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drawBsplineBasisDerivs.m
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drawBsplineBasisDerivs.m
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%
% Project: Approximation and Finite Elements in Isogeometric Problems
% Author: Luca Carlon
% Date: 2009.11.20
%
% Copyright (c) 2009-2021 Luca Carlon. All rights reserved.
%
% 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 [xi] = drawBsplineBasisDerivs(Xi, p)
% Draw the basis functions.
subplot(2, 1, 1);
hold on;
box on;
grid on;
title('(a)');
axis([Xi(1), Xi(end), 0, 1]);
n = length(Xi) - p - 2;
for i = 0:n
xi = Xi(1):0.01:Xi(end);
for j = 1:length(xi)
y(j) = computeBsplineBasis(p, n+p+1, Xi, i, xi(j));
end
for j = 1:length(xi)-1
if y(1, j) ~= 0 && y(1, j+1) ~= 0
plot([xi(1, j), xi(1, j+1)], [y(1, j), y(1, j+1)], 'Color', hsv2rgb([i/(n+1), 1, 1]));
end
end
clear y;
clear x;
[s, err] = sprintf('N_{i}^{%d}, i=0,...,%d', p, n);
ylabel(s);
xlabel('\xi');
end
% Draws the derivatives.
subplot(2, 1, 2);
hold on;
box on;
grid on;
title('(b)');
axis([Xi(1), Xi(end), -2, 2]);
n = length(Xi) - p - 2;
for i = 0:n
xi = Xi(1):0.01:Xi(end);
for j = 1:length(xi)
y(j) = computeBsplineBasisDeriv(p, Xi, i, xi(j), 1)(2);
end
for j = 2:(length(xi) - 2)
if y(j) ~= 0
if y(j+1) ~= 0
plot([xi(j), xi(j+1)], [y(j), y(j+1)], 'Color', hsv2rgb([i/(n+1), 1, 1]));
end
end
end
clear y;
clear x;
[s, err] = sprintf('N_{i}^{%d}'', i=0,...,%d', p, n);
ylabel(s);
xlabel('\xi');
end
endfunction