%%%%%%%%%%%%%%%%%%%%%%%%%%%% Same Side  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% SAMESIDE
% Usage: SAMESIDE(tri,X)
%
% Inputs:  tri - a triangle [P Q R] 
%          X   - a point   
%   
% Output:  returns 1 if R and X  are on the same side of the segment [P Q]
%          returns 0 otherwise     

function w = sameside(tri,X)             
%flops(0); f= []; t0 =clock; et =[];
   I = sqrt(-1);
   x = tri(1); 
   y = tri(2); 
   z = tri(3);
   m = (x+y)/2;                   % midpoint of Euclidean segment
   d = I*(x-y)/2;                 % vector orthogonal to vector to segment
   u = abs(m);                    % calculate some scalars 
   v = abs(d);                     
   rt = 2*real(m*conj(d))/(u^2-v^2-1);    
   s = rt/(1+sqrt(1+rt^2));              
   mc = m+s*d;                    % (euclidean) midpoint of H-segment       
   L = lft([x mc y], [-1 0 1]);   % LFT mapping H-segment to interval [-1 1]
   w  = imag(lftact(L,z));
   if (w < 0) L = [I 0; 0 -I]*L; end;     
   w = imag(lftact(L,X));