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annotate +grid/bspline.m @ 1198:2924b3a9b921 feature/d2_compatible

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Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
author Martin Almquist <malmquist@stanford.edu>
date Fri, 16 Aug 2019 14:30:28 -0700
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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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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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