/usr/share/octave/packages/nurbs-1.3.7/nrbcrvderiveval.m is in octave-nurbs 1.3.7-1build1.
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 | % NRBCRVDERIVEVAL: Evaluate n-th order derivatives of a NURBS curve.
%
% usage: skl = nrbcrvderiveval (crv, u, d)
%
% INPUT:
%
% crv : NURBS curve structure, see nrbmak
%
% u : parametric coordinate of the points where we compute the derivatives
%
% d : number of partial derivatives to compute
%
%
% OUTPUT:
%
% ck (i, j, l) = i-th component derived j-1 times at the l-th point.
%
% Adaptation of algorithm A4.2 from the NURBS book, pg127
%
% Copyright (C) 2010 Carlo de Falco, 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/>.
function ck = nrbcrvderiveval (crv, u, d)
ck = arrayfun (@(x) nrbcrvderiveval__ (crv, x, d), u, 'UniformOutput', false);
ck = cat (3, ck{:});
end
function ck = nrbcrvderiveval__ (crv, u, d)
persistent nc;
if isempty (nc)
nc = [0 0 0 0 0;
1 0 0 0 0;
2 1 0 0 0;
3 3 1 0 0;
4 6 4 1 0];
end
ck = zeros (3, d+1);
wders = curvederiveval (crv.number-1, crv.order-1, crv.knots, squeeze (crv.coefs(4, :)), u, d);
for idim = 1:3
Aders = curvederiveval (crv.number-1, crv.order-1, crv.knots, squeeze (crv.coefs(idim, :)), u, d);
ck(idim, 1) = Aders(1) / wders(1);
for k = 1:d
ck(idim, k+1) = (Aders(k+1) - sum (nc(k+1, 1:k) .* wders(2:k+1).' .* squeeze (ck(idim, k:-1:1)))) / wders(1);
end
end
end
%!test
%! knots = [0 0 0 1 1 1];
%! coefs(:,1) = [0; 0; 0; 1];
%! coefs(:,2) = [1; 0; 1; 1];
%! coefs(:,3) = [1; 1; 1; 2];
%! crv = nrbmak (coefs, knots);
%! u = linspace (0, 1, 100);
%! ck = nrbcrvderiveval (crv, u, 2);
%! w = @(x) 1 + x.^2;
%! dw = @(x) 2*x;
%! F1 = @(x) (2*x - x.^2)./w(x);
%! F2 = @(x) x.^2./w(x);
%! F3 = @(x) (2*x - x.^2)./w(x);
%! dF1 = @(x) (2 - 2*x)./w(x) - 2*(2*x - x.^2).*x./w(x).^2;
%! dF2 = @(x) 2*x./w(x) - 2*x.^3./w(x).^2;
%! dF3 = @(x) (2 - 2*x)./w(x) - 2*(2*x - x.^2).*x./w(x).^2;
%! d2F1 = @(x) -2./w(x) - 2*x.*(2-2*x)./w(x).^2 - (8*x-6*x.^2)./w(x).^2 + 8*x.^2.*(2*x-x.^2)./w(x).^3;
%! d2F2 = @(x) 2./w(x) - 4*x.^2./w(x).^2 - 6*x.^2./w(x).^2 + 8*x.^4./w(x).^3;
%! d2F3 = @(x) -2./w(x) - 2*x.*(2-2*x)./w(x).^2 - (8*x-6*x.^2)./w(x).^2 + 8*x.^2.*(2*x-x.^2)./w(x).^3;
%! assert ([F1(u); F2(u); F3(u)], squeeze(ck(:, 1, :)), 1e2*eps);
%! assert ([dF1(u); dF2(u); dF3(u)], squeeze(ck(:, 2, :)), 1e2*eps);
%! assert ([d2F1(u); d2F2(u); d2F3(u)], squeeze(ck(:, 3, :)), 1e2*eps);
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