/usr/share/octave/packages/nurbs-1.3.13/basisfunder.m is in octave-nurbs 1.3.13-4.
This file is owned by root:root, with mode 0o644.
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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 | function dersv = basisfunder (ii, pl, uu, u_knotl, nders)
% BASISFUNDER: B-Spline Basis function derivatives.
%
% Calling Sequence:
%
% ders = basisfunder (ii, pl, uu, k, nd)
%
% INPUT:
%
% ii - knot span index (see findspan)
% pl - degree of curve
% uu - parametric points
% k - knot vector
% nd - number of derivatives to compute
%
% OUTPUT:
%
% ders - ders(n, i, :) (i-1)-th derivative at n-th point
%
% Adapted from Algorithm A2.3 from 'The NURBS BOOK' pg72.
%
% See also:
%
% numbasisfun, basisfun, findspan
%
% Copyright (C) 2009,2011 Rafael Vazquez
%
% 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/>.
dersv = zeros(numel(uu), nders+1, pl+1);
for jj = 1:numel(uu)
i = ii(jj)+1; %% convert to base-1 numbering of knot spans
u = uu(jj);
ders = zeros(nders+1,pl+1);
ndu = zeros(pl+1,pl+1);
left = zeros(pl+1);
right = zeros(pl+1);
a = zeros(2,pl+1);
ndu(1,1) = 1;
for j = 1:pl
left(j+1) = u - u_knotl(i+1-j);
right(j+1) = u_knotl(i+j) - u;
saved = 0;
for r = 0:j-1
ndu(j+1,r+1) = right(r+2) + left(j-r+1);
temp = ndu(r+1,j)/ndu(j+1,r+1);
ndu(r+1,j+1) = saved + right(r+2)*temp;
saved = left(j-r+1)*temp;
end
ndu(j+1,j+1) = saved;
end
for j = 0:pl
ders(1,j+1) = ndu(j+1,pl+1);
end
for r = 0:pl
s1 = 0;
s2 = 1;
a(1,1) = 1;
for k = 1:nders %compute kth derivative
d = 0;
rk = r-k;
pk = pl-k;
if (r >= k)
a(s2+1,1) = a(s1+1,1)/ndu(pk+2,rk+1);
d = a(s2+1,1)*ndu(rk+1,pk+1);
end
if (rk >= -1)
j1 = 1;
else
j1 = -rk;
end
if ((r-1) <= pk)
j2 = k-1;
else
j2 = pl-r;
end
for j = j1:j2
a(s2+1,j+1) = (a(s1+1,j+1) - a(s1+1,j))/ndu(pk+2,rk+j+1);
d = d + a(s2+1,j+1)*ndu(rk+j+1,pk+1);
end
if (r <= pk)
a(s2+1,k+1) = -a(s1+1,k)/ndu(pk+2,r+1);
d = d + a(s2+1,k+1)*ndu(r+1,pk+1);
end
ders(k+1,r+1) = d;
j = s1;
s1 = s2;
s2 = j;
end
end
r = pl;
for k = 1:nders
for j = 0:pl
ders(k+1,j+1) = ders(k+1,j+1)*r;
end
r = r*(pl-k);
end
dersv(jj, :, :) = ders;
end
end
%!test
%! k = [0 0 0 0 1 1 1 1];
%! p = 3;
%! u = rand (1);
%! i = findspan (numel(k)-p-2, p, u, k);
%! ders = basisfunder (i, p, u, k, 1);
%! sumders = sum (squeeze(ders), 2);
%! assert (sumders(1), 1, 1e-15);
%! assert (sumders(2:end), 0, 1e-15);
%!test
%! k = [0 0 0 0 1/3 2/3 1 1 1 1];
%! p = 3;
%! u = rand (1);
%! i = findspan (numel(k)-p-2, p, u, k);
%! ders = basisfunder (i, p, u, k, 7);
%! sumders = sum (squeeze(ders), 2);
%! assert (sumders(1), 1, 1e-15);
%! assert (sumders(2:end), zeros(rows(squeeze(ders))-1, 1), 1e-13);
%!test
%! k = [0 0 0 0 1/3 2/3 1 1 1 1];
%! p = 3;
%! u = rand (100, 1);
%! i = findspan (numel(k)-p-2, p, u, k);
%! ders = basisfunder (i, p, u, k, 7);
%! for ii=1:10
%! sumders = sum (squeeze(ders(ii,:,:)), 2);
%! assert (sumders(1), 1, 1e-15);
%! assert (sumders(2:end), zeros(rows(squeeze(ders(ii,:,:)))-1, 1), 1e-13);
%! end
%! assert (ders(:, (p+2):end, :), zeros(numel(u), 8-p-1, p+1), 1e-13)
%! assert (all(all(ders(:, 1, :) <= 1)), true)
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