main/src/georegression/metric/Intersection2D_F64.java
public static Point2D_F64 intersection( LineSegment2D_F64 l_0, LineSegment2D_F64 l_1,
											Point2D_F64 ret ) {

		double a0 = l_0.b.x - l_0.a.x;
		double b0 = l_0.b.y - l_0.a.y;
		double a1 = l_1.b.x - l_1.a.x;
		double b1 = l_1.b.y - l_1.a.y;

		double top = b0 * ( l_1.a.x - l_0.a.x ) + a0 * ( l_0.a.y - l_1.a.y );
		double bottom = a0 * b1 - b0 * a1;

		if( bottom == 0 )
			return null;
		double t_1 = top / bottom;

		// does not intersect along the second line segment
		if( t_1 < 0 || t_1 > 1 )
			return null;

		top = b1 * ( l_0.a.x - l_1.a.x ) + a1 * ( l_1.a.y - l_0.a.y );
		bottom = a1 * b0 - b1 * a0;

		double t_0 = top / bottom;

		// does not intersect along the first line segment
		if( t_0 < 0 || t_0 > 1 )
			return null;

		if( ret == null ) {
			ret = new Point2D_F64();
		}

		ret.set( l_1.a.x + a1 * t_1, l_1.a.y + b1 * t_1 );

		return ret;
	}
public static Point2D_F64 intersection( LineSegment2D_F64 l_0, LineSegment2D_F64 l_1,
											Point2D_F64 ret ) {

		double a0 = l_0.b.x - l_0.a.x;
		double b0 = l_0.b.y - l_0.a.y;
		double a1 = l_1.b.x - l_1.a.x;
		double b1 = l_1.b.y - l_1.a.y;

		double top = b0 * ( l_1.a.x - l_0.a.x ) + a0 * ( l_0.a.y - l_1.a.y );
		double bottom = a0 * b1 - b0 * a1;

		if( bottom == 0 )
			return null;
		double t_1 = top / bottom;

		// does not intersect along the second line segment
		if( t_1 < 0 || t_1 > 1 )
			return null;

		top = b1 * ( l_0.a.x - l_1.a.x ) + a1 * ( l_1.a.y - l_0.a.y );
		bottom = a1 * b0 - b1 * a0;

		double t_0 = top / bottom;

		// does not intersect along the first line segment
		if( t_0 < 0 || t_0 > 1 )
			return null;

		if( ret == null ) {
			ret = new Point2D_F64();
		}

		ret.set( l_1.a.x + a1 * t_1, l_1.a.y + b1 * t_1 );

		return ret;
	}
Finds the point of intersection between two lines segments.

@param l_0 Line segment.
@param l_1 line segment.
@param ret storage for the point of intersection. If null a new point will be declared.
@return If the two lines intersect it returns the point of intersection.  null if they don't intersect or have infinite intersections.