function [a1,b1,a0,b0] = Conformal_2D(x_input,y_input,X_output,Y_output)
%%
% Calculates parameters $a,b,a_0,b_0$ in the following equation using least
% squares
%%
%
% $$X=a_1x+b_1y+a_0$$
%
% $$X=-b_1x+a_1y+b_0$$
%%
% *Arguments:*
%
% x_input is a $ntimes 1$ matrix containing x coordinate of control points
% in the input space
%
% y_input is a $ntimes 1$ matrix containing y coordinate of control points
% in the input space
%
% x_output is a $ntimes 1$ matrix containing x coordinate of control points
% in the output space
%
% y_output is a $ntimes 1$ matrix containing y coordinate of control points
% in the output space
%%
NumberOfPoints = size(x_input,1);
A = zeros(2*NumberOfPoints,1); % Coefficient matrix in AX = L
L = zeros(2*NumberOfPoints,1); % Right-hand matrix in AX = L
    for i = 1:NumberOfPoints
        A(2*i-1,1:4) = [x_input(i,1) y_input(i,1) 1 0];
    end
end