bspdegelev.m

强大的nurbs的工具箱 nurbs曲线

   end                                                    %     }
                                                          %     // end of insert knot
                                                          %
                                                          %     // degree elevate bezier
   for i=lbz:ph                                           %     for (i = lbz; i <= ph; i++)  {
      for ii=0:mc-1                                       %       for (ii = 0; ii < mc; ii++)
         ebpts(ii+1,i+1) = 0;                             %         ebpts[i][ii] = 0.0;
      end                                                    
      mpi = min(d, i);                                    %       mpi = min(d, i);
      for j=max(0,i-t):mpi                                %       for (j = max(0,i-t); j <= mpi; j++)
         for ii=0:mc-1                                    %         for (ii = 0; ii < mc; ii++)
            tmp1 = ebpts(ii+1,i+1); 
            tmp2 = bezalfs(j+1,i+1)*bpts(ii+1,j+1);
            ebpts(ii+1,i+1) = tmp1 + tmp2;                %           ebpts[i][ii] = ebpts[i][ii] + bezalfs[i][j]*bpts[j][ii];
         end                                                 
      end                                                    
   end                                                    %     }
                                                          %     // end of degree elevating bezier
                                                          %
   if oldr > 1                                            %     if (oldr > 1)  {
                                                          %       // must remove knot u=k[a] oldr times
      first = kind - 2;                                                    %       first = kind - 2;
      last = kind;                                        %       last = kind;
      den = ub - ua;                                      %       den = ub - ua;
      bet = floor((ub-ik(kind)) / den);                   %       bet = (ub-ik[kind-1]) / den;
                                                          %
                                                          %       // knot removal loop
      for tr=1:oldr-1                                     %       for (tr = 1; tr < oldr; tr++)  {
         i = first;                                       %         i = first;
         j = last;                                        %         j = last;
         kj = j - kind + 1;                               %         kj = j - kind + 1;
         while j-i > tr                                   %         while (j - i > tr)  {
                                                          %           // loop and compute the new control points
                                                          %           // for one removal step
            if i < cind                                   %           if (i < cind)  {
               alf = (ub-ik(i+1))/(ua-ik(i+1));           %             alf = (ub-ik[i])/(ua-ik[i]);
               for ii=0:mc-1                              %             for (ii = 0; ii < mc; ii++)
                  tmp1 = alf*ic(ii+1,i+1); 
                  tmp2 = (1-alf)*ic(ii+1,i); 
                  ic(ii+1,i+1) = tmp1 + tmp2;             %               ictrl[i][ii] = alf * ictrl[i][ii] + (1.0-alf) * ictrl[i-1][ii];
               end                                           
            end                                           %           }
            if j >= lbz                                   %           if (j >= lbz)  {
               if j-tr <= kind-ph+oldr                    %             if (j-tr <= kind-ph+oldr) {
                  gam = (ub-ik(j-tr+1)) / den;            %               gam = (ub-ik[j-tr]) / den;
                  for ii=0:mc-1                           %               for (ii = 0; ii < mc; ii++)
                     tmp1 = gam*ebpts(ii+1,kj+1); 
                     tmp2 = (1-gam)*ebpts(ii+1,kj+2); 
                     ebpts(ii+1,kj+1) = tmp1 + tmp2;      %                 ebpts[kj][ii] = gam*ebpts[kj][ii] + (1.0-gam)*ebpts[kj+1][ii];
                  end                                     %             }
               else                                       %             else  {
                  for ii=0:mc-1                           %               for (ii = 0; ii < mc; ii++)
                     tmp1 = bet*ebpts(ii+1,kj+1);                                     
                     tmp2 = (1-bet)*ebpts(ii+1,kj+2);                                     
                     ebpts(ii+1,kj+1) = tmp1 + tmp2;      %                 ebpts[kj][ii] = bet*ebpts[kj][ii] + (1.0-bet)*ebpts[kj+1][ii];
                  end                                        
               end                                        %             }
            end                                           %           }
            i = i + 1;                                    %           i++;
            j = j - 1;                                    %           j--;
            kj = kj - 1;                                  %           kj--;
         end                                              %         }
                                                          %
         first = first - 1;                               %         first--;
         last = last + 1;                                 %         last++;
      end                                                 %       }
   end                                                    %     }
                                                          %     // end of removing knot n=k[a]
                                                          %
                                                          %     // load the knot ua
   if a ~= d                                              %     if (a != d)
      for i=0:ph-oldr-1                                   %       for (i = 0; i < ph-oldr; i++)  {
         ik(kind+1) = ua;                                 %         ik[kind] = ua;
         kind = kind + 1;                                 %         kind++;
      end
   end                                                    %       }
                                                          %
                                                          %     // load ctrl pts into ic
      for j=lbz:rbz                                       %     for (j = lbz; j <= rbz; j++)  {
         for ii=0:mc-1                                    %       for (ii = 0; ii < mc; ii++)
            ic(ii+1,cind+1) = ebpts(ii+1,j+1);            %         ictrl[cind][ii] = ebpts[j][ii];
         end                                                 
         cind = cind + 1;                                 %       cind++;
      end                                                 %     }
                                                          %
      if b < m                                            %     if (b < m)  {
                                                          %       // setup for next pass thru loop
         for j=0:r-1                                      %       for (j = 0; j < r; j++)
            for ii=0:mc-1                                 %         for (ii = 0; ii < mc; ii++)
               bpts(ii+1,j+1) = Nextbpts(ii+1,j+1);       %           bpts[j][ii] = Nextbpts[j][ii];
            end                                           
         end                                              
         for j=r:d                                        %       for (j = r; j <= d; j++)
            for ii=0:mc-1                                 %         for (ii = 0; ii < mc; ii++)
               bpts(ii+1,j+1) = c(ii+1,b-d+j+1);          %           bpts[j][ii] = ctrl[b-d+j][ii];
            end                                              
         end                                                 
         a = b;                                           %       a = b;
         b = b+1;                                         %       b++;
         ua = ub;                                         %       ua = ub;
                                                          %     }
      else                                                %     else
                                                          %       // end knot
         for i=0:ph                                       %       for (i = 0; i <= ph; i++)
            ik(kind+i+1) = ub;                            %         ik[kind+i] = ub;
         end                                                 
      end                                                    
end                                                       %   }
% End big while loop                                      %   // end while loop
                                                          %
                                                          %   *nh = mh - ph - 1;
                                                          %
                                                          %   freevec2mat(ctrl);
                                                          %   freevec2mat(ictrl);
                                                          %   freematrix(bezalfs);
                                                          %   freematrix(bpts);
                                                          %   freematrix(ebpts);
                                                          %   freematrix(Nextbpts);
                                                          %   mxFree(alfs);
                                                          %
                                                          %   return(ierr);
                                                          % }

                                                          
function b = bincoeff(n,k)
%  Computes the binomial coefficient.
%
%      ( n )      n!
%      (   ) = --------
%      ( k )   k!(n-k)!
%
%  b = bincoeff(n,k)
%
%  Algorithm from 'Numerical Recipes in C, 2nd Edition' pg215.

                                                          % double bincoeff(int n, int k)
                                                          % {
b = floor(0.5+exp(factln(n)-factln(k)-factln(n-k)));      %   return floor(0.5+exp(factln(n)-factln(k)-factln(n-k)));
                                                          % }

function f = factln(n)
% computes ln(n!)
if n <= 1, f = 0; return, end
f = gammaln(n+1); %log(factorial(n));