Mercurial > octave-nkf

comparison scripts/plot/surfnorm.m @ 7189:e8d953d03f6a

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
[project @ 2007-11-26 20:42:09 by dbateman]
author dbateman
date Mon, 26 Nov 2007 20:42:11 +0000
parents
children b48a21816f2e
comparison
equal deleted inserted replaced
7188:fdd7cd70dc14 7189:e8d953d03f6a
1 ## Copyright (C) 2007 David Bateman
2 ##
3 ## This file is part of Octave.
4 ##
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.
9 ##
10 ## Octave is distributed in the hope that it will be useful, but
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 ## General Public License for more details.
14 ##
15 ## You should have received a copy of the GNU General Public License
16 ## along with Octave; see the file COPYING. If not, see
17 ## <http://www.gnu.org/licenses/>.
18
19 ## -*- texinfo -*-
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
27 ##
28 ## @example
29 ## [@var{x}, @var{y}] = meshgrid (1:size(@var{z}, 1),
30 ## 1:size(@var{z}, 2));
31 ## @end example
32 ##
33 ## If no return arguments are requested, a surface plot with the normal
34 ## vectors to the surface is plotted. Otherwise the componets of the normal
35 ## vectors at the mesh gridded points are returned in @var{nx}, @var{ny},
36 ## and @var{nz}.
37 ##
38 ## The normal vectors are calculated by taking the cross product of the
39 ## diagonals of eash of teh quadrilaterals in the meshgrid to find the
40 ## normal vectors of the centers of these quadrilaterals. The four nearest
41 ## normal vectors to the meshgrid points are then averaged to obtain the
42 ## normal to the surface at the meshgridded points.
43 ##
44 ## An example of the use of @code{surfnorm} is
45 ##
46 ## @example
47 ## surfnorm (peaks (25));
48 ## @end example
49 ## @seealso{surf, quiver3}
50 ## @end deftypefn
51
52 function varargout = surfnorm (varargin)
53
54 if (nargout > 0)
55 varargout = cell (nargout, 1);
56 else
57 varargout = cell (0, 0);
58 endif
59 if (isscalar (varargin{1}) && ishandle (varargin{1}))
60 h = varargin {1};
61 if (! strcmp (get (h, "type"), "axes"))
62 error ("surfnorm: expecting first argument to be an axes object");
63 endif
64 if (nargin != 2 && nargin != 4)
65 print_usage ();
66 endif
67 oldh = gca ();
68 unwind_protect
69 axes (h);
70 [varargout{:}] = __surfnorm__ (h, varargin{2:end});
71 unwind_protect_cleanup
72 axes (oldh);
73 end_unwind_protect
74 else
75 if (nargin != 1 && nargin != 3)
76 print_usage ();
77 endif
78 [varargout{:}] = __surfnorm__ (gca (), varargin{:});
79 endif
80
81 endfunction
82
83 function [Nx, Ny, Nz] = __surfnorm__ (h, varargin)
84
85 if (nargin == 2)
86 z = varargin{1};
87 [x, y] = meshgrid (1:size(z,1), 1:size(z,2));
88 ioff = 2;
89 else
90 x = varargin{1};
91 y = varargin{2};
92 z = varargin{3};
93 ioff = 4;
94 endif
95
96 if (nargout == 0)
97 newplot();
98 surf (x, y, z, varargin{ioff:end});
99 hold on;
100 endif
101
102 ## Make life easier, and avoid having to do the extrapolation later, do
103 ## a simpler linear extrapolation here. This is approximative, and works
104 ## badly for closed surfaces like spheres.
105 xx = [2 .* x(:,1) - x(:,2), x, 2 .* x(:,end) - x(:,end-1)];
106 xx = [2 .* xx(1,:) - xx(2,:); xx; 2 .* xx(end,:) - xx(end-1,:)];
107 yy = [2 .* y(:,1) - y(:,2), y, 2 .* y(:,end) - y(:,end-1)];
108 yy = [2 .* yy(1,:) - yy(2,:); yy; 2 .* yy(end,:) - yy(end-1,:)];
109 zz = [2 .* z(:,1) - z(:,2), z, 2 .* z(:,end) - z(:,end-1)];
110 zz = [2 .* zz(1,:) - zz(2,:); zz; 2 .* zz(end,:) - zz(end-1,:)];
111
112 u.x = xx(1:end-1,1:end-1) - xx(2:end,2:end);
113 u.y = yy(1:end-1,1:end-1) - yy(2:end,2:end);
114 u.z = zz(1:end-1,1:end-1) - zz(2:end,2:end);
115 v.x = xx(1:end-1,2:end) - xx(2:end,1:end-1);
116 v.y = yy(1:end-1,2:end) - yy(2:end,1:end-1);
117 v.z = zz(1:end-1,2:end) - zz(2:end,1:end-1);
118
119 c = cross ([u.x(:), u.y(:), u.z(:)], [v.x(:), v.y(:), v.z(:)]);
120 w.x = reshape (c(:,1), size(u.x));
121 w.y = reshape (c(:,2), size(u.y));
122 w.z = reshape (c(:,3), size(u.z));
123
124 ## Create normal vectors as mesh vectices from normals at mesh centers
125 nx = (w.x(1:end-1,1:end-1) + w.x(1:end-1,2:end) +
126 w.x(2:end,1:end-1) + w.x(2:end,2:end)) ./ 4;
127 ny = (w.y(1:end-1,1:end-1) + w.y(1:end-1,2:end) +
128 w.y(2:end,1:end-1) + w.y(2:end,2:end)) ./ 4;
129 nz = (w.z(1:end-1,1:end-1) + w.z(1:end-1,2:end) +
130 w.z(2:end,1:end-1) + w.z(2:end,2:end)) ./ 4;
131
132 ## Normalize the normal vectors
133 len = sqrt (nx.^2 + ny.^2 + nz.^2);
134 nx = nx ./ len;
135 ny = ny ./ len;
136 nz = nz ./ len;
137
138 if (nargout == 0)
139 plot3 ([x(:)'; x(:).' + nx(:).' ; NaN(size(x(:).'))](:),
140 [y(:)'; y(:).' + ny(:).' ; NaN(size(y(:).'))](:),
141 [z(:)'; z(:).' + nz(:).' ; NaN(size(z(:).'))](:),
142 varargin{ioff:end});
143 else
144 Nx = nx;
145 Ny = ny;
146 Nz = nz;
147 endif
148 endfunction
149
150 %!demo
151 %! [x, y, z] = peaks(10);
152 %! surfnorm (x, y, z);
153
154 %!demo
155 %! surfnorm (peaks(10));