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function [ A B C D ] = h3coeff( T, x0, t0, x1, t1, h1 )

%HERMITE Summary of this function goes here

%   Detailed explanation goes here



[ A B C D ] = h3coeff_D( T, x0, t0, x1, t1, h1 );



end



function [ A B C D ] = h3coeff_A( T, x0, t0, x1, t1 )



A = x0;

B = t0;

D = t0+t1+2*(x0-x1);

C = x1-x0-t0-D;



end



function [ A B C D ] = h3coeff_B( T, x0, t0, x1, t1 )



A = x0;

B = t0;

D = (h1*(t1+t0)+2*(x0-x1))/(h1*h1*h1);

C = (x1-x0-h1*t0-D*h1*h1*h1)/(h1*h1);



end



function [ A B C D ] = h3coeff_C( T, x0, t0, x1, t1 )



h1  = (x1-x0)'*T;

x1  = x1 - h1*T;



dh0 = T'*t0;

dh1 = T'*t1;



x0s = t0/dh0-T;

x1s = t1/dh1-T;



A = x0;

B = x0s+T;

D = (h1*(x1s+x0s)+2*(x0-x1))/(h1*h1*h1);

C = (x1-x0-h1*x0s-D*h1*h1*h1)/(h1*h1);



end



function [ A B C D ] = h3coeff_D( T, x0, t0, x1, t1, hh )



T = t0+t1;

T = T/norm(T);



DX = (x1-x0)';

%t0 = t0*(DX*T);

%t1 = t1*(DX*T);

t0 = t0*hh;

t1 = t1*hh;



A = x0;

B = t0;

D = t0+t1+2*(x0-x1);

C = x1-x0-t0-D;



end