% Compute the JACOBIAN of the transformation x,y --> ji,nu
% QUADRILATERAL ELEMENT
% input1: chi=[chi(1) chi(2)]=[ji nu] where the Jacobian will be evaluated
% input2: global node coordinates [x1;y1;x2;y2;x3;y3;x4;y4]
% output: jacobian matrix 2x2  [dx/dji dx/dnu;dy/dji dy/dnu];

function jaco=jacobian_2D4N(chi,xnod)
% N1=(1/4)*(1-ji)*(1-nu)
% N2=(1/4)*(1+ji)*(1-nu)
% N3=(1/4)*(1-ji)*(1+nu)
% N4=(1/4)*(1+ji)*(1+nu)
  ji=chi(1);nu=chi(2);
  d1_N1=-(1/4)*(1-nu);      % derivada de N1 respecto de ji
  d2_N1=-(1/4)*(1-ji);      % derivada de N1 respecto de nu
  d1_N2=+(1/4)*(1-nu);      % ...
  d2_N2=-(1/4)*(1+ji);
  d1_N3=+(1/4)*(1+nu);
  d2_N3=+(1/4)*(1+ji);
  d1_N4=-(1/4)*(1+nu);
  d2_N4=+(1/4)*(1-ji);
  
  jaco=zeros(2,2);
  jaco(1,1)=[d1_N1 0 d1_N2 0 d1_N3 0 d1_N4 0]*xnod;  % dx/dji
  jaco(2,1)=[0 d1_N1 0 d1_N2 0 d1_N3 0 d1_N4]*xnod;  % dy/dji
  jaco(1,2)=[d2_N1 0 d2_N2 0 d2_N3 0 d2_N4 0]*xnod;  % dx/dnu
  jaco(2,2)=[0 d2_N1 0 d2_N2 0 d2_N3 0 d2_N4]*xnod;  % dy/dnu
return