--- /dev/null
+## Copyright (C) 2005-2012 Hoxide Ma
+##
+## This file is part of Octave.
+##
+## Octave is free software; you can redistribute it and/or modify it
+## under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or (at
+## your option) any later version.
+##
+## Octave is distributed in the hope that it will be useful, but
+## WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+## General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with Octave; see the file COPYING. If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{zi} =} bicubic (@var{x}, @var{y}, @var{z}, @var{xi}, @var{yi}, @var{extrapval})
+##
+## Return a matrix @var{zi} corresponding to the bicubic
+## interpolations at @var{xi} and @var{yi} of the data supplied
+## as @var{x}, @var{y} and @var{z}. Points outside the grid are set
+## to @var{extrapval}.
+##
+## See @url{http://wiki.woodpecker.org.cn/moin/Octave/Bicubic}
+## for further information.
+## @seealso{interp2}
+## @end deftypefn
+
+## Bicubic interpolation method.
+## Author: Hoxide Ma <hoxide_dirac@yahoo.com.cn>
+
+function zi = bicubic (x, y, z, xi, yi, extrapval, spline_alpha)
+
+ if (nargin < 1 || nargin > 7)
+ print_usage ();
+ endif
+
+ if (nargin == 7 && isscalar(spline_alpha))
+ a = spline_alpha;
+ else
+ a = 0.5;
+ endif
+
+ if (nargin < 6)
+ extrapval = NaN;
+ endif
+
+ if (isa (x, "single") || isa (y, "single") || isa (z, "single")
+ || isa (xi, "single") || isa (yi, "single"))
+ myeps = eps("single");
+ else
+ myeps = eps;
+ endif
+
+ if (nargin <= 2)
+ ## bicubic (z) or bicubic (z, 2)
+ if (nargin == 1)
+ n = 1;
+ else
+ n = y;
+ endif
+ z = x;
+ x = [];
+ [rz, cz] = size (z);
+ s = linspace (1, cz, (cz-1)*pow2(n)+1);
+ t = linspace (1, rz, (rz-1)*pow2(n)+1);
+ elseif (nargin == 3)
+ if (! isvector (x) || ! isvector (y))
+ error ("bicubic: XI and YI must be vector");
+ endif
+ s = y;
+ t = z;
+ z = x;
+ [rz, cz] = size (z);
+ elseif (nargin == 5 || nargin == 6)
+ [rz, cz] = size (z) ;
+ if (isvector (x) && isvector (y))
+ if (rz != length (y) || cz != length (x))
+ error ("bicubic: length of X and Y must match the size of Z");
+ endif
+ elseif (size_equal (x, y) && size_equal (x, z))
+ x = x(1,:);
+ y = y(:,1);
+ else
+ error ("bicubic: X, Y and Z must be equal size matrices of same size");
+ endif
+
+ ## Mark values outside the lookup table.
+ xfirst_ind = find (xi < x(1));
+ xlast_ind = find (xi > x(cz));
+ yfirst_ind = find (yi < y(1));
+ ylast_ind = find (yi > y(rz));
+ ## Set value outside the table preliminary to min max index.
+ xi(xfirst_ind) = x(1);
+ xi(xlast_ind) = x(cz);
+ yi(yfirst_ind) = y(1);
+ yi(ylast_ind) = y(rz);
+
+
+ x = reshape (x, 1, cz);
+ x(cz) *= 1 + sign (x(cz))*myeps;
+ if (x(cz) == 0)
+ x(cz) = myeps;
+ endif;
+ xi = reshape (xi, 1, length (xi));
+ [m, i] = sort ([x, xi]);
+ o = cumsum (i <= cz);
+ xidx = o(find (i > cz));
+
+ y = reshape (y, rz, 1);
+ y(rz) *= 1 + sign (y(rz))*myeps;
+ if (y(rz) == 0)
+ y(rz) = myeps;
+ endif;
+ yi = reshape (yi, length (yi), 1);
+ [m, i] = sort ([y; yi]);
+ o = cumsum (i <= rz);
+ yidx = o([find(i > rz)]);
+
+ ## Set s and t used follow codes.
+ s = xidx + ((xi .- x(xidx))./(x(xidx+1) .- x(xidx)));
+ t = yidx + ((yi - y(yidx))./(y(yidx+1) - y(yidx)));
+ else
+ print_usage ();
+ endif
+
+ if (rz < 3 || cz < 3)
+ error ("bicubic: Z at least a 3 by 3 matrices");
+ endif
+
+ inds = floor (s);
+ d = find (s == cz);
+ s = s - floor (s);
+ inds(d) = cz-1;
+ s(d) = 1.0;
+
+ d = [];
+ indt = floor (t);
+ d = find (t == rz);
+ t = t - floor (t);
+ indt(d) = rz-1;
+ t(d) = 1.0;
+ d = [];
+
+ p = zeros (size (z) + 2);
+ p(2:rz+1,2:cz+1) = z;
+ p(1,:) = (6*(1-a))*p(2,:) - 3*p(3,:) + (6*a-2)*p(4,:);
+ p(rz+2,:) = (6*(1-a))*p(rz+1,:) - 3*p(rz,:) + (6*a-2)*p(rz-1,:);
+ p(:,1) = (6*(1-a))*p(:,2) - 3*p(:,3) + (6*a-2)*p(:,4);
+ p(:,cz+2) = (6*(1-a))*p(:,cz+1) - 3*p(:,cz) + (6*a-2)*p(:,cz-1);
+
+ ## Calculte the C1(t) C2(t) C3(t) C4(t) and C1(s) C2(s) C3(s) C4(s).
+ t2 = t.*t;
+ t3 = t2.*t;
+
+ ct0 = -a .* t3 + (2 * a) .* t2 - a .* t ; # -a G0
+ ct1 = (2-a) .* t3 + (-3+a) .* t2 + 1 ; # F0 - a G1
+ ct2 = (a-2) .* t3 + (-2 *a + 3) .* t2 + a .* t ; # F1 + a G0
+ ct3 = a .* t3 - a .* t2; # a G1
+ t = []; t2 = []; t3 = [];
+
+ s2 = s.*s;
+ s3 = s2.*s;
+
+ cs0 = -a .* s3 + (2 * a) .* s2 - a .*s ; # -a G0
+ cs1 = (2-a) .* s3 + (-3 + a) .* s2 + 1 ; # F0 - a G1
+ cs2 = (a-2) .* s3 + (-2 *a + 3) .* s2 + a .*s ; # F1 + a G0
+ cs3 = a .* s3 - a .* s2; # a G1
+ s = []; s2 = []; s3 = [];
+
+ cs0 = cs0([1,1,1,1],:);
+ cs1 = cs1([1,1,1,1],:);
+ cs2 = cs2([1,1,1,1],:);
+ cs3 = cs3([1,1,1,1],:);
+
+ lent = length (ct0);
+ lens = columns (cs0);
+ zi = zeros (lent, lens);
+
+ for i = 1:lent
+ it = indt(i);
+ int = [it, it+1, it+2, it+3];
+ zi(i,:) = ([ct0(i),ct1(i),ct2(i),ct3(i)]
+ * (p(int,inds) .* cs0 + p(int,inds+1) .* cs1
+ + p(int,inds+2) .* cs2 + p(int,inds+3) .* cs3));
+ endfor
+
+ ## Set points outside the table to extrapval.
+ if (! (isempty (xfirst_ind) && isempty (xlast_ind)))
+ zi(:, [xfirst_ind, xlast_ind]) = extrapval;
+ endif
+ if (! (isempty (yfirst_ind) && isempty (ylast_ind)))
+ zi([yfirst_ind; ylast_ind], :) = extrapval;
+ endif
+
+endfunction
+
+%!demo
+%! A=[13,-1,12;5,4,3;1,6,2];
+%! x=[0,1,4]+10; y=[-10,-9,-8];
+%! xi=linspace(min(x),max(x),17);
+%! yi=linspace(min(y),max(y),26)';
+%! mesh(xi,yi,bicubic(x,y,A,xi,yi));
+%! [x,y] = meshgrid(x,y);
+%! hold on; plot3(x(:),y(:),A(:),"b*"); hold off;
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff