--- a/NEWS	Sun Mar 22 19:23:03 2020 +0100
+++ b/NEWS	Sun Feb 16 20:19:05 2020 -0500
@@ -44,6 +44,15 @@
 - The function `griddata` now accepts 3-D inputs by passing data
 directly to `griddata3`.
 
+- Coordinate transformation functions `cart2sph`, `sph2cart`,
+`cart2pol`, and `pol2cart` can now accept either row or column vectors
+for coordinate inputs.  A single coordinate matrix with one variable per
+column can still be used as function input, but a single output variable
+will now contain just the first output coordinate, and will no longer
+return the full output coordinate matrix.  Output size matches the
+size of input vectors, or in the case of an input matrix will be column
+vectors with rows corresponding to the input coordinate matrix.
+
 ### Alphabetical list of new functions added in Octave 7
 
 * `rng`

--- a/scripts/general/cart2pol.m	Sun Mar 22 19:23:03 2020 +0100
+++ b/scripts/general/cart2pol.m	Sun Feb 16 20:19:05 2020 -0500
@@ -28,21 +28,47 @@
 ## @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})
-## @deftypefnx {} {@var{P} =} cart2pol (@dots{})
 ##
 ## 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 (@var{x}, @var{y} (, @var{z})).
+## represents the Cartesian coordinate pair (@var{x}, @var{y}) or triplet
+## (@var{x}, @var{y}, @var{z}).
 ##
-## @var{theta} describes the angle relative to the positive x-axis.
+## The outputs @var{theta}, @var{r} (, and @var{z}) 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 only a single return argument is requested then return a matrix @var{P}
-## where each row represents one polar/(cylindrical) coordinate
-## (@var{theta}, @var{phi} (, @var{z})).
+## @var{z}, if present, is unchanged by the transformation.
+##
+## The coordinate transformation is computed using:
+##
+## @tex
+## $$ \theta = \arctan \left ( {y \over x} \right ) $$
+## $$ r = \sqrt{x^2 + y^2} $$
+## $$ z = z $$
+## @end tex
+## @ifnottex
+##
+## @example
+## @group
+## @var{theta} = arctan (@var{y} / @var{x})
+## @var{r} = sqrt (@var{x}^2 + @var{y}^2)
+## @var{z} = @var{z}
+## @end group
+## @end example
+##
+## @end ifnottex
+##
+## @c FIXME: Remove this note in Octave 9.1 (two releases after 7.1).
+## Note: For @sc{matlab} compatibility, this function no longer returns a full
+## coordinate matrix when called with a single return argument.
 ## @seealso{pol2cart, cart2sph, sph2cart}
 ## @end deftypefn
 
@@ -53,44 +79,54 @@
   endif
 
   if (nargin == 1)
-    if (! (isnumeric (x) && ismatrix (x)
-           && (columns (x) == 2 || columns (x) == 3)))
-      error ("cart2pol: matrix input must have 2 or 3 columns [X, Y (, Z)]");
+    if (! (isnumeric (x) && ismatrix (x)))
+      error ("cart2pol: matrix input must be 2-D numeric array");
     endif
-    if (columns (x) == 3)
-      z = x(:,3);
+    if (isvector (x))
+      n = numel (x);
+      if (n != 2 && n != 3)
+        error ("cart2pol: matrix input must be a 2- or 3-element vector or a 2- or 3-column array");
+      endif
+      if (n == 3)
+        z = x(3);
+      endif
+      y = x(2);
+      x = x(1);
+    else
+      ncols = columns (x);
+      if (ncols != 2 && ncols != 3)
+        error ("cart2pol: matrix input must be a 2- or 3-element vector or a 2- or 3-column array");
+      endif
+
+      if (ncols == 3)
+        z = x(:,3);
+      endif
+      y = x(:,2);
+      x = x(:,1);
     endif
-    y = x(:,2);
-    x = x(:,1);
+
   elseif (nargin == 2)
-    if (! isnumeric (x) || ! isnumeric (y))
-      error ("cart2pol: X, Y must be numeric arrays of the same size, or scalar");
+    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 numeric arrays of the same size, or scalar");
+      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 of the same size, or scalar");
+    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 numeric arrays of the same size, or scalar");
+      error ("cart2pol: X, Y, Z must be the same size or scalars");
     endif
   endif
 
   theta = atan2 (y, x);
   r = sqrt (x .^ 2 + y .^ 2);
 
-  if (nargout <= 1)
-    if (isempty (z))
-      theta = [theta(:), r(:)];
-    else
-      theta = [theta(:), r(:), z(:)];
-    endif
-  endif
-
 endfunction
 
 
@@ -104,9 +140,16 @@
 %!test
 %! x = [0, 1, 2];
 %! y = [0, 1, 2];
-%! P = cart2pol (x, y);
-%! assert (P(:,1), [0; pi/4; pi/4], sqrt (eps));
-%! assert (P(:,2), sqrt (2)*[0; 1; 2], sqrt (eps));
+%! [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];
@@ -146,13 +189,23 @@
 
 %!test
 %! C = [0, 0; 1, 1; 2, 2];
-%! P = [0, 0; pi/4, sqrt(2); pi/4, 2*sqrt(2)];
-%! assert (cart2pol (C), P, sqrt (eps));
+%! [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];
-%! P = [0, 0, 0; pi/4, sqrt(2), 1; pi/4, 2*sqrt(2), 2];
-%! assert (cart2pol (C), P, sqrt (eps));
+%! [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);
@@ -179,15 +232,17 @@
 ## Test input validation
 %!error cart2pol ()
 %!error cart2pol (1,2,3,4)
-%!error <matrix input must have 2 or 3 columns> cart2pol ({1,2,3})
-%!error <matrix input must have 2 or 3 columns> cart2pol (ones (3,3,2))
-%!error <matrix input must have 2 or 3 columns> cart2pol ([1])
-%!error <matrix input must have 2 or 3 columns> cart2pol ([1,2,3,4])
-%!error <numeric arrays of the same size> cart2pol ({1,2,3}, [1,2,3])
-%!error <numeric arrays of the same size> cart2pol ([1,2,3], {1,2,3})
-%!error <numeric arrays of the same size> cart2pol (ones (3,3,3), ones (3,2,3))
-%!error <numeric arrays of the same size> cart2pol ({1,2,3}, [1,2,3], [1,2,3])
-%!error <numeric arrays of the same size> cart2pol ([1,2,3], {1,2,3}, [1,2,3])
-%!error <numeric arrays of the same size> cart2pol ([1,2,3], [1,2,3], {1,2,3})
-%!error <numeric arrays of the same size> cart2pol (ones (3,3,3), 1, ones (3,2,3))
-%!error <numeric arrays of the same size> cart2pol (ones (3,3,3), ones (3,2,3), 1)
+%!error <matrix input must be 2-D numeric array> cart2pol ({1,2,3})
+%!error <matrix input must be 2-D numeric array> cart2pol (ones (3,3,2))
+%!error <matrix input must be a 2- or 3-element> cart2pol ([1])
+%!error <matrix input must be a 2- or 3-element> cart2pol ([1,2,3,4])
+%!error <must be numeric arrays or scalars> cart2pol ({1,2,3}, [1,2,3])
+%!error <must be numeric arrays or scalars> cart2pol ([1,2,3], {1,2,3})
+%!error <must be the same size or scalars> cart2pol (ones (3,3,3), ones (3,2,3))
+%!error <must be the same size or scalars> cart2pol ([1; 1], [2, 2])
+%!error <must be the same size or scalars> cart2pol ([1; 1], [2, 2], [3, 3])
+%!error <must be numeric arrays or scalars> cart2pol ({1,2,3}, [1,2,3], [1,2,3])
+%!error <must be numeric arrays or scalars> cart2pol ([1,2,3], {1,2,3}, [1,2,3])
+%!error <must be numeric arrays or scalars> cart2pol ([1,2,3], [1,2,3], {1,2,3})
+%!error <must be the same size or scalars> cart2pol (ones (3,3,3), 1, ones (3,2,3))
+%!error <must be the same size or scalars> cart2pol (ones (3,3,3), ones (3,2,3), 1)

--- a/scripts/general/cart2sph.m	Sun Mar 22 19:23:03 2020 +0100
+++ b/scripts/general/cart2sph.m	Sun Feb 16 20:19:05 2020 -0500
@@ -26,22 +26,45 @@
 ## -*- texinfo -*-
 ## @deftypefn  {} {[@var{theta}, @var{phi}, @var{r}] =} cart2sph (@var{x}, @var{y}, @var{z})
 ## @deftypefnx {} {[@var{theta}, @var{phi}, @var{r}] =} cart2sph (@var{C})
-## @deftypefnx {} {@var{S} =} cart2sph (@dots{})
 ## Transform Cartesian coordinates to spherical 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 (@var{x}, @var{y}, @var{z}).
+## If called with a single matrix argument then each row of @var{C} must
+## represent a Cartesian coordinate triplet (@var{x}, @var{y}, @var{z}).
 ##
-## @var{theta} describes the angle relative to the positive x-axis.
+## The outputs @var{theta}, @var{phi}, @var{r} 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{phi} is the angle relative to the xy-plane.
+## @var{theta} describes the azimuth angle relative to the positive x-axis
+## measured in the xy-plane.
+##
+## @var{phi} is the elevation angle measured relative to the xy-plane.
 ##
 ## @var{r} is the distance to the origin @w{(0, 0, 0)}.
 ##
-## If only a single return argument is requested then return a matrix @var{S}
-## where each row represents one spherical coordinate
-## (@var{theta}, @var{phi}, @var{r}).
+## The coordinate transformation is computed using:
+##
+## @tex
+## $$ \theta = \arctan \left ({y \over x} \right ) $$
+## $$ \phi = \arctan \left ( {z \over {\sqrt{x^2+y^2}}} \right ) $$
+## $$ r = \sqrt{x^2 + y^2 + z^2} $$
+## @end tex
+## @ifnottex
+##
+## @example
+## @group
+## @var{theta} = arctan (@var{y} / @var{x})
+## @var{phi} = arctan (@var{z} / sqrt (@var{x}^2 + @var{y}^2))
+## @var{r} = sqrt (@var{x}^2 + @var{y}^2 + @var{z}^2)
+## @end group
+## @end example
+##
+## @end ifnottex
+##
+## @c FIXME: Remove this note in Octave 9.1 (two releases after 7.1).
+## Note: For @sc{matlab} compatibility, this function no longer returns a full
+## coordinate matrix when called with a single return argument.
 ## @seealso{sph2cart, cart2pol, pol2cart}
 ## @end deftypefn
 
@@ -52,19 +75,29 @@
   endif
 
   if (nargin == 1)
-    if (! (isnumeric (x) && ismatrix (x) && columns (x) == 3))
-      error ("cart2sph: matrix input must have 3 columns [X, Y, Z]");
+    if (! (isnumeric (x) && ismatrix (x)))
+      error ("cart2sph: matrix input C must be a 2-D numeric array");
+    elseif (columns (x) != 3 && numel (x) != 3)
+      error ("cart2sph: matrix input C must be a 3-element vector or 3-column array");
     endif
-    z = x(:,3);
-    y = x(:,2);
-    x = x(:,1);
+
+    if (numel (x) == 3)
+      z = x(3);
+      y = x(2);
+      x = x(1);
+    else
+      z = x(:,3);
+      y = x(:,2);
+      x = x(:,1);
+    endif
+
   else
-    if (! isnumeric (x) || ! isnumeric (y) || ! isnumeric (z))
-      error ("cart2sph: X, Y, Z must be numeric arrays of the same size, or scalar");
+    if (! (isnumeric (x) && isnumeric (y) && isnumeric (z)))
+      error ("cart2sph: X, Y, Z must be numeric arrays or scalars");
     endif
     [err, x, y, z] = common_size (x, y, z);
     if (err)
-      error ("cart2sph: X, Y, Z must be numeric arrays of the same size, or scalar");
+      error ("cart2sph: X, Y, Z must be the same size or scalars");
     endif
   endif
 
@@ -72,10 +105,6 @@
   phi = atan2 (z, sqrt (x .^ 2 + y .^ 2));
   r = sqrt (x .^ 2 + y .^ 2 + z .^ 2);
 
-  if (nargout <= 1)
-    theta = [theta(:), phi(:), r(:)];
-  endif
-
 endfunction
 
 
@@ -89,13 +118,22 @@
 %! assert (r, [0, 1, 2]*sqrt (3), eps);
 
 %!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);
+
+%!test
 %! x = 0;
 %! y = [0, 1, 2];
 %! z = [0, 1, 2];
-%! S = cart2sph (x, y, z);
-%! assert (S(:,1), [0; 1; 1] * pi/2, eps);
-%! assert (S(:,2), [0; 1; 1] * pi/4, eps);
-%! assert (S(:,3), [0; 1; 2] * sqrt (2), eps);
+%! [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];
@@ -103,17 +141,17 @@
 %! 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));
+%! assert (p, [0, 1, 1] * pi/4, eps);
+%! assert (r, [0, 1, 2] * sqrt (2), eps);
 
 %!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 (t, [0, 1, 1] * pi/4, eps);
 %! assert (p, [0, 0, 0]);
-%! assert (r, [0, 1, 2] * sqrt (2));
+%! assert (r, [0, 1, 2] * sqrt (2), eps);
 
 %!test
 %! x = 0;
@@ -121,13 +159,22 @@
 %! z = [0, 1, 2];
 %! [t, p, r] = cart2sph (x, y, z);
 %! assert (t, [0, 0, 0]);
-%! assert (p, [0, 1, 1] * pi/2);
+%! assert (p, [0, 1, 1] * pi/2, eps);
 %! assert (r, [0, 1, 2]);
 
 %!test
 %! C = [0, 0, 0; 1, 0, 1; 2, 0, 2];
-%! S = [0, 0, 0; 0, pi/4, sqrt(2); 0, pi/4, 2*sqrt(2)];
-%! assert (cart2sph (C), S, eps);
+%! [t, p, r] = cart2sph (C);
+%! assert (t, [0; 0; 0]);
+%! assert (p, [0; 1; 1] * pi/4, eps);
+%! assert (r, [0; 1; 2] * sqrt (2), eps);
+
+%!test
+%! C = [0, 0, 0; 1, 0, 1; 2, 0, 2; 1, 0, 1];
+%! [t, p, r] = cart2sph (C);
+%! assert (t, [0; 0; 0; 0]);
+%! assert (p, [0; 1; 1; 1] * pi/4, eps);
+%! assert (r, [0; 1; 2; 1] * sqrt (2), eps);
 
 %!test
 %! [x, y, z] = meshgrid ([0, 1], [0, 1], [0, 1]);
@@ -145,11 +192,13 @@
 %!error cart2sph ()
 %!error cart2sph (1,2)
 %!error cart2sph (1,2,3,4)
-%!error <matrix input must have 3 columns> cart2sph ({1,2,3})
-%!error <matrix input must have 3 columns> cart2sph (ones (3,3,2))
-%!error <matrix input must have 3 columns> cart2sph ([1,2,3,4])
-%!error <numeric arrays of the same size> cart2sph ({1,2,3}, [1,2,3], [1,2,3])
-%!error <numeric arrays of the same size> cart2sph ([1,2,3], {1,2,3}, [1,2,3])
-%!error <numeric arrays of the same size> cart2sph ([1,2,3], [1,2,3], {1,2,3})
-%!error <numeric arrays of the same size> cart2sph (ones (3,3,3), 1, ones (3,2,3))
-%!error <numeric arrays of the same size> cart2sph (ones (3,3,3), ones (3,2,3), 1)
+%!error <matrix input C must be a 2-D numeric array> cart2sph ({1,2,3})
+%!error <matrix input C must be a 2-D numeric array> cart2sph (ones (3,3,2))
+%!error <matrix input C must be a 3-element> cart2sph ([1,2,3,4])
+%!error <matrix input C must be a 3-element> cart2sph ([1,2,3,4; 1,2,3,4; 1,2,3,4])
+%!error <must be numeric arrays or scalars> cart2sph ({1,2,3}, [1,2,3], [1,2,3])
+%!error <must be numeric arrays or scalars> cart2sph ([1,2,3], {1,2,3}, [1,2,3])
+%!error <must be numeric arrays or scalars> cart2sph ([1,2,3], [1,2,3], {1,2,3})
+%!error <must be the same size or scalars> cart2sph ([1,2,3], [1,2,3], [1,2,3]')
+%!error <must be the same size or scalars> cart2sph (ones (3,3,3), 1, ones (3,2,3))
+%!error <must be the same size or scalars> cart2sph (ones (3,3,3), ones (3,2,3), 1)

--- a/scripts/general/pol2cart.m	Sun Mar 22 19:23:03 2020 +0100
+++ b/scripts/general/pol2cart.m	Sun Feb 16 20:19:05 2020 -0500
@@ -28,21 +28,43 @@
 ## @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})).
+## represents the polar coordinate pair (@var{theta}, @var{r}) or the
+## cylindrical triplet (@var{theta}, @var{r}, @var{z}).
+##
+## The outputs @var{x}, @var{y} (, and @var{z}) 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.
+## @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)}.
+##
+## @var{z}, if present, is unchanged by the transformation.
+##
+## The coordinate transformation is computed using:
 ##
-## @var{r} is the distance to the z-axis (0, 0, z).
+## @tex
+## $$ x = r \cos \theta $$
+## $$ y = r \sin \theta $$
+## $$ z = z $$
+## @end tex
+## @ifnottex
 ##
-## 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})).
+## @example
+## @var{x} = @var{r} * cos (@var{theta})
+## @var{y} = @var{r} * sin (@var{theta})
+## @var{z} = @var{z}
+## @end example
+##
+## @end ifnottex
+## @c FIXME: Remove this note in Octave 9.1 (two releases after 7.1).
+## Note: For @sc{matlab} compatibility, this function no longer returns a full
+## coordinate matrix when called with a single return argument.
 ## @seealso{cart2pol, sph2cart, cart2sph}
 ## @end deftypefn
 
@@ -53,44 +75,55 @@
   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)]");
+    if (! (isnumeric (theta) && ismatrix (theta)))
+      error ("cart2pol: matrix input P must be 2-D numeric array");
     endif
-    if (columns (theta) == 3)
-      z = theta(:,3);
+    if (isvector (theta))
+      n = numel (theta);
+      if (n != 2 && n != 3)
+        error ("cart2pol: matrix input must be a 2- or 3-element vector or a 2- or 3-column array");
+      endif
+      if (n == 3)
+        z = theta(3);
+      endif
+      r = theta(2);
+      theta = theta(1);
+
+    else
+      ncols = columns(theta);
+      if (ncols != 2 && ncols != 3)
+        error ("cart2pol: matrix input must be a 2- or 3-element vector or a 2- or 3-column array");
+      endif
+
+      if (ncols == 3)
+        z = theta(:,3);
+      endif
+      r = theta(:,2);
+      theta = theta(:,1);
     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");
+    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 numeric arrays of the same size, or scalar");
+      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 of the same size, or scalar");
+    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 numeric arrays of the same size, or scalar");
+      error ("pol2cart: THETA, R, Z must be the same size or scalars");
     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
 
 
@@ -98,32 +131,42 @@
 %! 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));
+%! 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];
-%! C = pol2cart (t, r);
-%! assert (C(:,1), [0; 1; 2], sqrt (eps));
-%! assert (C(:,2), [0; 1; 2], sqrt (eps));
+%! [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], sqrt (eps));
-%! assert (y, [0, 1, 2], sqrt (eps));
+%! 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], sqrt (eps));
-%! assert (y, [0, 0, 0], sqrt (eps));
+%! assert (x, [0, 1, 2], eps);
+%! assert (y, [0, 0, 0], eps);
 %! assert (z2, z);
 
 %!test
@@ -146,13 +189,23 @@
 
 %!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));
+%! [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];
-%! C = [0, 0, 0; 1, 1, 1; 2, 2, 2];
-%! assert (pol2cart (P), C, sqrt (eps));
+%! [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);
@@ -182,15 +235,17 @@
 ## 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)
+%!error <matrix input P must be 2-D numeric array> pol2cart ({1,2,3})
+%!error <matrix input P must be 2-D numeric array> pol2cart (ones (3,3,2))
+%!error <matrix input must be a 2- or 3-element> pol2cart ([1])
+%!error <matrix input must be a 2- or 3-element> pol2cart ([1,2,3,4])
+%!error <must be numeric arrays or scalars> pol2cart ({1,2,3}, [1,2,3])
+%!error <must be numeric arrays or scalars> pol2cart ([1,2,3], {1,2,3})
+%!error <must be the same size or scalars> pol2cart (ones (3,3,3), ones (3,2,3))
+%!error <must be the same size or scalars> pol2cart ([1; 1], [2, 2])
+%!error <must be the same size or scalars> pol2cart ([1; 1], [2, 2], [3, 3])
+%!error <must be numeric arrays or scalars> pol2cart ({1,2,3}, [1,2,3], [1,2,3])
+%!error <must be numeric arrays or scalars> pol2cart ([1,2,3], {1,2,3}, [1,2,3])
+%!error <must be numeric arrays or scalars> pol2cart ([1,2,3], [1,2,3], {1,2,3})
+%!error <must be the same size or scalars> pol2cart (ones (3,3,3), 1, ones (3,2,3))
+%!error <must be the same size or scalars> pol2cart (ones (3,3,3), ones (3,2,3), 1)

--- a/scripts/general/sph2cart.m	Sun Mar 22 19:23:03 2020 +0100
+++ b/scripts/general/sph2cart.m	Sun Feb 16 20:19:05 2020 -0500
@@ -26,22 +26,43 @@
 ## -*- texinfo -*-
 ## @deftypefn  {} {[@var{x}, @var{y}, @var{z}] =} sph2cart (@var{theta}, @var{phi}, @var{r})
 ## @deftypefnx {} {[@var{x}, @var{y}, @var{z}] =} sph2cart (@var{S})
-## @deftypefnx {} {@var{C} =} sph2cart (@dots{})
 ## Transform spherical coordinates to Cartesian coordinates.
 ##
 ## The inputs @var{theta}, @var{phi}, and @var{r} must be the same shape, or
 ## scalar.  If called with a single matrix argument then each row of @var{S}
-## represents the spherical coordinate (@var{theta}, @var{phi}, @var{r}).
+## must represent a spherical coordinate triplet (@var{theta}, @var{phi},
+## @var{r}).
 ##
-## @var{theta} describes the angle relative to the positive x-axis.
+## The outputs @var{x}, @var{y}, @var{z} match the shape of the inputs.  For a
+## matrix input @var{S} the outputs are column vectors with rows corresponding
+## to the rows of the input matrix.
 ##
-## @var{phi} is the angle relative to the xy-plane.
+## @var{theta} describes the azimuth angle relative to the positive x-axis
+## measured in the xy-plane.
+##
+## @var{phi} is the elevation angle measured relative to the xy-plane.
 ##
 ## @var{r} is the distance to the origin @w{(0, 0, 0)}.
 ##
-## 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}).
+## The coordinate transformation is computed using:
+##
+## @tex
+## $$ x = r \cos \phi  \cos \theta $$
+## $$ y = r \cos \phi  \sin \theta $$
+## $$ z = r \sin \phi $$
+## @end tex
+## @ifnottex
+##
+## @example
+## @var{x} = r * cos (@var{phi}) * cos (@var{theta})
+## @var{y} = r * cos (@var{phi}) * sin (@var{theta})
+## @var{z} = r * sin (@var{phi})
+## @end example
+##
+## @end ifnottex
+## @c FIXME: Remove this note in Octave 9.1 (two releases after 7.1).
+## Note: For @sc{matlab} compatibility, this function no longer returns a full
+## coordinate matrix when called with a single return argument.
 ## @seealso{cart2sph, pol2cart, cart2pol}
 ## @end deftypefn
 
@@ -52,19 +73,30 @@
   endif
 
   if (nargin == 1)
-    if (! (isnumeric (theta) && ismatrix (theta) && columns (theta) == 3))
-      error ("sph2cart: matrix input must have 3 columns [THETA, PHI, R]");
+    if (! (isnumeric (theta) && ismatrix (theta)))
+      error ("sph2cart: matrix input must be a 2-D numeric array");
+    endif
+    if (columns (theta) != 3 && numel (theta) != 3)
+      error ("sph2cart: matrix input must be a 3-element vector or 3-column array");
     endif
-    r = theta(:,3);
-    phi = theta(:,2);
-    theta = theta(:,1);
+
+    if (numel (theta) == 3)
+      r = theta(3);
+      phi = theta(2);
+      theta = theta(1);
+    else
+      r = theta(:,3);
+      phi = theta(:,2);
+      theta = theta(:,1);
+    endif
+
   else
-    if (! isnumeric (theta) || ! isnumeric (phi) || ! isnumeric (r))
-      error ("sph2cart: THETA, PHI, R must be numeric arrays of the same size, or scalar");
+    if (! (isnumeric (theta) && isnumeric (phi) && isnumeric (r)))
+      error ("sph2cart: THETA, PHI, R must be numeric arrays or scalars");
     endif
     [err, theta, phi, r] = common_size (theta, phi, r);
     if (err)
-      error ("sph2cart: THETA, PHI, R must be numeric arrays of the same size, or scalar");
+      error ("sph2cart: THETA, PHI, R must be the same size or scalars");
     endif
   endif
 
@@ -72,10 +104,6 @@
   y = r .* cos (phi) .* sin (theta);
   z = r .* sin (phi);
 
-  if (nargout <= 1)
-    x = [x(:), y(:), z(:)];
-  endif
-
 endfunction
 
 
@@ -89,13 +117,22 @@
 %! assert (z, [0, 0, 0]);
 
 %!test
+%! t = [0; 0; 0];
+%! p = [0; 0; 0];
+%! r = [0; 1; 2];
+%! [x, y, z] = sph2cart (t, p, r);
+%! assert (x, [0; 1; 2]);
+%! assert (y, [0; 0; 0]);
+%! assert (z, [0; 0; 0]);
+
+%!test
 %! t = 0;
 %! p = [0, 0, 0];
 %! r = [0, 1, 2];
-%! C = sph2cart (t, p, r);
-%! assert (C(:,1), r(:));
-%! assert (C(:,2), [0; 0; 0]);
-%! assert (C(:,3), [0; 0; 0]);
+%! [x, y, z] = sph2cart (t, p, r);
+%! assert (x, [0, 1, 2]);
+%! assert (y, [0, 0, 0]);
+%! assert (z, [0, 0, 0]);
 
 %!test
 %! t = [0, 0, 0];
@@ -123,8 +160,18 @@
 
 %!test
 %! S = [ 0, 0, 1; 0.5*pi, 0, 1; pi, 0, 1];
-%! C = [ 1, 0, 0; 0, 1, 0; -1, 0, 0];
-%! assert (sph2cart (S), C, eps);
+%! [x, y, z] = sph2cart (S);
+%! assert (x, [1; 0; -1], eps);
+%! assert (y, [0; 1; 0], eps);
+%! assert (z, [0; 0; 0], eps);
+
+%!test
+%! S = [ 0, 0, 1; 0.5*pi, 0, 1; pi, 0, 1; pi, pi, 1];
+%! [x, y, z] = sph2cart (S);
+%! assert (x, [1; 0; -1; 1], eps);
+%! assert (y, [0; 1; 0; 0], eps);
+%! assert (z, [0; 0; 0; 0], eps);
+
 
 %!test
 %! [t, p, r] = meshgrid ([0, pi/2], [0, pi/2], [0, 1]);
@@ -143,11 +190,13 @@
 %!error sph2cart ()
 %!error sph2cart (1,2)
 %!error sph2cart (1,2,3,4)
-%!error <matrix input must have 3 columns> sph2cart ({1,2,3})
-%!error <matrix input must have 3 columns> sph2cart (ones (3,3,2))
-%!error <matrix input must have 3 columns> sph2cart ([1,2,3,4])
-%!error <numeric arrays of the same size> sph2cart ({1,2,3}, [1,2,3], [1,2,3])
-%!error <numeric arrays of the same size> sph2cart ([1,2,3], {1,2,3}, [1,2,3])
-%!error <numeric arrays of the same size> sph2cart ([1,2,3], [1,2,3], {1,2,3})
-%!error <numeric arrays of the same size> sph2cart (ones (3,3,3), 1, ones (3,2,3))
-%!error <numeric arrays of the same size> sph2cart (ones (3,3,3), ones (3,2,3), 1)
+%!error <matrix input must be a 2-D numeric array> sph2cart ({1,2,3})
+%!error <matrix input must be a 2-D numeric array> sph2cart (ones (3,3,2))
+%!error <matrix input must be a 3-element> sph2cart ([1,2,3,4])
+%!error <matrix input must be a 3-element> sph2cart ([1,2,3,4; 1,2,3,4; 1,2,3,4])
+%!error <must be numeric arrays or scalars> sph2cart ({1,2,3}, [1,2,3], [1,2,3])
+%!error <must be numeric arrays or scalars> sph2cart ([1,2,3], {1,2,3}, [1,2,3])
+%!error <must be numeric arrays or scalars> sph2cart ([1,2,3], [1,2,3], {1,2,3})
+%!error <must be the same size or scalars> sph2cart ([1,2,3], [1,2,3], [1,2,3]')
+%!error <must be the same size or scalars> sph2cart (ones (3,3,3), 1, ones (3,2,3))
+%!error <must be the same size or scalars> sph2cart (ones (3,3,3), ones (3,2,3), 1)

--- a/scripts/plot/draw/lightangle.m	Sun Mar 22 19:23:03 2020 +0100
+++ b/scripts/plot/draw/lightangle.m	Sun Feb 16 20:19:05 2020 -0500
@@ -122,7 +122,7 @@
     pos -= get (hax, "CameraTarget");
   endif
 
-  pos = sph2cart (az, el, norm (pos));
+  [pos(1), pos(2), pos(3)] = sph2cart (az, el, norm (pos));
 
   if (strcmp (get (hl, "Style"), "local"))
     pos += get (hax, "CameraTarget");

--- a/scripts/plot/draw/surfl.m	Sun Mar 22 19:23:03 2020 +0100
+++ b/scripts/plot/draw/surfl.m	Sun Feb 16 20:19:05 2020 -0500
@@ -156,7 +156,7 @@
 
     ## Get view vector (vv).
     [az, el] = view ();
-    vv = sph2cart ((az - 90) * pi/180.0, el * pi/180.0, 1.0);
+    [vv(1), vv(2), vv(3)] = sph2cart ((az - 90) * pi/180.0, el * pi/180.0, 1.0);
 
     if (! have_lv)
       ## Calculate light vector (lv) from view vector.