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bspkntins.m

%% Copyright (C) 2003 Mark Spink, 2007 Daniel Claxton
%% 
%% This program 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 2 of the License, or
%% (at your option) any later version.
%% 
%% This program 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 this program; if not, see <http://www.gnu.org/licenses/>.

function [ic,ik] = bspkntins(d,c,k,u)

% BSPKNTINS:  Insert knots into a B-Spline
%
% Calling Sequence:
% 
%   [ic,ik] = bspkntins(d,c,k,u)
%
%  INPUT:
% 
%    d - spline degree             integer
%    c - control points            double  matrix(mc,nc)      
%    k - knot sequence             double  vector(nk) 
%    u - new knots                 double  vector(nu)               
% 
%  OUTPUT:
% 
%    ic - new control points double  matrix(mc,nc+nu) 
%    ik - new knot sequence  double  vector(nk+nu)
% 
%  Modified version of Algorithm A5.4 from 'The NURBS BOOK' pg164.
% 

[mc,nc] = size(c);
nu = numel(u);
nk = numel(k);
                                                     % 
                                                     % int bspkntins(int d, double *c, int mc, int nc, double *k, int nk,
                                                     %               double *u, int nu, double *ic, double *ik)
                                                     % {
                                                     %   int ierr = 0;
                                                     %   int a, b, r, l, i, j, m, n, s, q, ind;
                                                     %   double alfa;
                                                     %
                                                     %   double **ctrl  = vec2mat(c, mc, nc);
ic = zeros(mc,nc+nu);                                %   double **ictrl = vec2mat(ic, mc, nc+nu);
ik = zeros(1,nk+nu);
                                                     %
n = size(c,2) - 1;                                   %   n = nc - 1;
r = length(u) - 1;                                   %   r = nu - 1;
                                                     %
m = n + d + 1;                                       %   m = n + d + 1;
a = findspan(n, d, u(1), k);                         %   a = findspan(n, d, u[0], k);
b = findspan(n, d, u(r+1), k);                       %   b = findspan(n, d, u[r], k);
b = b+1;                                             %   ++b;
                                                     %
for q=0:mc-1                                         %   for (q = 0; q < mc; q++)  {
   for j=0:a-d, ic(q+1,j+1) = c(q+1,j+1); end        %     for (j = 0; j <= a-d; j++) ictrl[j][q] = ctrl[j][q];
   for j=b-1:n, ic(q+1,j+r+2) = c(q+1,j+1); end      %     for (j = b-1; j <= n; j++) ictrl[j+r+1][q] = ctrl[j][q];
end                                                  %   }

for j=0:a, ik(j+1) = k(j+1); end                     %   for (j = 0; j <= a; j++)   ik[j] = k[j];
for j=b+d:m, ik(j+r+2) = k(j+1); end                 %   for (j = b+d; j <= m; j++) ik[j+r+1] = k[j];
                                                     %
i = b + d - 1;                                       %   i = b + d - 1;
s = b + d + r;                                       %   s = b + d + r;

for j=r:-1:0                                         %   for (j = r; j >= 0; j--) {
   while u(j+1) <= k(i+1) && i > a                   %     while (u[j] <= k[i] && i > a) {
       for q=0:mc-1                                  %       for (q = 0; q < mc; q++)
           ic(q+1,s-d) = c(q+1,i-d);                 %         ictrl[s-d-1][q] = ctrl[i-d-1][q];
       end                                              
       ik(s+1) = k(i+1);                             %       ik[s] = k[i];
       s = s - 1;                                    %       --s;
       i = i - 1;                                    %       --i;
   end                                               %     }
   
   for q=0:mc-1                                      %     for (q = 0; q < mc; q++)
       ic(q+1,s-d) = ic(q+1,s-d+1);                  %       ictrl[s-d-1][q] = ictrl[s-d][q];
   end

   for l=1:d                                         %     for (l = 1; l <= d; l++)  {
       ind = s - d + l;                              %       ind = s - d + l;
       alfa = ik(s+l+1) - u(j+1);                    %       alfa = ik[s+l] - u[j];
       if abs(alfa) == 0                             %       if (fabs(alfa) == 0.0)
           for q=0:mc-1                              %         for (q = 0; q < mc; q++)
               ic(q+1,ind) = ic(q+1,ind+1);          %           ictrl[ind-1][q] = ictrl[ind][q];
           end
       else                                          %       else  {
           alfa = alfa/(ik(s+l+1) - k(i-d+l+1));     %         alfa /= (ik[s+l] - k[i-d+l]);
           for q=0:mc-1                              %         for (q = 0; q < mc; q++)
               tmp = (1-alfa)*ic(q+1,ind+1);
               ic(q+1,ind) = alfa*ic(q+1,ind) + tmp; %           ictrl[ind-1][q] = alfa*ictrl[ind-1][q]+(1.0-alfa)*ictrl[ind][q];
           end
       end                                           %       }
   end                                               %     }
   %
   ik(s+1) = u(j+1);                                 %     ik[s] = u[j];
   s = s - 1;                                        %     --s;
end                                                  %   }
                                                     %
                                                     %   freevec2mat(ctrl);
                                                     %   freevec2mat(ictrl);
                                                     %
                                                     %   return ierr;
                                                     % }


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