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annotate +grid/bspline.m @ 1031:2ef20d00b386 feature/advectionRV

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For easier comparison, return both the first order and residual viscosity when evaluating the residual. Add the first order and residual viscosity to the state of the RungekuttaRV time steppers
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 17 Jan 2019 10:25:06 +0100
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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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