endfunction
+%!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 (z, z2);
+
+%!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 (z, z2);
+
+%!test
+%! x = 0;
+%! y = 0;
+%! z = [0, 1, 2];
+%! [t, r, z2] = cart2pol (x, y, z);
+%! assert (t, 0);
+%! assert (r, 0);
+%! assert (z, z2);
+
--- a/scripts/general/cart2sph.m
+++ b/scripts/general/cart2sph.m
@@ -19,7 +19,7 @@
 ## -*- texinfo -*-
 ## @deftypefn {Function File} {[@var{theta}, @var{phi}, @var{r}] =} cart2sph (@var{x}, @var{y}, @var{z})
 ## Transform cartesian to spherical coordinates.
-## @var{x}, @var{y} and @var{z} must be of same shape.
+## @var{x}, @var{y} and @var{z} must be of same shape, or scalar.
 ## @var{theta} describes the angle relative to the x-axis.
 ## @var{phi} is the angle relative to the xy-plane.
 ## @var{r} is the distance to the origin (0, 0, 0).
@@ -29,20 +29,60 @@
 ## Author: Kai Habel <kai.habel@gmx.de>
 ## Adapted-by: jwe
 
-function [Theta, Phi, R] = cart2sph (X, Y, Z)
+function [theta, phi, r] = cart2sph (x, y, z)
 
   if (nargin != 3)
     print_usage ();
   endif
 
-  if (! (ismatrix (X) && ismatrix (Y) && ismatrix (Z))
-      || ! size_equal (X, Y)
-      || ! size_equal (X, Z))
-    error ("cart2sph: arguments must be matrices of same size");
+  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)))
+
+    theta = atan2 (y, x);
+    phi = atan2 (z, sqrt (x .^ 2 + y .^ 2));
+    r = sqrt (x .^ 2 + y .^ 2 + z .^ 2);
+
+  else
+    error ("cart2sph: arguments must be matrices of same size, or scalar");
   endif
 
-  Theta = atan2 (Y, X);
-  Phi = atan2 (Z, sqrt (X .^ 2 + Y .^ 2));
-  R = sqrt (X .^ 2 + Y .^ 2 + Z .^ 2);
+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);
 
-endfunction
+%!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));
+
--- a/scripts/general/pol2cart.m
+++ b/scripts/general/pol2cart.m
@@ -20,7 +20,7 @@
 ## @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})
 ## Transform polar or cylindrical to cartesian coordinates.
-## @var{theta}, @var{r} (and @var{z}) must be of same shape.
+## @var{theta}, @var{r} (and @var{z}) must be of same shape, or scalar.
 ## @var{theta} describes the angle relative to the x-axis.
 ## @var{r} is the distance to the z-axis (0, 0, z).
 ## @seealso{cart2pol, cart2sph, sph2cart}
@@ -29,7 +29,7 @@
 ## Author: Kai Habel <kai.habel@gmx.de>
 ## Adapted-by: jwe
 
-function [X, Y, Z] = pol2cart (Theta, R, Z)
+function [x, y, z] = pol2cart (theta, r, z)
 
   if (nargin < 2 || nargin > 3)
     error ("pol2cart: number of arguments must be 2 or 3");
@@ -39,17 +39,67 @@
     error ("pol2cart: number of output arguments must not be greater than number of input arguments");
   endif
 
-  if (! (ismatrix (Theta) && ismatrix (R))
-      || ! size_equal (Theta, R) && ! isscalar (Theta) && ! isscalar (R)
-      || (nargin == 3
-          && (! ismatrix (Z)
-              || (! isscalar (Z)
-                  && (! (isscalar (R) || size_equal (R, Z))
-		      || ! (isscalar(Theta) || size_equal (Theta, Z)))))))
-    error ("pol2cart: arguments must be matrices of same size or scalar");
+   if ((ismatrix (theta) && ismatrix (r) && (nargin == 2 || ismatrix (z)))
+       && (size_equal (theta, r) || isscalar (theta) || isscalar (r))
+       && (nargin == 2 || size_equal (theta, z) || isscalar (theta) || isscalar (z))
+       && (nargin == 2 || size_equal (r, z) || isscalar (r) || isscalar (z)))
+
+    x = cos (theta) .* r;
+    y = sin (theta) .* r;
+
+  else
+    error ("pol2cart: arguments must be matrices of same size, or scalar");
   endif
 
-  X = cos (Theta) .* R;
-  Y = sin (Theta) .* R;
+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);
 
-endfunction
+%!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);
+
--- a/scripts/general/sph2cart.m
+++ b/scripts/general/sph2cart.m
@@ -19,7 +19,7 @@
 ## -*- texinfo -*-
 ## @deftypefn {Function File} {[@var{x}, @var{y}, @var{z}] =} sph2cart (@var{theta}, @var{phi}, @var{r})
 ## Transform spherical to cartesian coordinates.
-## @var{x}, @var{y} and @var{z} must be of same shape.
+## @var{x}, @var{y} and @var{z} must be of same shape, or scalar.
 ## @var{theta} describes the angle relative to the x-axis.
 ## @var{phi} is the angle relative to the xy-plane.
 ## @var{r} is the distance to the origin (0, 0, 0).
@@ -29,20 +29,60 @@
 ## Author: Kai Habel <kai.habel@gmx.de>
 ## Adapted-by: jwe
 
-function [X, Y, Z] = sph2cart (Theta, Phi, R)
+function [x, y, z] = sph2cart (theta, phi, r)
 
   if (nargin != 3)
     print_usage ();
   endif
 
-  if ((! (ismatrix (Theta) && ismatrix (Phi) && ismatrix (R)))
-      || (! size_equal (Theta, Phi))
-      || (! size_equal (Theta, R)))
-    error ("sph2cart: arguments must be matrices of same size");
+  if ((ismatrix (theta) && ismatrix (phi) && ismatrix (r))
+      && (size_equal (theta, phi) || isscalar (theta) || isscalar (phi))
+      && (size_equal (theta, r) || isscalar (theta) || isscalar (r))
+      && (size_equal (phi, r) || isscalar (phi) || isscalar (r)))
+
+    x = r .* cos (phi) .* cos (theta);
+    y = r .* cos (phi) .* sin (theta);
+    z = r .* sin (phi);
+
+  else
+    error ("sph2cart: arguments must be matrices of same size, or scalar");
   endif
 
-  X = R .* cos (Phi) .* cos (Theta);
-  Y = R .* cos (Phi) .* sin (Theta);
-  Z = R .* sin (Phi);
+endfunction
+
+%!test
+%! t = [0, 0, 0];
+%! p = [0, 0, 0];
+%! r = [0, 1, 2];
+%! [x, y, z] = sph2cart (t, p, r);
+%! assert (x, r);
+%! assert (y, [0, 0, 0]);
+%! assert (z, [0, 0, 0]);
 
-endfunction
+%!test
+%! t = 0;
+%! p = [0, 0, 0];
+%! r = [0, 1, 2];
+%! [x, y, z] = sph2cart (t, p, r);
+%! assert (x, r);
+%! assert (y, [0, 0, 0]);
+%! assert (z, [0, 0, 0]);
+
+%!test
+%! t = [0, 0, 0];
+%! p = 0;
+%! r = [0, 1, 2];
+%! [x, y, z] = sph2cart (t, p, r);
+%! assert (x, r);
+%! assert (y, [0, 0, 0]);
+%! assert (z, [0, 0, 0]);
+
+%!test
+%! t = [0, 0.5, 1]*pi;
+%! p = [0, 0, 0];
+%! r = 1;
+%! [x, y, z] = sph2cart (t, p, r);
+%! assert (x, [1, 0, -1], eps);
+%! assert (y, [0, 1, 0], eps);
+%! assert (z, [0, 0, 0], eps);
+