Home > Matching_SYM_LSM > src > Functions > Splines > LSM_fy_cubic_interpolation.m

LSM_fy_cubic_interpolation

PURPOSE ^

B-spline interpolation x-derivative

SYNOPSIS ^

function zx=LSM_fy_cubic_interpolation(x,y,f)

DESCRIPTION ^

 B-spline interpolation x-derivative

 f   = N x M array of function values 
 x,y = real coordinates \in [2:N-2,2:M-1]

 zx   = interpolated value of x-gradient

 wf 08/2012

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function zx=LSM_fy_cubic_interpolation(x,y,f)
0002 % B-spline interpolation x-derivative
0003 %
0004 % f   = N x M array of function values
0005 % x,y = real coordinates \in [2:N-2,2:M-1]
0006 %
0007 % zx   = interpolated value of x-gradient
0008 %
0009 % wf 08/2012
0010 
0011 i=floor(x);
0012 j=floor(y);
0013 u=x-i;
0014 v=y-j;
0015 p=[1 u u^2 u^3]';
0016 q=[1 v v^2 v^3]';
0017 M=  1/2*[  0  2  0  0 ;
0018          -1  0  1  0;
0019           2 -5  4 -1;
0020          -1  3 -3  1];
0021 M1= 1/2*[  -1   0   1   0;
0022            4 -10   8  -2;
0023           -3   9  -9   3;
0024            0   0   0   0];  
0025 Fij = [f(i-1,j-1), f(i-1,j), f(i-1,j+1), f(i-1,j+2);...
0026        f(i  ,j-1), f(i  ,j), f(i  ,j+1), f(i  ,j+2);...
0027        f(i+1,j-1), f(i+1,j), f(i+1,j+1), f(i+1,j+2);...
0028        f(i+2,j-1), f(i+2,j), f(i+2,j+1), f(i+2,j+2);...
0029         ];   
0030 zx=p'*M*Fij*M1'*q;
0031 end

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