/usr/share/octave/packages/nurbs-1.3.10/surfderiveval.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 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 | function skl = surfderiveval (n, p, U, m, q, V, P, u, v, d)
%
% SURFDERIVEVAL: Compute the derivatives of a B-spline surface
%
% usage: skl = surfderiveval (n, p, U, m, q, V, P, u, v, d)
%
% INPUT:
%
% n+1, m+1 = number of control points
% p, q = spline order
% U, V = knots
% P = control points
% u,v = evaluation points
% d = derivative order
%
% OUTPUT:
%
% skl (k+1, l+1) = surface differentiated k
% times in the u direction and l
% times in the v direction
%
% Adaptation of algorithm A3.8 from the NURBS book, pg115
%
% Copyright (C) 2009 Carlo de Falco
%
% 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/>.
skl = zeros (d+1, d+1);
du = min (d, p);
dv = min (d, q);
uspan = findspan (n, p, u, U);
for ip=0:p
Nu(1:ip+1,ip+1) = basisfun (uspan, u, ip, U)';
end
vspan = findspan (m, q, v, V);
for ip=0:q
Nv(1:ip+1,ip+1) = basisfun (vspan, v, ip, V)';
end
pkl = surfderivcpts (n, p, U, m, q, V, P, d, uspan-p, uspan, ...
vspan-q, vspan);
for k = 0:du
dd = min (d-k, dv);
for l = 0:dd
skl(k+1,l+1) =0;
for i=0:q-l
tmp = 0;
for j = 0:p-k
tmp = tmp + Nu(j+1,p-k+1) * pkl(k+1,l+1,j+1,i+1);
end
skl(k+1,l+1) = skl(k+1,l+1) + Nv(i+1,q-l+1)*tmp;
end
end
end
end
%!shared srf
%!test
%! k = [0 0 0 1 1 1];
%! c = [0 1/2 1];
%! [coef(2,:,:), coef(1,:,:)] = meshgrid (c, c);
%! srf = nrbmak (coef, {k, k});
%! skl = surfderiveval (srf.number(1)-1, ...
%! srf.order(1)-1, ...
%! srf.knots{1}, ...
%! srf.number(2)-1, ...
%! srf.order(2)-1, ...
%! srf.knots{2},...
%! squeeze(srf.coefs(1,:,:)), .5, .5, 1) ;
%! assert (skl, [.5 0; 1 0])
%!test
%! srf = nrbkntins (srf, {[], rand(1,2)});
%! skl = surfderiveval (srf.number(1)-1,...
%! srf.order(1)-1, ...
%! srf.knots{1},...
%! srf.number(2)-1,...
%! srf.order(2)-1, ...
%! srf.knots{2},...
%! squeeze(srf.coefs(1,:,:)), .5, .5, 1) ;
%! assert (skl, [.5 0; 1 0], 100*eps)
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