1 function [ic,ik] = bspkntins(d,c,k,u)
3 % BSPKNTINS: Insert knots into a B-Spline
7 % [ic,ik] = bspkntins(d,c,k,u)
11 % d - spline degree integer
12 % c - control points double matrix(mc,nc)
13 % k - knot sequence double vector(nk)
14 % u - new knots double vector(nu)
18 % ic - new control points double matrix(mc,nc+nu)
19 % ik - new knot sequence double vector(nk+nu)
21 % Modified version of Algorithm A5.4 from 'The NURBS BOOK' pg164.
23 % Copyright (C) 2000 Mark Spink, 2007 Daniel Claxton, 2010 Rafael Vazquez
25 % This program is free software: you can redistribute it and/or modify
26 % it under the terms of the GNU General Public License as published by
27 % the Free Software Foundation, either version 2 of the License, or
28 % (at your option) any later version.
30 % This program is distributed in the hope that it will be useful,
31 % but WITHOUT ANY WARRANTY; without even the implied warranty of
32 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
33 % GNU General Public License for more details.
35 % You should have received a copy of the GNU General Public License
36 % along with this program. If not, see <http://www.gnu.org/licenses/>.
43 % int bspkntins(int d, double *c, int mc, int nc, double *k, int nk,
44 % double *u, int nu, double *ic, double *ik)
47 % int a, b, r, l, i, j, m, n, s, q, ind;
50 % double **ctrl = vec2mat(c, mc, nc);
51 ic = zeros(mc,nc+nu); % double **ictrl = vec2mat(ic, mc, nc+nu);
54 n = size(c,2) - 1; % n = nc - 1;
55 r = length(u) - 1; % r = nu - 1;
57 m = n + d + 1; % m = n + d + 1;
58 a = findspan(n, d, u(1), k); % a = findspan(n, d, u[0], k);
59 b = findspan(n, d, u(r+1), k); % b = findspan(n, d, u[r], k);
62 for q=0:mc-1 % for (q = 0; q < mc; q++) {
63 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];
64 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];
67 for j=0:a, ik(j+1) = k(j+1); end % for (j = 0; j <= a; j++) ik[j] = k[j];
68 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];
70 i = b + d - 1; % i = b + d - 1;
71 s = b + d + r; % s = b + d + r;
73 for j=r:-1:0 % for (j = r; j >= 0; j--) {
74 while u(j+1) <= k(i+1) && i > a % while (u[j] <= k[i] && i > a) {
75 for q=0:mc-1 % for (q = 0; q < mc; q++)
76 ic(q+1,s-d) = c(q+1,i-d); % ictrl[s-d-1][q] = ctrl[i-d-1][q];
78 ik(s+1) = k(i+1); % ik[s] = k[i];
83 for q=0:mc-1 % for (q = 0; q < mc; q++)
84 ic(q+1,s-d) = ic(q+1,s-d+1); % ictrl[s-d-1][q] = ictrl[s-d][q];
87 for l=1:d % for (l = 1; l <= d; l++) {
88 ind = s - d + l; % ind = s - d + l;
89 alfa = ik(s+l+1) - u(j+1); % alfa = ik[s+l] - u[j];
90 if abs(alfa) == 0 % if (fabs(alfa) == 0.0)
91 for q=0:mc-1 % for (q = 0; q < mc; q++)
92 ic(q+1,ind) = ic(q+1,ind+1); % ictrl[ind-1][q] = ictrl[ind][q];
95 alfa = alfa/(ik(s+l+1) - k(i-d+l+1)); % alfa /= (ik[s+l] - k[i-d+l]);
96 for q=0:mc-1 % for (q = 0; q < mc; q++)
97 tmp = (1-alfa)*ic(q+1,ind+1);
98 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];
103 ik(s+1) = u(j+1); % ik[s] = u[j];
108 % freevec2mat(ictrl);