--- /dev/null
+function [N, Nder] = tbasisfun (u, p, U)
+%
+% TBASISFUN: Compute a B- or T-Spline basis function, and its derivatives, from its local knot vector.
+%
+% usage:
+%
+% [N, Nder] = tbasisfun (u, p, U)
+% [N, Nder] = tbasisfun ([u; v], [p q], {U, V})
+% [N, Nder] = tbasisfun ([u; v; w], [p q r], {U, V, W})
+%
+% INPUT:
+%
+% u or [u; v] : points in parameter space where the basis function is to be
+% evaluated
+%
+% U or {U, V} : local knot vector
+%
+% p or [p q] : polynomial order of the basis function
+%
+% OUTPUT:
+%
+% N : basis function evaluated at the given parametric points
+% Nder : basis function gradient evaluated at the given parametric points
+%
+% Copyright (C) 2009 Carlo de Falco
+% Copyright (C) 2012 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/>.
+
+ if (~ iscell (U))
+ U = sort (U);
+ if (numel (U) ~= p+2)
+ error ('tbasisfun: knot vector and degree do not correspond')
+ end
+
+ if (nargout == 1)
+ N = onebasisfun__ (u, p, U);
+ else
+ [N, Nder] = onebasisfunder__ (u, p, U);
+ end
+
+ elseif (size(U,2) == 2)
+ U{1} = sort(U{1}); U{2} = sort(U{2});
+ if (numel(U{1}) ~= p(1)+2 || numel(U{2}) ~= p(2)+2)
+ error ('tbasisfun: knot vector and degree do not correspond')
+ end
+
+ if (nargout == 1)
+ Nu = onebasisfun__ (u(1,:), p(1), U{1});
+ Nv = onebasisfun__ (u(2,:), p(2), U{2});
+
+ N = Nu.*Nv;
+ elseif (nargout == 2)
+ [Nu, Ndu] = onebasisfunder__ (u(1,:), p(1), U{1});
+ [Nv, Ndv] = onebasisfunder__ (u(2,:), p(2), U{2});
+
+ N = Nu.*Nv;
+ Nder(1,:) = Ndu.*Nv;
+ Nder(2,:) = Nu.*Ndv;
+ end
+
+ elseif (size(U,2) == 3)
+ U{1} = sort(U{1}); U{2} = sort(U{2}); U{3} = sort(U{3});
+ if (numel(U{1}) ~= p(1)+2 || numel(U{2}) ~= p(2)+2 || numel(U{3}) ~= p(3)+2)
+ error ('tbasisfun: knot vector and degree do not correspond')
+ end
+
+ if (nargout == 1)
+ Nu = onebasisfun__ (u(1,:), p(1), U{1});
+ Nv = onebasisfun__ (u(2,:), p(2), U{2});
+ Nw = onebasisfun__ (u(3,:), p(3), U{3});
+
+ N = Nu.*Nv.*Nw;
+ else
+ [Nu, Ndu] = onebasisfunder__ (u(1,:), p(1), U{1});
+ [Nv, Ndv] = onebasisfunder__ (u(2,:), p(2), U{2});
+ [Nw, Ndw] = onebasisfunder__ (u(3,:), p(3), U{3});
+
+ N = Nu.*Nv.*Nw;
+ Nder(1,:) = Ndu.*Nv.*Nw;
+ Nder(2,:) = Nu.*Ndv.*Nw;
+ Nder(3,:) = Nu.*Nv.*Ndw;
+ end
+ end
+
+end
+
+%!demo
+%! U = {[0 0 1/2 1 1], [0 0 0 1 1]};
+%! p = [3, 3];
+%! [X, Y] = meshgrid (linspace(0, 1, 30));
+%! u = [X(:), Y(:)]';
+%! N = tbasisfun (u, p, U);
+%! surf (X, Y, reshape (N, size(X)))
+%! title('Basis function associated to a local knot vector')
+%! hold off
+
+%!test
+%! U = [0 1/2 1];
+%! p = 1;
+%! u = [0.3 0.4 0.6 0.7];
+%! [N, Nder] = tbasisfun (u, p, U);
+%! assert (N, [0.6 0.8 0.8 0.6], 1e-12);
+%! assert (Nder, [2 2 -2 -2], 1e-12);
+
+%!test
+%! U = {[0 1/2 1] [0 1/2 1]};
+%! p = [1 1];
+%! u = [0.3 0.4 0.6 0.7; 0.3 0.4 0.6 0.7];
+%! [N, Nder] = tbasisfun (u, p, U);
+%! assert (N, [0.36 0.64 0.64 0.36], 1e-12);
+%! assert (Nder, [1.2 1.6 -1.6 -1.2; 1.2 1.6 -1.6 -1.2], 1e-12);
+
+%!test
+%! U = {[0 1/2 1] [0 1/2 1] [0 1/2 1]};
+%! p = [1 1 1];
+%! u = [0.4 0.4 0.6 0.6; 0.4 0.4 0.6 0.6; 0.4 0.6 0.4 0.6];
+%! [N, Nder] = tbasisfun (u, p, U);
+%! assert (N, [0.512 0.512 0.512 0.512], 1e-12);
+%! assert (Nder, [1.28 1.28 -1.28 -1.28; 1.28 1.28 -1.28 -1.28; 1.28 -1.28 1.28 -1.28], 1e-12);
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