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annotate +grid/bspline.m @ 1037:2d7ba44340d0 feature/burgers1d

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Pass scheme specific parameters as cell array. This will enabale constructDiffOps to be more general. In addition, allow for schemes returning function handles as diffOps, which is currently how non-linear schemes such as Burgers1d are implemented.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 18 Jan 2019 09:02:02 +0100
parents 4f7930d2d2c4
children
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4f7930d2d2c4 Added function to calculate bspline.
Jonatan Werpers <jonatan@werpers.com>
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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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6
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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