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surfnorm.m: Overhaul for Matlab compatibility. * surfnorm.m: Redo docstring. Use better input validation and accept optional property/value pairs for surface object. Fix incorrect meshgrid call reversing x and y. Color the surface normals red for compatibility with Matlab. Use in-place division operation for better performance. Add tests for input validation.
author Rik <rik@octave.org>
date Sun, 20 Jul 2014 13:26:10 -0700
parents d63878346099
children
comparison
equal deleted inserted replaced
18943:714ce8ca71ea 18947:91f626902d17
17 ## <http://www.gnu.org/licenses/>. 17 ## <http://www.gnu.org/licenses/>.
18 18
19 ## -*- texinfo -*- 19 ## -*- texinfo -*-
20 ## @deftypefn {Function File} {} surfnorm (@var{x}, @var{y}, @var{z}) 20 ## @deftypefn {Function File} {} surfnorm (@var{x}, @var{y}, @var{z})
21 ## @deftypefnx {Function File} {} surfnorm (@var{z}) 21 ## @deftypefnx {Function File} {} surfnorm (@var{z})
22 ## @deftypefnx {Function File} {} surfnorm (@dots{}, @var{prop}, @var{val}, @dots{})
23 ## @deftypefnx {Function File} {} surfnorm (@var{hax}, @dots{})
22 ## @deftypefnx {Function File} {[@var{nx}, @var{ny}, @var{nz}] =} surfnorm (@dots{}) 24 ## @deftypefnx {Function File} {[@var{nx}, @var{ny}, @var{nz}] =} surfnorm (@dots{})
23 ## @deftypefnx {Function File} {} surfnorm (@var{h}, @dots{}) 25 ## Find the vectors normal to a meshgridded surface.
24 ## Find the vectors normal to a meshgridded surface. The meshed gridded 26 ##
25 ## surface is defined by @var{x}, @var{y}, and @var{z}. If @var{x} and 27 ## If @var{x} and @var{y} are vectors, then a typical vertex is
26 ## @var{y} are not defined, then it is assumed that they are given by 28 ## (@var{x}(j), @var{y}(i), @var{z}(i,j)). Thus, columns of @var{z} correspond
29 ## to different @var{x} values and rows of @var{z} correspond to different
30 ## @var{y} values. If only a single input @var{z} is given then @var{x} is
31 ## taken to be @code{1:rows (@var{z})} and @var{y} is
32 ## @code{1:columns (@var{z})}.
33 ##
34 ## If no return arguments are requested, a surface plot with the normal
35 ## vectors to the surface is plotted.
36 ##
37 ## Any property/value input pairs are assigned to the surface object.
38 ##
39 ## If the first argument @var{hax} is an axes handle, then plot into this axis,
40 ## rather than the current axes returned by @code{gca}.
41 ##
42 ## If output arguments are requested then the components of the normal
43 ## vectors are returne in @var{nx}, @var{ny}, and @var{nz} and no plot is
44 ## made.
45 ##
46 ## An example of the use of @code{surfnorm} is
27 ## 47 ##
28 ## @example 48 ## @example
29 ## @group 49 ## surfnorm (peaks (25));
30 ## [@var{x}, @var{y}] = meshgrid (1:rows (@var{z}),
31 ## 1:columns (@var{z}));
32 ## @end group
33 ## @end example 50 ## @end example
34 ## 51 ##
35 ## If no return arguments are requested, a surface plot with the normal 52 ## Algorithm: The normal vectors are calculated by taking the cross product
36 ## vectors to the surface is plotted. Otherwise the components of the normal 53 ## of the diagonals of each of the quadrilaterals in the meshgrid to find the
37 ## vectors at the mesh gridded points are returned in @var{nx}, @var{ny},
38 ## and @var{nz}.
39 ##
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 54 ## normal vectors of the centers of these quadrilaterals. The four nearest
43 ## normal vectors to the meshgrid points are then averaged to obtain the 55 ## normal vectors to the meshgrid points are then averaged to obtain the
44 ## normal to the surface at the meshgridded points. 56 ## normal to the surface at the meshgridded points.
45 ## 57 ##
46 ## An example of the use of @code{surfnorm} is 58 ## @seealso{isonormals, quiver3, surf, meshgrid}
47 ##
48 ## @example
49 ## surfnorm (peaks (25));
50 ## @end example
51 ## @seealso{surf, quiver3}
52 ## @end deftypefn 59 ## @end deftypefn
53 60
54 function [Nx, Ny, Nz] = surfnorm (varargin) 61 function [Nx, Ny, Nz] = surfnorm (varargin)
55 62
56 [hax, varargin, nargin] = __plt_get_axis_arg__ ("surfnorm", varargin{:}); 63 [hax, varargin, nargin] = __plt_get_axis_arg__ ("surfnorm", varargin{:});
57 64
58 if (nargin != 1 && nargin != 3) 65 if (nargin == 0 || nargin == 2)
59 print_usage (); 66 print_usage ();
60 endif 67 endif
61 68
62 if (nargin == 1) 69 if (nargin == 1)
63 z = varargin{1}; 70 z = varargin{1};
64 [x, y] = meshgrid (1:rows (z), 1:columns (z)); 71 [x, y] = meshgrid (1:columns (z), 1:rows (z));
65 ioff = 2; 72 ioff = 2;
66 else 73 else
67 x = varargin{1}; 74 x = varargin{1};
68 y = varargin{2}; 75 y = varargin{2};
69 z = varargin{3}; 76 z = varargin{3};
70 ioff = 4; 77 ioff = 4;
71 endif 78 endif
72 79
73 if (!ismatrix (z) || isvector (z) || isscalar (z)) 80 if (iscomplex (z) || iscomplex (x) || iscomplex (y))
74 error ("surfnorm: Z argument must be a matrix"); 81 error ("surfnorm: X, Y, and Z must be 2-D real matrices");
75 endif 82 endif
76 if (! size_equal (x, y, z)) 83 if (! size_equal (x, y, z))
77 error ("surfnorm: X, Y, and Z must have the same dimensions"); 84 error ("surfnorm: X, Y, and Z must have the same dimensions");
78 endif 85 endif
79 86
80 ## Make life easier, and avoid having to do the extrapolation later, do 87 ## Do a linear extrapolation for mesh points on the boundary so that the mesh
81 ## a simpler linear extrapolation here. This is approximative, and works 88 ## is increased by 1 on each side. This allows each original meshgrid point
82 ## badly for closed surfaces like spheres. 89 ## to be surrounded by four quadrilaterals and the same calculation can be
83 xx = [2 .* x(:,1) - x(:,2), x, 2 .* x(:,end) - x(:,end-1)]; 90 ## used for interior and boundary points. The extrapolation works badly for
84 xx = [2 .* xx(1,:) - xx(2,:); xx; 2 .* xx(end,:) - xx(end-1,:)]; 91 ## closed surfaces like spheres.
85 yy = [2 .* y(:,1) - y(:,2), y, 2 .* y(:,end) - y(:,end-1)]; 92 xx = [2 * x(:,1) - x(:,2), x, 2 * x(:,end) - x(:,end-1)];
86 yy = [2 .* yy(1,:) - yy(2,:); yy; 2 .* yy(end,:) - yy(end-1,:)]; 93 xx = [2 * xx(1,:) - xx(2,:); xx; 2 * xx(end,:) - xx(end-1,:)];
87 zz = [2 .* z(:,1) - z(:,2), z, 2 .* z(:,end) - z(:,end-1)]; 94 yy = [2 * y(:,1) - y(:,2), y, 2 * y(:,end) - y(:,end-1)];
88 zz = [2 .* zz(1,:) - zz(2,:); zz; 2 .* zz(end,:) - zz(end-1,:)]; 95 yy = [2 * yy(1,:) - yy(2,:); yy; 2 * yy(end,:) - yy(end-1,:)];
96 zz = [2 * z(:,1) - z(:,2), z, 2 * z(:,end) - z(:,end-1)];
97 zz = [2 * zz(1,:) - zz(2,:); zz; 2 * zz(end,:) - zz(end-1,:)];
89 98
90 u.x = xx(1:end-1,1:end-1) - xx(2:end,2:end); 99 u.x = xx(1:end-1,1:end-1) - xx(2:end,2:end);
91 u.y = yy(1:end-1,1:end-1) - yy(2:end,2:end); 100 u.y = yy(1:end-1,1:end-1) - yy(2:end,2:end);
92 u.z = zz(1:end-1,1:end-1) - zz(2:end,2:end); 101 u.z = zz(1:end-1,1:end-1) - zz(2:end,2:end);
93 v.x = xx(1:end-1,2:end) - xx(2:end,1:end-1); 102 v.x = xx(1:end-1,2:end) - xx(2:end,1:end-1);
99 w.y = reshape (c(:,2), size (u.y)); 108 w.y = reshape (c(:,2), size (u.y));
100 w.z = reshape (c(:,3), size (u.z)); 109 w.z = reshape (c(:,3), size (u.z));
101 110
102 ## Create normal vectors as mesh vectices from normals at mesh centers 111 ## Create normal vectors as mesh vectices from normals at mesh centers
103 nx = (w.x(1:end-1,1:end-1) + w.x(1:end-1,2:end) + 112 nx = (w.x(1:end-1,1:end-1) + w.x(1:end-1,2:end) +
104 w.x(2:end,1:end-1) + w.x(2:end,2:end)) ./ 4; 113 w.x(2:end,1:end-1) + w.x(2:end,2:end)) / 4;
105 ny = (w.y(1:end-1,1:end-1) + w.y(1:end-1,2:end) + 114 ny = (w.y(1:end-1,1:end-1) + w.y(1:end-1,2:end) +
106 w.y(2:end,1:end-1) + w.y(2:end,2:end)) ./ 4; 115 w.y(2:end,1:end-1) + w.y(2:end,2:end)) / 4;
107 nz = (w.z(1:end-1,1:end-1) + w.z(1:end-1,2:end) + 116 nz = (w.z(1:end-1,1:end-1) + w.z(1:end-1,2:end) +
108 w.z(2:end,1:end-1) + w.z(2:end,2:end)) ./ 4; 117 w.z(2:end,1:end-1) + w.z(2:end,2:end)) / 4;
109 118
119 ## FIXME: According to Matlab documentation the vertex normals
120 ## returned are not normalized.
110 ## Normalize the normal vectors 121 ## Normalize the normal vectors
111 len = sqrt (nx.^2 + ny.^2 + nz.^2); 122 len = sqrt (nx.^2 + ny.^2 + nz.^2);
112 nx = nx ./ len; 123 nx ./= len;
113 ny = ny ./ len; 124 ny ./= len;
114 nz = nz ./ len; 125 nz ./= len;
115 126
116 if (nargout == 0) 127 if (nargout == 0)
117 oldfig = []; 128 oldfig = [];
118 if (! isempty (hax)) 129 if (! isempty (hax))
119 oldfig = get (0, "currentfigure"); 130 oldfig = get (0, "currentfigure");
123 134
124 surf (x, y, z, varargin{ioff:end}); 135 surf (x, y, z, varargin{ioff:end});
125 old_hold_state = get (hax, "nextplot"); 136 old_hold_state = get (hax, "nextplot");
126 unwind_protect 137 unwind_protect
127 set (hax, "nextplot", "add"); 138 set (hax, "nextplot", "add");
128 plot3 ([x(:)'; x(:).' + nx(:).' ; NaN(size(x(:).'))](:), 139
129 [y(:)'; y(:).' + ny(:).' ; NaN(size(y(:).'))](:), 140 ## FIXME: Scale unit normals by data aspect ratio in order for
130 [z(:)'; z(:).' + nz(:).' ; NaN(size(z(:).'))](:), 141 ## normals to appear correct.
131 varargin{ioff:end}); 142 ##daratio = daspect (hax);
143 ##daspect ("manual");
144 ##len = norm (daratio);
145 ## This assumes an even meshgrid which isn't a great assumption
146 ##dx = x(1,2) - x(1,1);
147 ##dy = y(2,1) - y(1,1);
148 ##nx *= daratio(1);
149 ##ny *= daratio(2);
150 ##nz *= daratio(3);
151 ##len = sqrt (nx.^2 + ny.^2 + nz.^2);
152 ##nx ./= len;
153 ##ny ./= len;
154 ##nz ./= len;
155 plot3 ([x(:).'; x(:).' + nx(:).' ; NaN(size(x(:).'))](:),
156 [y(:).'; y(:).' + ny(:).' ; NaN(size(y(:).'))](:),
157 [z(:).'; z(:).' + nz(:).' ; NaN(size(z(:).'))](:),
158 "r");
132 unwind_protect_cleanup 159 unwind_protect_cleanup
133 set (hax, "nextplot", old_hold_state); 160 set (hax, "nextplot", old_hold_state);
134 end_unwind_protect 161 end_unwind_protect
135 162
136 unwind_protect_cleanup 163 unwind_protect_cleanup
148 175
149 176
150 %!demo 177 %!demo
151 %! clf; 178 %! clf;
152 %! colormap ('default'); 179 %! colormap ('default');
153 %! [x, y, z] = peaks (10); 180 %! surfnorm (peaks (32));
154 %! surfnorm (x, y, z); 181 %! shading interp;
182 %! title ({'surfnorm() shows surface and normals at each vertex', ...
183 %! 'peaks() function with 32 faces'});
155 184
156 %!demo 185 %!demo
157 %! clf; 186 %! clf;
158 %! colormap ('default'); 187 %! colormap ('default');
159 %! surfnorm (peaks (10)); 188 %! [x, y, z] = sombrero (10);
160 189 %! surfnorm (x, y, z);
161 %!demo 190
162 %! clf; 191 %% Test input validation
163 %! colormap ('default'); 192 %!error surfnorm ()
164 %! surfnorm (peaks (32)); 193 %!error surfnorm (1,2)
165 %! shading interp; 194 %!error <X, Y, and Z must be 2-D real matrices> surfnorm (i)
166 195 %!error <X, Y, and Z must be 2-D real matrices> surfnorm (i, 1, 1)
196 %!error <X, Y, and Z must be 2-D real matrices> surfnorm (1, i, 1)
197 %!error <X, Y, and Z must be 2-D real matrices> surfnorm (1, 1, i)
198 %!error <X, Y, and Z must have the same dimensions> surfnorm ([1 2], 1, 1)
199 %!error <X, Y, and Z must have the same dimensions> surfnorm (1, [1 2], 1)
200 %!error <X, Y, and Z must have the same dimensions> surfnorm (1, 1, [1 2])
201