drawNURBSKnotInsertion.m

%
% Project: Approximation and Finite Elements in Isogeometric Problems
% Author:  Luca Carlon
% Date:    2009.11.30
%
% 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/>.
%

% Definition of the control points.
P = [1, 0; 1, 1; 0, 1; -1, 1; -1, 0; -1, -1; 0, -1; 1, -1; 1, 0];
% Definition of the weigths.
w = [1, 1./sqrt(2), 1, 1./sqrt(2), 1, 1./sqrt(2), 1, 1./sqrt(2), 1];
% Weighted control points.
Pw(:, 1) = P(:, 1).*w';
Pw(:, 2) = P(:, 2).*w';
Pw(:, 3) = w';
% Definition of the knot vector.
Xi = [0, 0, 0, 0.25, 0.25, 0.5, 0.5, 0.75, 0.75, 1, 1, 1];
% Variable.
xi = linspace(0, 1, 1000);
% Deinition of the scalars.
n = 8;
p = 2;

subplot(2, 2, 1);
hold on;
axis([-1.5, 1.5, -1.5, 1.5]);
grid on;
box on;
title('(a)');
xlabel('x');
ylabel('y');
drawNURBSCurve(n, p, Xi, Pw);

subplot(2, 2, 3);
hold on;
grid on;
box on;
title('(b)');
s = sprintf('R_{i}^{%d}, i=0,...,%d', p, n);
xlabel('\xi');
ylabel(s);
drawNURBSBasisFuns(n, p, Xi, w);

[nBarP, barXi, barPw] = curveKnotIns(n, p, Xi, Pw, 0.6, 6, 0, 1);
[nBarP, barXi, barPw] = curveKnotIns(nBarP, p, barXi, barPw, 0.3, 4, 0, 1);

subplot(2, 2, 2);
hold on;
axis([-1.5, 1.5, -1.5, 1.5]);
grid on;
box on;
title('(c)');
xlabel('x');
ylabel('y');
drawNURBSCurve(nBarP, p, barXi, barPw);

subplot(2, 2, 4);
hold on;
grid on;
box on;
title('(d)');
s = sprintf('R_{i}^{%d}, i=0,...,%d', p, n);
xlabel('\xi');
ylabel(s);
drawNURBSBasisFuns(nBarP, p, barXi, barPw(1:end, 3)');