--- /dev/null
+function ck = nrbcrvderiveval (crv, u, d)
+
+%
+% 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 2 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 (3, d+1, numel(u));
+
+ for iu = 1:numel(u);
+ wders = squeeze (curvederiveval (crv.number-1, crv.order-1, ...
+ crv.knots, squeeze (crv.coefs(4, :)), u(iu), d));
+
+ for idim = 1:3
+ Aders = squeeze (curvederiveval (crv.number-1, crv.order-1, ...
+ crv.knots, squeeze (crv.coefs(idim, :)), u(iu), d));
+ for k=0:d
+ v = Aders(k+1);
+ for i=1:k
+ v = v - nchoosek(k,i)*wders(i+1)*ck(idim, k-i+1, iu);
+ end
+ ck(idim, k+1, iu) = v/wders(1);
+ end
+ 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, 10);
+%! 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);