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1 ## Copyright (C) 2012 Martin Helm |
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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} tetramesh (@var{T}, @var{X}) |
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21 ## @deftypefnx {Function File} tetramesh (@var{T}, @var{X}, @var{C}) |
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22 ## @deftypefnx {Function File} {[@var{h}] =} tetramesh (...) |
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23 ## @deftypefnx {Function File} {[@var{h}] =} tetramesh (..., @var{PROP}, @var{VAL}) |
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24 ## |
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25 ## The function displays the tetrahedrons defined in the m by 4 matrix @var{T} |
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26 ## as 3D patches. @var{T} is usually the output of a Delaunay triangulation of a |
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27 ## 3D set of points. |
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28 ## Every row of @var{T} contains four indices into the n by 3 matrix @var{X} |
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29 ## of the vertices of a tetrahedron. |
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30 ## Every row in @var{X} represents one point in 3D space. |
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31 ## |
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32 ## If the vector @var{C} is supplied it must contain indices into the current |
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33 ## colormap. Called without @var{C} it is set to 1:m, where m is the number of |
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34 ## tetrahedrons, the indices are scaled to map to the full range of the colormap. |
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35 ## If more tetrahedrons than entries in the colormap are given the entries of |
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36 ## @var{C} are cyclic repeated. |
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37 ## |
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38 ## When called with one output argument @var{H} it returns a vector of patch |
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39 ## handles,each representing one tetrahedron in the order given by @var{T}. |
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40 ## One use case for @var{H} is to turn the respective patch 'Visible' property |
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41 ## 'on' or 'off'. |
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42 ## |
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43 ## Calling tetramesh(...,'param','value','param','value'...) passes all |
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44 ## option/value pairs directly as additional arguments to the patch function for |
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45 ## every tetrahedron. |
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46 ## |
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47 ## The command |
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48 ## |
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49 ##@example |
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50 ## @group |
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51 ## demo tetramesh |
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52 ## @end group |
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53 ## @end example |
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54 ## |
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55 ## @noindent |
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56 ## will show some examples how to use it. |
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57 #### @seealso{patch} |
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58 ## @end deftypefn |
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59 |
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60 ## Author: Martin Helm <martin@mhelm.de> |
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61 |
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62 function [h] = tetramesh (varargin) |
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63 |
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64 [reg, prop] = parseparams (varargin); |
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65 |
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66 if (length (reg) < 2 || length (reg) > 3) |
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67 print_usage () |
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68 endif |
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69 |
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70 T = reg{1}; |
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71 X = reg{2}; |
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72 |
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73 if (! ismatrix (T) || size (T, 2) != 4) |
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74 error ("tetramesh: T must be a n by 4 matrix") |
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75 endif |
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76 if (! ismatrix (X) || size (X, 2) != 3) |
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77 error ("tetramesh: X must be a n by 3 matrix") |
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78 endif |
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79 |
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80 size_T = size (T, 1); |
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81 colmap = colormap (); |
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82 |
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83 # do we need to enable gnuplot workaround? |
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84 shrink = strcmp (graphics_toolkit (), "gnuplot"); |
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85 |
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86 if (length (reg) < 3) |
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87 size_colmap = size (colmap, 1); |
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88 C = mod ((1:size_T)' - 1, size_colmap) + 1; |
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89 if (size_T < size_colmap && size_T > 1) |
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90 # expand to the available range of colors |
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91 C = floor ((C - 1) * (size_colmap - 1) / (size_T - 1)) + 1; |
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92 endif |
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93 else |
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94 C = reg{3}; |
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95 if (! isvector (C) || size_T != length (C)) |
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96 error ("tetramesh: C must be a vector of the same length as T") |
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97 endif |
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98 endif |
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99 |
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100 h = zeros (1, size_T); |
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101 if (shrink) |
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102 # tiny reduction of the tetrahedron size to help gnuplot by |
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103 # avoiding identical faces with different colors |
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104 for ii = 1:size_T |
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105 [th, p] = __shrink__ ([1 2 3 4], X(T(ii, :), :), 1 - 1e-7); |
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106 h(ii) = patch ("Faces", th, "Vertices", p, "FaceColor", ... |
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107 colmap(C(ii), :), prop{:}); |
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108 endfor |
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109 else |
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110 for ii = 1:size_T |
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111 th = [1 2 3; 2 3 4; 3 4 1; 4 1 2]; |
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112 h(ii) = patch ("Faces", th, "Vertices", X(T(ii, :), :), "FaceColor", ... |
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113 colmap(C(ii), :), prop{:}); |
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114 endfor |
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115 endif |
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116 |
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117 if (nargout == 0) #return nothing |
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118 clear h; |
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119 endif |
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120 endfunction |
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121 |
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122 ## shrink the tetrahedron relative to its center of gravity |
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123 function [tri, p] = __shrink__ (T, X, sf) |
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124 midpoint = repmat (sum (X(T, :), 1) / 4, 12, 1); |
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125 p = [X([1 2 3], :); X([2 3 4], :); X([3 4 1], :); X([4 1 2], :)]; |
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126 p = sf * (p - midpoint) + midpoint; |
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127 tri = reshape (1:12, 3, 4)'; |
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128 endfunction |
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129 |
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130 %!demo |
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131 %! d = [-1 1]; |
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132 %! [x,y,z] = meshgrid (d, d, d); |
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133 %! x = [x(:); 0]; |
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134 %! y = [y(:); 0]; |
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135 %! z = [z(:); 0]; |
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136 %! tetra = delaunay3 (x, y, z); |
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137 %! X = [x(:) y(:) z(:)]; |
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138 %! clf () |
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139 %! colormap (jet (64)) |
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140 %! h = tetramesh (tetra, X); |
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141 %! for ii=1:2:length(h); |
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142 %! set(h(ii), "Visible", "off"); |
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143 %! endfor |
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144 %! axis equal |
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145 %! view (30, 20) |
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146 %! title ("Using jet (64), every other tetrahedron invisible") |
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147 |
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148 %!demo |
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149 %! d = [-1 1]; |
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150 %! [x,y,z] = meshgrid (d, d, d); |
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151 %! x = [x(:); 0]; |
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152 %! y = [y(:); 0]; |
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153 %! z = [z(:); 0]; |
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154 %! tetra = delaunay3 (x, y, z); |
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155 %! X = [x(:) y(:) z(:)]; |
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156 %! clf () |
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157 %! colormap (gray (256)); |
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158 %! tetramesh (tetra, X, 21:20:241, "EdgeColor", "w") |
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159 %! axis equal |
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160 %! view (30, 20) |
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161 %! title ("Using gray (256) and white edges") |
