bspdegelev.m

强大的nurbs的工具箱 nurbs曲线

function [ic,ik] = bspdegelev(d,c,k,t)
% 
% Function Name:
% 
%   bspdegevel - Degree elevate a univariate B-Spline.
% 
% Calling Sequence:
% 
%   [ic,ik] = bspdegelev(d,c,k,t)
% 
% Parameters:
% 
%   d	: Degree of the B-Spline.
% 
%   c	: Control points, matrix of size (dim,nc).
% 
%   k	: Knot sequence, row vector of size nk.
% 
%   t	: Raise the B-Spline degree t times.
% 
%   ic	: Control points of the new B-Spline.
% 
%   ik	: Knot vector of the new B-Spline.
% 
% Description:
% 
%   Degree elevate a univariate B-Spline. This function provides an
%   interface to a toolbox 'C' routine.

[mc,nc] = size(c);
                                                          %
                                                          % int bspdegelev(int d, double *c, int mc, int nc, double *k, int nk,
                                                          %                int t, int *nh, double *ic, double *ik)
                                                          % {
                                                          %   int row,col;
                                                          %
                                                          %   int ierr = 0;
                                                          %   int i, j, q, s, m, ph, ph2, mpi, mh, r, a, b, cind, oldr, mul;
                                                          %   int n, lbz, rbz, save, tr, kj, first, kind, last, bet, ii;
                                                          %   double inv, ua, ub, numer, den, alf, gam;
                                                          %   double **bezalfs, **bpts, **ebpts, **Nextbpts, *alfs;
                                                          %
                                                          %   double **ctrl  = vec2mat(c, mc, nc);
% ic = zeros(mc,nc*(t));                                  %   double **ictrl = vec2mat(ic, mc, nc*(t+1));
                                                          %
n = nc - 1;                                               %   n = nc - 1;
                                                          %
bezalfs =  zeros(d+1,d+t+1);                              %   bezalfs = matrix(d+1,d+t+1);
bpts = zeros(mc,d+1);                                     %   bpts = matrix(mc,d+1);
ebpts = zeros(mc,d+t+1);                                  %   ebpts = matrix(mc,d+t+1);
Nextbpts = zeros(mc,d+1);                                 %   Nextbpts = matrix(mc,d+1);
alfs = zeros(d,1);                                        %   alfs = (double *) mxMalloc(d*sizeof(double));
                                                          %
m = n + d + 1;                                            %   m = n + d + 1;
ph = d + t;                                               %   ph = d + t;
ph2 = floor(ph / 2);                                      %   ph2 = ph / 2;
                                                          %
                                                          %   // compute bezier degree elevation coefficeients
bezalfs(1,1) = 1;                                         %   bezalfs[0][0] = bezalfs[ph][d] = 1.0;
bezalfs(d+1,ph+1) = 1;                                    %

for i=1:ph2                                               %   for (i = 1; i <= ph2; i++) {
   inv = 1/bincoeff(ph,i);                                %     inv = 1.0 / bincoeff(ph,i);
   mpi = min(d,i);                                        %     mpi = min(d,i);
                                                          %
   for j=max(0,i-t):mpi                                   %     for (j = max(0,i-t); j <= mpi; j++)
       bezalfs(j+1,i+1) = inv*bincoeff(d,j)*bincoeff(t,i-j);  %       bezalfs[i][j] = inv * bincoeff(d,j) * bincoeff(t,i-j);
   end                                                       
end                                                       %   }
                                                          %
for i=ph2+1:ph-1                                          %   for (i = ph2+1; i <= ph-1; i++) {
   mpi = min(d,i);                                        %     mpi = min(d, i);
   for j=max(0,i-t):mpi                                   %     for (j = max(0,i-t); j <= mpi; j++)
       bezalfs(j+1,i+1) = bezalfs(d-j+1,ph-i+1);          %       bezalfs[i][j] = bezalfs[ph-i][d-j];
   end                                                       
end                                                       %   }
                                                          %
mh = ph;                                                  %   mh = ph;      
kind = ph+1;                                              %   kind = ph+1;
r = -1;                                                   %   r = -1;
a = d;                                                    %   a = d;
b = d+1;                                                  %   b = d+1;
cind = 1;                                                 %   cind = 1;
ua = k(1);                                                %   ua = k[0]; 
                                                          %
for ii=0:mc-1                                             %   for (ii = 0; ii < mc; ii++)
   ic(ii+1,1) = c(ii+1,1);                                %     ictrl[0][ii] = ctrl[0][ii];
end                                                       %
for i=0:ph                                                %   for (i = 0; i <= ph; i++)
   ik(i+1) = ua;                                          %     ik[i] = ua;
end                                                       %
                                                          %   // initialise first bezier seg
for i=0:d                                                 %   for (i = 0; i <= d; i++)
   for ii=0:mc-1                                          %     for (ii = 0; ii < mc; ii++)
      bpts(ii+1,i+1) = c(ii+1,i+1);                       %       bpts[i][ii] = ctrl[i][ii];
   end                                                       
end                                                       %
                                                          %   // big loop thru knot vector
while b < m                                               %   while (b < m)  {
   i = b;                                                 %     i = b;
   while b < m && k(b+1) == k(b+2)                        %     while (b < m && k[b] == k[b+1])
      b = b + 1;                                          %       b++;
   end                                                    %
   mul = b - i + 1;                                       %     mul = b - i + 1;
   mh = mh + mul + t;                                     %     mh += mul + t;
   ub = k(b+1);                                           %     ub = k[b];
   oldr = r;                                              %     oldr = r;
   r = d - mul;                                           %     r = d - mul;
                                                          %
                                                          %     // insert knot u(b) r times
   if oldr > 0                                            %     if (oldr > 0)
      lbz = floor((oldr+2)/2);                            %       lbz = (oldr+2) / 2;
   else                                                   %     else
      lbz = 1;                                            %       lbz = 1;
   end                                                    %
   
   if r > 0                                               %     if (r > 0)
      rbz = ph - floor((r+1)/2);                          %       rbz = ph - (r+1)/2;
   else                                                   %     else
      rbz = ph;                                           %       rbz = ph;
   end                                                    %
   
   if r > 0                                               %     if (r > 0) {
                                                          %       // insert knot to get bezier segment
      numer = ub - ua;                                    %       numer = ub - ua;
      for q=d:-1:mul+1                                    %       for (q = d; q > mul; q--)
         alfs(q-mul) = numer / (k(a+q+1)-ua);             %         alfs[q-mul-1] = numer / (k[a+q]-ua);
      end                                           
      
      for j=1:r                                           %       for (j = 1; j <= r; j++)  {
         save = r - j;                                    %         save = r - j;
         s = mul + j;                                     %         s = mul + j;
                                                          %
         for q=d:-1:s                                     %         for (q = d; q >= s; q--)
            for ii=0:mc-1                                 %           for (ii = 0; ii < mc; ii++)
               tmp1 = alfs(q-s+1)*bpts(ii+1,q+1); 
               tmp2 = (1-alfs(q-s+1))*bpts(ii+1,q); 
               bpts(ii+1,q+1) = tmp1 + tmp2;              %             bpts[q][ii] = alfs[q-s]*bpts[q][ii]+(1.0-alfs[q-s])*bpts[q-1][ii];
            end                                              
         end                                              %
         
         for ii=0:mc-1                                    %         for (ii = 0; ii < mc; ii++)
            Nextbpts(ii+1,save+1) = bpts(ii+1,d+1);       %           Nextbpts[save][ii] = bpts[d][ii];
         end                                                 
      end                                                 %       }