Mercurial > octave-nkf
annotate scripts/general/bicubic.m @ 11523:fd0a3ac60b0e
update copyright notices
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Fri, 14 Jan 2011 05:47:45 -0500 |
| parents | eb9e0b597d61 |
| children | c792872f8942 |
| rev | line source |
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| 11523 | 1 ## Copyright (C) 2005-2011 Hoxide Ma |
| 5837 | 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 | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 5837 | 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 | |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 5837 | 18 |
| 19 ## -*- texinfo -*- | |
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20 ## @deftypefn {Function File} {@var{zi} =} bicubic (@var{x}, @var{y}, @var{z}, @var{xi}, @var{yi}, @var{extrapval}) |
| 5837 | 21 ## |
| 6653 | 22 ## Return a matrix @var{zi} corresponding to the bicubic |
| 5838 | 23 ## interpolations at @var{xi} and @var{yi} of the data supplied |
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24 ## as @var{x}, @var{y} and @var{z}. Points outside the grid are set |
| 8828 | 25 ## to @var{extrapval}. |
| 5837 | 26 ## |
| 6702 | 27 ## See @url{http://wiki.woodpecker.org.cn/moin/Octave/Bicubic} |
| 28 ## for further information. | |
| 5838 | 29 ## @seealso{interp2} |
| 5837 | 30 ## @end deftypefn |
| 31 | |
| 32 ## Bicubic interpolation method. | |
| 33 ## Author: Hoxide Ma <hoxide_dirac@yahoo.com.cn> | |
| 34 | |
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35 function zi = bicubic (x, y, z, xi, yi, extrapval, spline_alpha) |
| 5837 | 36 |
| 6702 | 37 if (nargin < 1 || nargin > 7) |
| 5837 | 38 print_usage (); |
| 39 endif | |
| 40 | |
| 6702 | 41 if (nargin == 7 && isscalar(spline_alpha)) |
| 5837 | 42 a = spline_alpha |
| 43 else | |
| 44 a = 0.5; | |
| 45 endif | |
| 46 | |
| 6702 | 47 if (nargin < 6) |
| 48 extrapval = NaN; | |
| 49 endif | |
| 50 | |
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51 if (isa (x, "single") || isa (y, "single") || isa (z, "single") |
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52 || isa (xi, "single") || isa (yi, "single")) |
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53 myeps = eps("single"); |
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54 else |
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55 myeps = eps; |
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56 endif |
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57 |
| 5838 | 58 if (nargin <= 2) |
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59 ## bicubic (z) or bicubic (z, 2) |
| 5837 | 60 if (nargin == 1) |
| 61 n = 1; | |
| 62 else | |
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63 n = y; |
| 5837 | 64 endif |
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65 z = x; |
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66 x = []; |
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67 [rz, cz] = size (z); |
| 5838 | 68 s = linspace (1, cz, (cz-1)*pow2(n)+1); |
| 69 t = linspace (1, rz, (rz-1)*pow2(n)+1); | |
| 5837 | 70 elseif (nargin == 3) |
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71 if (! isvector (x) || ! isvector (y)) |
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72 error ("bicubic: XI and YI must be vector"); |
| 5837 | 73 endif |
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74 s = y; |
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75 t = z; |
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76 z = x; |
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77 [rz, cz] = size (z); |
| 5837 | 78 elseif (nargin == 5 || nargin == 6) |
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79 [rz, cz] = size (z) ; |
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80 if (isvector (x) && isvector (y)) |
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81 if (rz != length (y) || cz != length (x)) |
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82 error ("bicubic: length of X and Y must match the size of Z"); |
| 5837 | 83 endif |
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84 elseif (size_equal (x, y) && size_equal (x, z)) |
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85 x = x(1,:); |
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86 y = y(:,1); |
| 5837 | 87 else |
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88 error ("bicubic: X, Y and Z must be equal size matrices of same size"); |
| 5837 | 89 endif |
| 90 | |
| 8506 | 91 ## Mark values outside the lookup table. |
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92 xfirst_ind = find (xi < x(1)); |
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93 xlast_ind = find (xi > x(cz)); |
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94 yfirst_ind = find (yi < y(1)); |
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95 ylast_ind = find (yi > y(rz)); |
| 8506 | 96 ## Set value outside the table preliminary to min max index. |
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97 xi(xfirst_ind) = x(1); |
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98 xi(xlast_ind) = x(cz); |
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99 yi(yfirst_ind) = y(1); |
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100 yi(ylast_ind) = y(rz); |
| 5837 | 101 |
| 102 | |
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103 x = reshape (x, 1, cz); |
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104 x(cz) *= 1 + sign (x(cz))*myeps; |
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105 if (x(cz) == 0) |
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106 x(cz) = myeps; |
| 5837 | 107 endif; |
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108 xi = reshape (xi, 1, length (xi)); |
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109 [m, i] = sort ([x, xi]); |
| 5838 | 110 o = cumsum (i <= cz); |
| 111 xidx = o(find (i > cz)); | |
| 5837 | 112 |
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113 y = reshape (y, rz, 1); |
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114 y(rz) *= 1 + sign (y(rz))*myeps; |
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115 if (y(rz) == 0) |
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116 y(rz) = myeps; |
| 5837 | 117 endif; |
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118 yi = reshape (yi, length (yi), 1); |
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119 [m, i] = sort ([y; yi]); |
| 5838 | 120 o = cumsum (i <= rz); |
| 8507 | 121 yidx = o([find(i > rz)]); |
| 5837 | 122 |
| 8506 | 123 ## Set s and t used follow codes. |
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124 s = xidx + ((xi .- x(xidx))./(x(xidx+1) .- x(xidx))); |
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125 t = yidx + ((yi - y(yidx))./(y(yidx+1) - y(yidx))); |
| 5837 | 126 else |
| 127 print_usage (); | |
| 128 endif | |
| 129 | |
| 130 if (rz < 3 || cz < 3) | |
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131 error ("bicubic: Z at least a 3 by 3 matrices"); |
| 5837 | 132 endif |
| 133 | |
| 5838 | 134 inds = floor (s); |
| 135 d = find (s == cz); | |
| 136 s = s - floor (s); | |
| 5837 | 137 inds(d) = cz-1; |
| 138 s(d) = 1.0; | |
| 139 | |
| 140 d = []; | |
| 5838 | 141 indt = floor (t); |
| 142 d = find (t == rz); | |
| 143 t = t - floor (t); | |
| 5837 | 144 indt(d) = rz-1; |
| 145 t(d) = 1.0; | |
| 146 d = []; | |
| 147 | |
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148 p = zeros (size (z) + 2); |
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149 p(2:rz+1,2:cz+1) = z; |
| 8507 | 150 p(1,:) = (6*(1-a))*p(2,:) - 3*p(3,:) + (6*a-2)*p(4,:); |
| 151 p(rz+2,:) = (6*(1-a))*p(rz+1,:) - 3*p(rz,:) + (6*a-2)*p(rz-1,:); | |
| 152 p(:,1) = (6*(1-a))*p(:,2) - 3*p(:,3) + (6*a-2)*p(:,4); | |
| 153 p(:,cz+2) = (6*(1-a))*p(:,cz+1) - 3*p(:,cz) + (6*a-2)*p(:,cz-1); | |
| 5837 | 154 |
| 8506 | 155 ## Calculte the C1(t) C2(t) C3(t) C4(t) and C1(s) C2(s) C3(s) C4(s). |
| 8507 | 156 t2 = t.*t; |
| 157 t3 = t2.*t; | |
| 5837 | 158 |
| 8507 | 159 ct0 = -a .* t3 + (2 * a) .* t2 - a .* t ; # -a G0 |
| 5837 | 160 ct1 = (2-a) .* t3 + (-3+a) .* t2 + 1 ; # F0 - a G1 |
| 161 ct2 = (a-2) .* t3 + (-2 *a + 3) .* t2 + a .* t ; # F1 + a G0 | |
| 162 ct3 = a .* t3 - a .* t2; # a G1 | |
| 8507 | 163 t = []; t2 = []; t3 = []; |
| 5837 | 164 |
| 8507 | 165 s2 = s.*s; |
| 166 s3 = s2.*s; | |
| 5837 | 167 |
| 8507 | 168 cs0 = -a .* s3 + (2 * a) .* s2 - a .*s ; # -a G0 |
| 5837 | 169 cs1 = (2-a) .* s3 + (-3 + a) .* s2 + 1 ; # F0 - a G1 |
| 170 cs2 = (a-2) .* s3 + (-2 *a + 3) .* s2 + a .*s ; # F1 + a G0 | |
| 171 cs3 = a .* s3 - a .* s2; # a G1 | |
| 8507 | 172 s = []; s2 = []; s3 = []; |
| 5837 | 173 |
| 174 cs0 = cs0([1,1,1,1],:); | |
| 175 cs1 = cs1([1,1,1,1],:); | |
| 176 cs2 = cs2([1,1,1,1],:); | |
| 177 cs3 = cs3([1,1,1,1],:); | |
| 178 | |
| 5838 | 179 lent = length (ct0); |
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180 lens = columns (cs0); |
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181 zi = zeros (lent, lens); |
| 5837 | 182 |
| 183 for i = 1:lent | |
| 184 it = indt(i); | |
| 185 int = [it, it+1, it+2, it+3]; | |
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186 zi(i,:) = ([ct0(i),ct1(i),ct2(i),ct3(i)] |
| 10549 | 187 * (p(int,inds) .* cs0 + p(int,inds+1) .* cs1 |
| 188 + p(int,inds+2) .* cs2 + p(int,inds+3) .* cs3)); | |
| 5837 | 189 endfor |
| 190 | |
| 8506 | 191 ## Set points outside the table to extrapval. |
| 5837 | 192 if (! (isempty (xfirst_ind) && isempty (xlast_ind))) |
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193 zi(:, [xfirst_ind, xlast_ind]) = extrapval; |
| 5837 | 194 endif |
| 195 if (! (isempty (yfirst_ind) && isempty (ylast_ind))) | |
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196 zi([yfirst_ind; ylast_ind], :) = extrapval; |
| 5837 | 197 endif |
| 198 | |
| 199 endfunction | |
| 200 | |
| 201 %!demo | |
| 202 %! A=[13,-1,12;5,4,3;1,6,2]; | |
| 203 %! x=[0,1,4]+10; y=[-10,-9,-8]; | |
| 204 %! xi=linspace(min(x),max(x),17); | |
| 6702 | 205 %! yi=linspace(min(y),max(y),26)'; |
| 5837 | 206 %! mesh(xi,yi,bicubic(x,y,A,xi,yi)); |
| 207 %! [x,y] = meshgrid(x,y); | |
| 208 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |