/usr/share/octave/packages/nurbs-1.3.10/curvederiveval.m is in octave-nurbs 1.3.10-1.
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 | function ck = curvederiveval (n, p, U, P, u, d)
%
% CURVEDERIVEVAL: Compute the derivatives of a B-spline curve.
%
% usage: ck = curvederiveval (n, p, U, P, u, d)
%
% INPUT:
%
% n+1 = number of control points
% p = spline order
% U = knots
% P = control points
% u = evaluation point
% d = derivative order
%
% OUTPUT:
%
% ck (k+1) = curve differentiated k times
%
% Adaptation of algorithm A3.4 from the NURBS book, pg99
%
% Copyright (C) 2009 Carlo de Falco
% Copyright (C) 2010 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/>.
ck = zeros (d+1, 1);
du = min (d, p);
span = findspan (n, p, u, U);
N = zeros (p+1, p+1);
for ip=0:p
N(1:ip+1,ip+1) = basisfun (span, u, ip, U)';
end
pk = curvederivcpts (n, p, U, P, du, span-p, span);
for k = 0:du
for j = 0:p-k
ck(k+1) = ck(k+1) + N(j+1,p-k+1)*pk(k+1,j+1);
end
end
end
%!test
%! k = [0 0 0 1 1 1];
%! coefs(:,1) = [0;0;0;1];
%! coefs(:,2) = [1;0;1;1];
%! coefs(:,3) = [1;1;1;1];
%! crv = nrbmak (coefs, k);
%! ck = curvederiveval (crv.number-1, crv.order-1, crv.knots, squeeze (crv.coefs(1,:,:)), 0.5, 2);
%! assert(ck, [0.75; 1; -2]);
%! ck = curvederiveval (crv.number-1, crv.order-1, crv.knots, squeeze (crv.coefs(2,:,:)), 0.5, 2);
%! assert(ck, [0.25; 1; 2]);
%! ck = curvederiveval (crv.number-1, crv.order-1, crv.knots, squeeze (crv.coefs(3,:,:)), 0.5, 2);
%! assert(ck, [0.75; 1; -2]);
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