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bspderiv.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 [dc,dk] = bspderiv(d,c,k)

% BSPDERIV:  B-Spline derivative
% 
%  MATLAB SYNTAX:
% 
%         [dc,dk] = bspderiv(d,c,k)
%  
%  INPUT:
% 
%    d - degree of the B-Spline
%    c - control points          double  matrix(mc,nc)
%    k - knot sequence           double  vector(nk)
% 
%  OUTPUT:
% 
%    dc - control points of the derivative     double  matrix(mc,nc)
%    dk - knot sequence of the derivative      double  vector(nk)
% 
%  Modified version of Algorithm A3.3 from 'The NURBS BOOK' pg98.

[mc,nc] = size(c);
nk = numel(k);
                                                     %
                                                     % int bspderiv(int d, double *c, int mc, int nc, double *k, int nk, double *dc,
                                                     %              double *dk)
                                                     % {
                                                     %   int ierr = 0;
                                                     %   int i, j, tmp;
                                                     %
                                                     %   // control points
                                                     %   double **ctrl = vec2mat(c,mc,nc);
                                                     %
                                                     %   // control points of the derivative
dc = zeros(mc,nc-1);                                 %   double **dctrl = vec2mat(dc,mc,nc-1);
                                                     %
for i=0:nc-2                                         %   for (i = 0; i < nc-1; i++) {
   tmp = d / (k(i+d+2) - k(i+2));                    %     tmp = d / (k[i+d+1] - k[i+1]);
   for j=0:mc-1                                      %     for (j = 0; j < mc; j++) {
       dc(j+1,i+1) = tmp*(c(j+1,i+2) - c(j+1,i+1));  %       dctrl[i][j] = tmp * (ctrl[i+1][j] - ctrl[i][j]);
   end                                               %     }
end                                                  %   }
                                                     %
dk = zeros(1,nk-2);                                  %   j = 0;
for i=1:nk-2                                         %   for (i = 1; i < nk-1; i++)
   dk(i) = k(i+1);                                   %     dk[j++] = k[i];
end                                                  %
                                                     %   freevec2mat(dctrl);
                                                     %   freevec2mat(ctrl);
                                                     %
                                                     %   return ierr;
                                                     % }

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