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