Far out intersection points for lines which are almost parallel

I am plotting a large number of connected edges on a canvas, all of which are arranged in a way that some specific extension to these edges always gives an intersection point with another extended edge. This point is needed for further calculations - it is not relevant in the context of what appears on the canvas. My code works great for the general case, but if the edge's respective extensions go far out, the intersections do not always exist (however, the lines are not parallel) - at least not within the scope of this program. Does anyone have any ideas to improve the precision of this code? I am actually working with BigDecimals later, but for the plotting steps I initially thought it would suffice to use double.

This one extends the edge to both sides:

public Line2D.Double ExteLine(Point2D p, Point2D q){
   double slope, y3, y4;
   slope = (q.getY() - p.getY())/(q.getX() - p.getX());
   y3 = (slope * (100000 - p.getX())) + p.getY();
   y4 = (slope * (-100000 - p.getX())) + p.getY();
   Point2D out1 = new Point2D.Double(100000, y3);
   Point2D out2 = new Point2D.Double(-100000, y4);
   Line2D.Double line = new Line2D.Double(out1, out2);
   return line; }

This one finds the intersection:

public Point2D.Double getIntersectionPoint(Line2D.Double line1, Line2D.Double line2) {
if (! line1.intersectsLine(line2)) { 
  System.out.println("No intersection"); 
  return null;} 
  double s1 = line1.getX1(),
        sp2 = line1.getY1(),
        rx = line1.getX2()-s1,
        ry = line1.getY2()-sp2;
  double qx = line2.getX1(),
        qy = line2.getY1(),
        sx = line2.getX2()-qx,
        sy = line2.getY2()-qy;
  double det = sx*ry - sy*rx;
  if (det == 0) { System.out.println("Det = 0");
    return null;} 
  else {
    double z = (sx*(qy-sp2)+sy*(s1-qx))/det;
    if (z==0 ||  z==1) return null;  
    return new Point2D.Double(
      (double)(s1+z*rx), (double)(sp2+z*ry));
  }
}