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annotate +grid/bspline.m @ 774:66eb4a2bbb72 feature/grids

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Remove default scaling of the system. The scaling doens't seem to help actual solutions. One example that fails in the flexural code. With large timesteps the solutions seems to blow up. One particular example is profilePresentation on the tdb_presentation_figures branch with k = 0.0005
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 18 Jul 2018 15:42:52 -0700
parents 4f7930d2d2c4
children
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4f7930d2d2c4 Added function to calculate bspline.
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1 % Calculates a D dimensional p-order bspline at t with knots T and control points P.
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2 % T = [t0 t1 t2 ... tm] is a 1 x (m+1) vector with non-decresing elements and t0 = 0 tm = 1.
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3 % P = [P0 P1 P2 ... Pn] is a D x (n+1) matrix.
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4
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5 % knots p+1 to m-p-1 are the internal knots
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7 % Implemented from: http://mathworld.wolfram.com/B-Spline.html
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8 function C = bspline(t,p,P,T)
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9 m = length(T) - 1;
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10 n = size(P,2) - 1;
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11 D = size(P,1);
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12
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13 assert(p == m - n - 1);
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14
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15 C = zeros(D,length(t));
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16
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17 for i = 0:n
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18 for k = 1:D
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19 C(k,:) = C(k,:) + P(k,1+i)*B(i,p,t,T);
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20 end
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21 end
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22
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23 % Curve not defined for t = 1 ? Ugly fix:
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24 I = find(t == 1);
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25 C(:,I) = repmat(P(:,end),[1,length(I)]);
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26 end
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27
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28 function o = B(i, j, t, T)
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29 if j == 0
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30 o = T(1+i) <= t & t < T(1+i+1);
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31 return
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32 end
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33
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34 if T(1+i+j)-T(1+i) ~= 0
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35 a = (t-T(1+i))/(T(1+i+j)-T(1+i));
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36 else
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37 a = t*0;
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38 end
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39
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40 if T(1+i+j+1)-T(1+i+1) ~= 0
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41 b = (T(1+i+j+1)-t)/(T(1+i+j+1)-T(1+i+1));
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42 else
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43 b = t*0;
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44 end
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45
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46 o = a.*B(i, j-1, t, T) + b.*B(i+1, j-1, t, T);
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47 end