1 ## Copyright (C) 2009-2012 Martin Helm
3 ## This file is part of Octave.
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
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 ## General Public License for more details.
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16 ## along with Octave; see the file COPYING. If not, see
17 ## <http://www.gnu.org/licenses/>.
19 ## Author: Martin Helm <martin@mhelm.de>
22 ## @deftypefn {Function File} {[@var{vxyz}, @var{idx}, @var{frac}] =} __interp_cube__ (@var{x}, @var{y}, @var{z}, @var{val}, @var{v})
23 ## Undocumented internal function.
26 function [Vxyz, idx, frac] = __interp_cube__(x, y, z, val, v, req = "values" )
27 if (ismatrix (x) && ndims (x) == 3 && ismatrix (y) && ndims (y) == 3 ...
28 && ismatrix (z) && ndims (z) == 3 && size_equal (x, y, z, val))
29 x = squeeze (x(1,:,1))(:);
30 y = squeeze (y(:,1,1))(:);
31 z = squeeze (z(1,1,:))(:);
32 elseif (isvector (x) && isvector (y) && isvector (z) )
37 error("__interp_cube__: X, Y, Z have wrong dimensions");
39 if (size (val) != [length(x), length(y), length(z)])
40 error ("__interp_cube__: VAL has wrong dimensions");
43 error ( "v has to be N*3 matrix");
46 error ("__interp_cube__: Invalid request parameter use 'values', 'normals' or 'normals8'");
49 Vxyz = idx = frac = [];
55 [Vxyz, idx, frac] = interp_cube_trilin (x, y, z, val, v);
57 [idx, frac] = cube_idx (x, y, z, v);
59 dx = x(2:end) - x(1:end-1);
60 dy = y(2:end) - y(1:end-1);
61 dz = z(2:end) - z(1:end-1);
62 dx = 0.5 .* [dx;dx(end)](idx(:,2));
63 dy = 0.5 .* [dy;dy(end)](idx(:,1));
64 dz = 0.5 .* [dz;dz(end)](idx(:,3));
66 p000 = [v(:, 1) - dx, v(:, 2) - dy, v(:, 3) - dz];
67 p100 = [v(:, 1) + dx, v(:, 2) - dy, v(:, 3) - dz];
68 p010 = [v(:, 1) - dx, v(:, 2) + dy, v(:, 3) - dz];
69 p001 = [v(:, 1) - dx, v(:, 2) - dy, v(:, 3) + dz];
70 p011 = [v(:, 1) - dx, v(:, 2) + dy, v(:, 3) + dz];
71 p101 = [v(:, 1) + dx, v(:, 2) - dy, v(:, 3) + dz];
72 p110 = [v(:, 1) + dx, v(:, 2) + dy, v(:, 3) - dz];
73 p111 = [v(:, 1) + dx, v(:, 2) + dy, v(:, 3) + dz];
75 v000 = interp_cube_trilin (x, y, z, val, p000);
76 v100 = interp_cube_trilin (x, y, z, val, p100);
77 v010 = interp_cube_trilin (x, y, z, val, p010);
78 v001 = interp_cube_trilin (x, y, z, val, p001);
79 v011 = interp_cube_trilin (x, y, z, val, p011);
80 v101 = interp_cube_trilin (x, y, z, val, p101);
81 v110 = interp_cube_trilin (x, y, z, val, p110);
82 v111 = interp_cube_trilin (x, y, z, val, p111);
84 Dx = -v000 .+ v100 .- v010 .- v001 .- v011 .+ v101 .+ v110 .+ v111;
85 Dy = -v000 .- v100 .+ v010 .- v001 .+ v011 .- v101 .+ v110 .+ v111;
86 Dz = -v000 .- v100 .- v010 .+ v001 .+ v011 .+ v101 .- v110 .+ v111;
87 Vxyz = 0.5 .* [Dx./dx, Dy./dy, Dz./dz];
89 [idx, frac] = cube_idx (x, y, z, v);
91 dx = x(2:end) - x(1:end-1);
92 dy = y(2:end) - y(1:end-1);
93 dz = z(2:end) - z(1:end-1);
94 dx = [dx;dx(end)](idx(:,2));
95 dy = [dy;dy(end)](idx(:,1));
96 dz = [dz;dz(end)](idx(:,3));
97 [Dx, Dy, Dz, idx, frac] = interp_cube_trilin_grad (x, y, z, val, v);
98 Vxyz = [Dx./dx, Dy./dy, Dz./dz];
100 error ("__interp_cube__: Invalid request type '%s', use 'values', 'normals' or 'normals8'", req);
104 function [Vxyz, idx, frac] = interp_cube_trilin(x, y, z, val, v)
105 [idx, frac] = cube_idx (x(:), y(:), z(:), v);
107 i000 = sub2ind (sval, idx(:, 1), idx(:, 2), idx(:, 3));
108 i100 = sub2ind (sval, idx(:, 1)+1, idx(:, 2), idx(:, 3));
109 i010 = sub2ind (sval, idx(:, 1), idx(:, 2)+1, idx(:, 3));
110 i001 = sub2ind (sval, idx(:, 1), idx(:, 2), idx(:, 3)+1);
111 i101 = sub2ind (sval, idx(:, 1)+1, idx(:, 2), idx(:, 3)+1);
112 i011 = sub2ind (sval, idx(:, 1), idx(:, 2)+1, idx(:, 3)+1);
113 i110 = sub2ind (sval, idx(:, 1)+1, idx(:, 2)+1, idx(:, 3));
114 i111 = sub2ind (sval, idx(:, 1)+1, idx(:, 2)+1, idx(:, 3)+1 );
119 val( i000 ) .* (1 .- Bx) .* (1 .- By) .* (1 .- Bz) .+ ...
120 val( i100 ) .* Bx .* (1 .- By) .* (1 .- Bz) .+ ...
121 val( i010 ) .* (1 .- Bx) .* By .* (1 .- Bz) .+ ...
122 val( i001 ) .* (1 .- Bx) .* (1 .- By) .* Bz .+ ...
123 val( i011 ) .* (1 .- Bx) .* By .* Bz .+ ...
124 val( i101 ) .* Bx .* (1 .- By) .* Bz .+ ...
125 val( i110 ) .* Bx .* By .* (1 .- Bz) .+ ...
126 val( i111 ) .* Bx .* By .* Bz;
129 function [Dx, Dy, Dz, idx, frac] = interp_cube_trilin_grad(x, y, z, val, v)
130 [idx, frac] = cube_idx (x(:), y(:), z(:), v);
132 i000 = sub2ind (sval, idx(:, 1), idx(:, 2), idx(:, 3));
133 i100 = sub2ind (sval, idx(:, 1)+1, idx(:, 2), idx(:, 3));
134 i010 = sub2ind (sval, idx(:, 1), idx(:, 2)+1, idx(:, 3));
135 i001 = sub2ind (sval, idx(:, 1), idx(:, 2), idx(:, 3)+1);
136 i101 = sub2ind (sval, idx(:, 1)+1, idx(:, 2), idx(:, 3)+1);
137 i011 = sub2ind (sval, idx(:, 1), idx(:, 2)+1, idx(:, 3)+1);
138 i110 = sub2ind (sval, idx(:, 1)+1, idx(:, 2)+1, idx(:, 3));
139 i111 = sub2ind (sval, idx(:, 1)+1, idx(:, 2)+1, idx(:, 3)+1 );
144 val( i000 ) .* -1 .* (1 .- By) .* (1 .- Bz) .+ ...
145 val( i100 ) .* (1 .- By) .* (1 .- Bz) .+ ...
146 val( i010 ) .* -1 .* By .* (1 .- Bz) .+ ...
147 val( i001 ) .* -1 .* (1 .- By) .* Bz .+ ...
148 val( i011 ) .* -1 .* By .* Bz .+ ...
149 val( i101 ) .* (1 .- By) .* Bz .+ ...
150 val( i110 ) .* By .* (1 .- Bz) .+ ...
151 val( i111 ) .* By .* Bz;
153 val( i000 ) .* (1 .- Bx) .* -1 .* (1 .- Bz) .+ ...
154 val( i100 ) .* Bx .* -1 .* (1 .- Bz) .+ ...
155 val( i010 ) .* (1 .- Bx) .* (1 .- Bz) .+ ...
156 val( i001 ) .* (1 .- Bx) .* -1 .* Bz .+ ...
157 val( i011 ) .* (1 .- Bx) .* Bz .+ ...
158 val( i101 ) .* Bx .* -1 .* Bz .+ ...
159 val( i110 ) .* Bx .* (1 .- Bz) .+ ...
160 val( i111 ) .* Bx .* Bz;
162 val( i000 ) .* (1 .- Bx) .* (1 .- By) .* -1 .+ ...
163 val( i100 ) .* Bx .* (1 .- By) .* -1 .+ ...
164 val( i010 ) .* (1 .- Bx) .* By .* -1 .+ ...
165 val( i001 ) .* (1 .- Bx) .* (1 .- By) .+ ...
166 val( i011 ) .* (1 .- Bx) .* By + ...
167 val( i101 ) .* Bx .* (1 .- By) .+ ...
168 val( i110 ) .* Bx .* By .* -1 .+ ...
169 val( i111 ) .* Bx .* By;
172 function [idx, frac] = cube_idx(x, y, z, v)
173 idx = zeros (size (v));
174 frac = zeros (size (v));
175 idx(:, 2) = lookup (x(2:end-1), v(:, 1)) + 1;
176 frac(:, 2) = (v(:, 1) - x(idx(:, 2)) )...
177 ./ (x(idx(:, 2)+1) - x(idx(:, 2)));
178 idx(:, 1) = lookup (y(2:end-1), v(:, 2)) + 1;
179 frac(:, 1) = (v(:, 2) - y(idx(:, 1))) ...
180 ./ (y(idx(:, 1)+1) - y(idx(:, 1)));
181 idx(:, 3) = lookup (z(2:end-1), v(:, 3)) + 1;
182 frac(:, 3) = (v(:, 3) - z(idx(:, 3))) ...
183 ./ (z(idx(:, 3)+1) - z(idx(:, 3)));