Mercurial > hg > octave-lyh
annotate scripts/plot/surfnorm.m @ 9042:97aa01a85ea4
Merge documentation cleanup changes to main branch.
| author | Rik <rdrider0-list@yahoo.com> |
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| date | Wed, 25 Mar 2009 18:13:08 -0700 |
| parents | dbd0c77e575e |
| children | 1bf0ce0930be |
| rev | line source |
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| 8920 | 1 ## Copyright (C) 2007, 2008, 2009 David Bateman |
| 7189 | 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{}) | |
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24 ## Find the vectors normal to a meshgridded surface. The meshed gridded |
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25 ## surface is defined by @var{x}, @var{y}, and @var{z}. If @var{x} and |
| 7189 | 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 | |
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34 ## vectors to the surface is plotted. Otherwise the components of the normal |
| 7189 | 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 | |
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39 ## diagonals of each of the quadrilaterals in the meshgrid to find the |
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40 ## normal vectors of the centers of these quadrilaterals. The four nearest |
| 7189 | 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 | |
| 7215 | 52 function [Nx, Ny, Nz] = surfnorm (varargin) |
| 7189 | 53 |
| 7215 | 54 [h, varargin, nargin] = __plt_get_axis_arg__ ((nargout != 0), "surfnorm", |
| 55 varargin{:}); | |
| 56 | |
| 57 if (nargin != 1 && nargin != 3) | |
| 58 print_usage (); | |
| 7189 | 59 endif |
| 60 | |
| 7215 | 61 if (nargin == 1) |
| 7189 | 62 z = varargin{1}; |
| 63 [x, y] = meshgrid (1:size(z,1), 1:size(z,2)); | |
| 64 ioff = 2; | |
| 65 else | |
| 66 x = varargin{1}; | |
| 67 y = varargin{2}; | |
| 68 z = varargin{3}; | |
| 69 ioff = 4; | |
| 70 endif | |
| 71 | |
| 72 if (nargout == 0) | |
| 73 endif | |
| 74 | |
| 75 ## Make life easier, and avoid having to do the extrapolation later, do | |
| 76 ## a simpler linear extrapolation here. This is approximative, and works | |
| 77 ## badly for closed surfaces like spheres. | |
| 78 xx = [2 .* x(:,1) - x(:,2), x, 2 .* x(:,end) - x(:,end-1)]; | |
| 79 xx = [2 .* xx(1,:) - xx(2,:); xx; 2 .* xx(end,:) - xx(end-1,:)]; | |
| 80 yy = [2 .* y(:,1) - y(:,2), y, 2 .* y(:,end) - y(:,end-1)]; | |
| 81 yy = [2 .* yy(1,:) - yy(2,:); yy; 2 .* yy(end,:) - yy(end-1,:)]; | |
| 82 zz = [2 .* z(:,1) - z(:,2), z, 2 .* z(:,end) - z(:,end-1)]; | |
| 83 zz = [2 .* zz(1,:) - zz(2,:); zz; 2 .* zz(end,:) - zz(end-1,:)]; | |
| 84 | |
| 85 u.x = xx(1:end-1,1:end-1) - xx(2:end,2:end); | |
| 86 u.y = yy(1:end-1,1:end-1) - yy(2:end,2:end); | |
| 87 u.z = zz(1:end-1,1:end-1) - zz(2:end,2:end); | |
| 88 v.x = xx(1:end-1,2:end) - xx(2:end,1:end-1); | |
| 89 v.y = yy(1:end-1,2:end) - yy(2:end,1:end-1); | |
| 90 v.z = zz(1:end-1,2:end) - zz(2:end,1:end-1); | |
| 91 | |
| 92 c = cross ([u.x(:), u.y(:), u.z(:)], [v.x(:), v.y(:), v.z(:)]); | |
| 93 w.x = reshape (c(:,1), size(u.x)); | |
| 94 w.y = reshape (c(:,2), size(u.y)); | |
| 95 w.z = reshape (c(:,3), size(u.z)); | |
| 96 | |
| 97 ## Create normal vectors as mesh vectices from normals at mesh centers | |
| 98 nx = (w.x(1:end-1,1:end-1) + w.x(1:end-1,2:end) + | |
| 99 w.x(2:end,1:end-1) + w.x(2:end,2:end)) ./ 4; | |
| 100 ny = (w.y(1:end-1,1:end-1) + w.y(1:end-1,2:end) + | |
| 101 w.y(2:end,1:end-1) + w.y(2:end,2:end)) ./ 4; | |
| 102 nz = (w.z(1:end-1,1:end-1) + w.z(1:end-1,2:end) + | |
| 103 w.z(2:end,1:end-1) + w.z(2:end,2:end)) ./ 4; | |
| 104 | |
| 105 ## Normalize the normal vectors | |
| 106 len = sqrt (nx.^2 + ny.^2 + nz.^2); | |
| 107 nx = nx ./ len; | |
| 108 ny = ny ./ len; | |
| 109 nz = nz ./ len; | |
| 110 | |
| 111 if (nargout == 0) | |
| 7215 | 112 oldh = gca (); |
| 113 unwind_protect | |
| 114 axes (h); | |
| 115 newplot (); | |
| 116 surf (x, y, z, varargin{ioff:end}); | |
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117 old_hold_state = get (h, "nextplot"); |
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118 unwind_protect |
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119 set (h, "nextplot", "add"); |
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120 plot3 ([x(:)'; x(:).' + nx(:).' ; NaN(size(x(:).'))](:), |
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121 [y(:)'; y(:).' + ny(:).' ; NaN(size(y(:).'))](:), |
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122 [z(:)'; z(:).' + nz(:).' ; NaN(size(z(:).'))](:), |
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123 varargin{ioff:end}); |
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124 unwind_protect_cleanup |
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125 set (h, "nextplot", old_hold_state); |
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126 end_unwind_protect |
| 7215 | 127 unwind_protect_cleanup |
| 128 axes (oldh); | |
| 129 end_unwind_protect | |
| 7189 | 130 else |
| 131 Nx = nx; | |
| 132 Ny = ny; | |
| 133 Nz = nz; | |
| 134 endif | |
| 7216 | 135 |
| 7189 | 136 endfunction |
| 137 | |
| 138 %!demo | |
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139 %! colormap (jet (64)) |
| 7189 | 140 %! [x, y, z] = peaks(10); |
| 141 %! surfnorm (x, y, z); | |
| 142 | |
| 143 %!demo | |
| 144 %! surfnorm (peaks(10)); | |
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145 |
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146 %!demo |
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147 %! surfnorm (peaks(32)); |
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148 %! shading interp |