1 ## Copyright (C) 2007-2012 David Bateman
3 ## This file is part of Octave.
5 ## Octave is free software; you can redistribute it and/or modify it
6 ## under the terms of the GNU General Public License as published by
7 ## the Free Software Foundation; either version 3 of the License, or (at
8 ## your option) any later version.
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 ## General Public License for more details.
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16 ## along with Octave; see the file COPYING. If not, see
17 ## <http://www.gnu.org/licenses/>.
20 ## @deftypefn {Function File} {} surfnorm (@var{x}, @var{y}, @var{z})
21 ## @deftypefnx {Function File} {} surfnorm (@var{z})
22 ## @deftypefnx {Function File} {[@var{nx}, @var{ny}, @var{nz}] =} surfnorm (@dots{})
23 ## @deftypefnx {Function File} {} surfnorm (@var{h}, @dots{})
24 ## Find the vectors normal to a meshgridded surface. The meshed gridded
25 ## surface is defined by @var{x}, @var{y}, and @var{z}. If @var{x} and
26 ## @var{y} are not defined, then it is assumed that they are given by
30 ## [@var{x}, @var{y}] = meshgrid (1:size (@var{z}, 1),
31 ## 1:size (@var{z}, 2));
35 ## If no return arguments are requested, a surface plot with the normal
36 ## vectors to the surface is plotted. Otherwise the components of the normal
37 ## vectors at the mesh gridded points are returned in @var{nx}, @var{ny},
40 ## The normal vectors are calculated by taking the cross product of the
41 ## diagonals of each of the quadrilaterals in the meshgrid to find the
42 ## normal vectors of the centers of these quadrilaterals. The four nearest
43 ## normal vectors to the meshgrid points are then averaged to obtain the
44 ## normal to the surface at the meshgridded points.
46 ## An example of the use of @code{surfnorm} is
49 ## surfnorm (peaks (25));
51 ## @seealso{surf, quiver3}
54 function [Nx, Ny, Nz] = surfnorm (varargin)
56 [h, varargin, nargin] = __plt_get_axis_arg__ ((nargout != 0), "surfnorm",
59 if (nargin != 1 && nargin != 3)
65 [x, y] = meshgrid (1:size(z,1), 1:size(z,2));
74 if (!ismatrix (z) || isvector (z) || isscalar (z))
75 error ("surfnorm: Z argument must be a matrix");
77 if (! size_equal (x, y, z))
78 error ("surfnorm: X, Y, and Z must have the same dimensions");
81 ## Make life easier, and avoid having to do the extrapolation later, do
82 ## a simpler linear extrapolation here. This is approximative, and works
83 ## badly for closed surfaces like spheres.
84 xx = [2 .* x(:,1) - x(:,2), x, 2 .* x(:,end) - x(:,end-1)];
85 xx = [2 .* xx(1,:) - xx(2,:); xx; 2 .* xx(end,:) - xx(end-1,:)];
86 yy = [2 .* y(:,1) - y(:,2), y, 2 .* y(:,end) - y(:,end-1)];
87 yy = [2 .* yy(1,:) - yy(2,:); yy; 2 .* yy(end,:) - yy(end-1,:)];
88 zz = [2 .* z(:,1) - z(:,2), z, 2 .* z(:,end) - z(:,end-1)];
89 zz = [2 .* zz(1,:) - zz(2,:); zz; 2 .* zz(end,:) - zz(end-1,:)];
91 u.x = xx(1:end-1,1:end-1) - xx(2:end,2:end);
92 u.y = yy(1:end-1,1:end-1) - yy(2:end,2:end);
93 u.z = zz(1:end-1,1:end-1) - zz(2:end,2:end);
94 v.x = xx(1:end-1,2:end) - xx(2:end,1:end-1);
95 v.y = yy(1:end-1,2:end) - yy(2:end,1:end-1);
96 v.z = zz(1:end-1,2:end) - zz(2:end,1:end-1);
98 c = cross ([u.x(:), u.y(:), u.z(:)], [v.x(:), v.y(:), v.z(:)]);
99 w.x = reshape (c(:,1), size(u.x));
100 w.y = reshape (c(:,2), size(u.y));
101 w.z = reshape (c(:,3), size(u.z));
103 ## Create normal vectors as mesh vectices from normals at mesh centers
104 nx = (w.x(1:end-1,1:end-1) + w.x(1:end-1,2:end) +
105 w.x(2:end,1:end-1) + w.x(2:end,2:end)) ./ 4;
106 ny = (w.y(1:end-1,1:end-1) + w.y(1:end-1,2:end) +
107 w.y(2:end,1:end-1) + w.y(2:end,2:end)) ./ 4;
108 nz = (w.z(1:end-1,1:end-1) + w.z(1:end-1,2:end) +
109 w.z(2:end,1:end-1) + w.z(2:end,2:end)) ./ 4;
111 ## Normalize the normal vectors
112 len = sqrt (nx.^2 + ny.^2 + nz.^2);
122 surf (x, y, z, varargin{ioff:end});
123 old_hold_state = get (h, "nextplot");
125 set (h, "nextplot", "add");
126 plot3 ([x(:)'; x(:).' + nx(:).' ; NaN(size(x(:).'))](:),
127 [y(:)'; y(:).' + ny(:).' ; NaN(size(y(:).'))](:),
128 [z(:)'; z(:).' + nz(:).' ; NaN(size(z(:).'))](:),
130 unwind_protect_cleanup
131 set (h, "nextplot", old_hold_state);
133 unwind_protect_cleanup
146 %! colormap (jet (64))
147 %! [x, y, z] = peaks(10);
148 %! surfnorm (x, y, z);
152 %! surfnorm (peaks(10));
156 %! surfnorm (peaks(32));