--- /dev/null
+## Copyright (C) 2007-2012 David Bateman
+##
+## This file is part of Octave.
+##
+## Octave is free software; you can redistribute it and/or modify it
+## under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or (at
+## your option) any later version.
+##
+## Octave is distributed in the hope that it will be useful, but
+## WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+## General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with Octave; see the file COPYING. If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} surfnorm (@var{x}, @var{y}, @var{z})
+## @deftypefnx {Function File} {} surfnorm (@var{z})
+## @deftypefnx {Function File} {[@var{nx}, @var{ny}, @var{nz}] =} surfnorm (@dots{})
+## @deftypefnx {Function File} {} surfnorm (@var{h}, @dots{})
+## Find the vectors normal to a meshgridded surface. The meshed gridded
+## surface is defined by @var{x}, @var{y}, and @var{z}. If @var{x} and
+## @var{y} are not defined, then it is assumed that they are given by
+##
+## @example
+## @group
+## [@var{x}, @var{y}] = meshgrid (1:size (@var{z}, 1),
+## 1:size (@var{z}, 2));
+## @end group
+## @end example
+##
+## If no return arguments are requested, a surface plot with the normal
+## vectors to the surface is plotted. Otherwise the components of the normal
+## vectors at the mesh gridded points are returned in @var{nx}, @var{ny},
+## and @var{nz}.
+##
+## The normal vectors are calculated by taking the cross product of the
+## diagonals of each of the quadrilaterals in the meshgrid to find the
+## normal vectors of the centers of these quadrilaterals. The four nearest
+## normal vectors to the meshgrid points are then averaged to obtain the
+## normal to the surface at the meshgridded points.
+##
+## An example of the use of @code{surfnorm} is
+##
+## @example
+## surfnorm (peaks (25));
+## @end example
+## @seealso{surf, quiver3}
+## @end deftypefn
+
+function [Nx, Ny, Nz] = surfnorm (varargin)
+
+ [h, varargin, nargin] = __plt_get_axis_arg__ ((nargout != 0), "surfnorm",
+ varargin{:});
+
+ if (nargin != 1 && nargin != 3)
+ print_usage ();
+ endif
+
+ if (nargin == 1)
+ z = varargin{1};
+ [x, y] = meshgrid (1:size(z,1), 1:size(z,2));
+ ioff = 2;
+ else
+ x = varargin{1};
+ y = varargin{2};
+ z = varargin{3};
+ ioff = 4;
+ endif
+
+ if (!ismatrix (z) || isvector (z) || isscalar (z))
+ error ("surfnorm: Z argument must be a matrix");
+ endif
+ if (! size_equal (x, y, z))
+ error ("surfnorm: X, Y, and Z must have the same dimensions");
+ endif
+
+ ## Make life easier, and avoid having to do the extrapolation later, do
+ ## a simpler linear extrapolation here. This is approximative, and works
+ ## badly for closed surfaces like spheres.
+ xx = [2 .* x(:,1) - x(:,2), x, 2 .* x(:,end) - x(:,end-1)];
+ xx = [2 .* xx(1,:) - xx(2,:); xx; 2 .* xx(end,:) - xx(end-1,:)];
+ yy = [2 .* y(:,1) - y(:,2), y, 2 .* y(:,end) - y(:,end-1)];
+ yy = [2 .* yy(1,:) - yy(2,:); yy; 2 .* yy(end,:) - yy(end-1,:)];
+ zz = [2 .* z(:,1) - z(:,2), z, 2 .* z(:,end) - z(:,end-1)];
+ zz = [2 .* zz(1,:) - zz(2,:); zz; 2 .* zz(end,:) - zz(end-1,:)];
+
+ u.x = xx(1:end-1,1:end-1) - xx(2:end,2:end);
+ u.y = yy(1:end-1,1:end-1) - yy(2:end,2:end);
+ u.z = zz(1:end-1,1:end-1) - zz(2:end,2:end);
+ v.x = xx(1:end-1,2:end) - xx(2:end,1:end-1);
+ v.y = yy(1:end-1,2:end) - yy(2:end,1:end-1);
+ v.z = zz(1:end-1,2:end) - zz(2:end,1:end-1);
+
+ c = cross ([u.x(:), u.y(:), u.z(:)], [v.x(:), v.y(:), v.z(:)]);
+ w.x = reshape (c(:,1), size(u.x));
+ w.y = reshape (c(:,2), size(u.y));
+ w.z = reshape (c(:,3), size(u.z));
+
+ ## Create normal vectors as mesh vectices from normals at mesh centers
+ nx = (w.x(1:end-1,1:end-1) + w.x(1:end-1,2:end) +
+ w.x(2:end,1:end-1) + w.x(2:end,2:end)) ./ 4;
+ ny = (w.y(1:end-1,1:end-1) + w.y(1:end-1,2:end) +
+ w.y(2:end,1:end-1) + w.y(2:end,2:end)) ./ 4;
+ nz = (w.z(1:end-1,1:end-1) + w.z(1:end-1,2:end) +
+ w.z(2:end,1:end-1) + w.z(2:end,2:end)) ./ 4;
+
+ ## Normalize the normal vectors
+ len = sqrt (nx.^2 + ny.^2 + nz.^2);
+ nx = nx ./ len;
+ ny = ny ./ len;
+ nz = nz ./ len;
+
+ if (nargout == 0)
+ oldh = gca ();
+ unwind_protect
+ axes (h);
+ newplot ();
+ surf (x, y, z, varargin{ioff:end});
+ old_hold_state = get (h, "nextplot");
+ unwind_protect
+ set (h, "nextplot", "add");
+ plot3 ([x(:)'; x(:).' + nx(:).' ; NaN(size(x(:).'))](:),
+ [y(:)'; y(:).' + ny(:).' ; NaN(size(y(:).'))](:),
+ [z(:)'; z(:).' + nz(:).' ; NaN(size(z(:).'))](:),
+ varargin{ioff:end});
+ unwind_protect_cleanup
+ set (h, "nextplot", old_hold_state);
+ end_unwind_protect
+ unwind_protect_cleanup
+ axes (oldh);
+ end_unwind_protect
+ else
+ Nx = nx;
+ Ny = ny;
+ Nz = nz;
+ endif
+
+endfunction
+
+%!demo
+%! clf
+%! colormap (jet (64))
+%! [x, y, z] = peaks(10);
+%! surfnorm (x, y, z);
+
+%!demo
+%! clf
+%! surfnorm (peaks(10));
+
+%!demo
+%! clf
+%! surfnorm (peaks(32));
+%! shading interp
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff