function [x_i,y_i] = line_intersect_c(A1,B1,C1,A2,B2,C2)
% function [x_i,y_i] = line_intersect_c(A1,B1,C1,A2,B2,C2)
% This function checks to see if two lines,
% both in the plane z = 0, intersect.
% If they do, it returns the coordinates of the
% point of intersection and plots the point.
% If the lines don't intersect, it returns values of
% Inf (infinity) for x and y, and no plot is produced.
% Input parameters
% A1, B1, C1 = coefficients of equation for line 1
% (A1)(x) + (B1)(y) = C1
% A2, B2, C2 = coefficients of equation for line 2
% (A2)(x) + (B2)(y) = C2
% The equations of the lines are
% A1.*x + B1.*y = C1
% A2.*x + B2.*y = C2
% or, in matrix form [A][X] = [B]
% |A1 B1| |x| = |C1|
% |A2 B2| |y| = |C2|
% Example
% [x_i,y_i] = line_intersect_c(1,2,3,4,5,6)
% Name: Steve Martel
% Date: 9/15/04

% Set up matrices for simultaneous linear equations 
A = [A1 B1;A2 B2];
B = [C1;C2]
% Find the solution for the point of intersection [X]
X = A\B;
x_i = X(1);
y_i = X(2);

% Plot the intersection, extending the lines a bit from that point
% Prepare two subplots, the first showing the x- and y- intercepts
% of the lines, the second showing their intersection
x_int_1 = C1./A1;
x_int_2 = C2./A2;
y_int_1 = C1./B1;
y_int_2 = C2./B2;

figure(1)
clf
subplot(1,2,1)
plot([x_int_1 0],[0 y_int_1],'b',[x_int_2 0],[0 y_int_2],'r')
title (['Lines intersect at x = ',num2str(x_i),' y = ',num2str(y_i)])
xlabel('x')
ylabel('y')
    
subplot(1,2,2)
plot(x_i,y_i,'+')
title (['Lines intersect at x = ',num2str(x_i),' y = ',num2str(y_i)])
xlabel('x')
ylabel('y')