/usr/share/octave/packages/nurbs-1.3.7/bspdegelev.m is in octave-nurbs 1.3.7-1build1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 | function [ic,ik] = bspdegelev(d,c,k,t)
% BSPDEGELEV: Degree elevate a univariate B-Spline.
%
% Calling Sequence:
%
% [ic,ik] = bspdegelev(d,c,k,t)
%
% INPUT:
%
% 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.
%
% OUTPUT:
%
% ic - Control points of the new B-Spline.
% ik - Knot vector of the new B-Spline.
%
% Copyright (C) 2000 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 3 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/>.
[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 % }
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);
end % }
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)));
end % }
function f = factln(n)
% computes ln(n!)
if n <= 1, f = 0; return, end
f = gammaln(n+1); %log(factorial(n));
end
|