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annotate +grid/bspline.m @ 577:e45c9b56d50d feature/grids

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Add an Empty grid class The need turned up for the flexural code when we may or may not have a grid for the open water and want to plot that solution. In case there is no open water we need an empty grid to plot the empty gridfunction against to avoid errors.
author Jonatan Werpers <jonatan@werpers.com>
date Thu, 07 Sep 2017 09:16:12 +0200
parents 4f7930d2d2c4
children
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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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15 C = zeros(D,length(t));
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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