octave_packages/nurbs-1.3.6/bspderiv.m

   1 function [dc,dk] = bspderiv(d,c,k)
   2
   3 % BSPDERIV:  B-Spline derivative.
   4 %
   5 %  MATLAB SYNTAX:
   6 %
   7 %         [dc,dk] = bspderiv(d,c,k)
   8 %
   9 %  INPUT:
  10 %
  11 %    d - degree of the B-Spline
  12 %    c - control points          double  matrix(mc,nc)
  13 %    k - knot sequence           double  vector(nk)
  14 %
  15 %  OUTPUT:
  16 %
  17 %    dc - control points of the derivative     double  matrix(mc,nc)
  18 %    dk - knot sequence of the derivative      double  vector(nk)
  19 %
  20 %  Modified version of Algorithm A3.3 from 'The NURBS BOOK' pg98.
  21 %
  22 %    Copyright (C) 2000 Mark Spink, 2007 Daniel Claxton
  23 %
  24 %    This program is free software: you can redistribute it and/or modify
  25 %    it under the terms of the GNU General Public License as published by
  26 %    the Free Software Foundation, either version 2 of the License, or
  27 %    (at your option) any later version.
  28
  29 %    This program is distributed in the hope that it will be useful,
  30 %    but WITHOUT ANY WARRANTY; without even the implied warranty of
  31 %    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  32 %    GNU General Public License for more details.
  33 %
  34 %    You should have received a copy of the GNU General Public License
  35 %    along with this program.  If not, see <http://www.gnu.org/licenses/>.
  36
  37 [mc,nc] = size(c);
  38 nk = numel(k);
  39                                                      %
  40                                                      % int bspderiv(int d, double *c, int mc, int nc, double *k, int nk, double *dc,
  41                                                      %              double *dk)
  42                                                      % {
  43                                                      %   int ierr = 0;
  44                                                      %   int i, j, tmp;
  45                                                      %
  46                                                      %   // control points
  47                                                      %   double **ctrl = vec2mat(c,mc,nc);
  48                                                      %
  49                                                      %   // control points of the derivative
  50 dc = zeros(mc,nc-1);                                 %   double **dctrl = vec2mat(dc,mc,nc-1);
  51                                                      %
  52 for i=0:nc-2                                         %   for (i = 0; i < nc-1; i++) {
  53    tmp = d / (k(i+d+2) - k(i+2));                    %     tmp = d / (k[i+d+1] - k[i+1]);
  54    for j=0:mc-1                                      %     for (j = 0; j < mc; j++) {
  55        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]);
  56    end                                               %     }
  57 end                                                  %   }
  58                                                      %
  59 dk = zeros(1,nk-2);                                  %   j = 0;
  60 for i=1:nk-2                                         %   for (i = 1; i < nk-1; i++)
  61    dk(i) = k(i+1);                                   %     dk[j++] = k[i];
  62 end                                                  %
  63                                                      %   freevec2mat(dctrl);
  64                                                      %   freevec2mat(ctrl);
  65                                                      %
  66                                                      %   return ierr;
  67 end                                                  % }