public class Main extends  Application {




    private double[] makeLineEquation(Point2D a1, Point2D a2){
        double A = a1.getY() - a2.getY();
        double B = a2.getX() - a1.getX();
        double C = a1.getX() * a2.getY() - a2.getX() * a1.getY();

       System.out.println(A + "x + " + B + "y + " + C + " = 0");
       return new double[] {A, B, C};
    }

    private boolean isLineCrossesEllipse(Point2D a1, Point2D a2, Ellipse ellipse){
        //(x1-x0)^2/a^2 + (y1-y0)^2/b^2 < 1
       // (x2-x0)^2/a^2 + (y2-y0)^2/b^2 > 1
      double x1 = Math.pow(a1.getX() - ellipse.getCenterX(),2) / Math.pow(ellipse.getRadiusX(),2);
      double y1 = Math.pow(a1.getY() - ellipse.getCenterY(),2) / Math.pow(ellipse.getRadiusY(),2);

      double x2 = Math.pow(a2.getX() - ellipse.getCenterX(),2) / Math.pow(ellipse.getRadiusX(),2);
      double y2 = Math.pow(a2.getY() - ellipse.getCenterY(),2) / Math.pow(ellipse.getRadiusY(),2);

      //(x1-x0)^2/a^2 + (y1-y0)^2/b^2 > 1
      // (x2-x0)^2/a^2 + (y2-y0)^2/b^2 < 1

      if(x1 + y1 <1 && x2 + y2 >1 || x1 + y1 >1 && x2 + y2 <1)
          return  true;

        return false;
    }
    private Point2D pointBelongsSegment(Point2D interP1, Point2D interP2, Point2D segP1,
                                        Point2D segP2){
       //if((interP1.getX() - segP1.getX()) * (segP2.getY() - segP1.getY()) -
         //      (interP1.getY() - segP1.getY()) * (segP2.getX() - segP1.getX())==0 ){
           if(interP1.getX() > segP1.getX() && interP1.getX() < segP2.getX() ||
                   interP1.getX() > segP2.getX() && interP1.getX() < segP1.getX() )
               return interP1;
           else return interP2;

    }

    public Point2D interactionPoints(Point2D a1, Point2D a2, Ellipse ellipse){

        double [] coefs = makeLineEquation(a1, a2);
        double A = coefs[0];
        double B = coefs [1];
        double C = coefs[2];

        double A1;
        double B1;
        double C1;

        double D;
        double y1;
        double y2;
        double x1;
        double x2;

        double a = ellipse.getRadiusX();
        double b = ellipse.getRadiusY();
        double x0 = ellipse.getCenterX();
        double y0 = ellipse.getCenterY();
        System.out.println("A = " + A + " B = " + B + " C = " + C);


        if (isLineCrossesEllipse(a1,a2, ellipse)) {
            if (A == 0) {

                A1 = b*b;
                B1 = - 2*x0*b*b;
                C1 = b*b*x0*x0 + a*a*C*C / (B*B) + 2*y0*a*a*C/B + a*a*y0*y0 - a*a*b*b;

                D = Math.sqrt(Math.pow(B1, 2) - 4 * A1 * C1);
                x1 = (- B1 + D)/ (2 * A1);
                x2 = (- B1 - D)/ (2 * A1);
                y1 = - C/B;
                y2 = y1;

                System.out.println("IF x1 y1 = " + x1 + " " + y1 + " x2 y2 = " + x2 + " " + y2);
            }
            else {

                A1 = Math.pow((b * B) / A, 2) + Math.pow(a, 2);

                B1 = (Math.pow(b, 2) * 2 * B * C) / Math.pow(A, 2) + (Math.pow(b, 2) * 2 * B * x0) / A -
                        Math.pow(a, 2) * 2 * y0;

                C1 = Math.pow(a * y0, 2) - Math.pow(a * b, 2) + Math.pow(b * x0, 2) +
                        (2 * x0 * C * Math.pow(b, 2)) / A + Math.pow((b * C) / A, 2);


                D = Math.sqrt(Math.pow(B1, 2) - 4 * A1 * C1);
                y1 = (-B1 + D) / (2 * A1);
                y2 = (-B1 - D) / (2 * A1);
                x1 = (-C - B * y1) / A;
                x2 = (-C - B * y2) / A;
                System.out.println("x1 y1 = " + x1 + " " + y1 + " x2 y2 = " + x2 + " " + y2);

            }
            Point2D interactionP = pointBelongsSegment(new Point2D(x1,y1),
                    new Point2D(x2,y2),a1,a2);
            System.out.println("interaction point is x: " + interactionP.getX()
                    + " y: " + interactionP.getY());
            return interactionP;
        }
        else {


      System.out.println("Any interections or 2 interection");


        }

                    return new Point2D(0,0);



    }



    @Override
    public void start(Stage stage) throws Exception {
        HBox hbox = new HBox();
        stage.setScene(new Scene(hbox));
        stage.sizeToScene();
        stage.show();

        Ellipse ellipse = new Ellipse();
        ellipse.setCenterX(3);
        ellipse.setCenterY(0);
        ellipse.setRadiusX(3);
        ellipse.setRadiusY(2);

      Point2D  a1 = new Point2D(-2,1); //center of first ellipse
      Point2D  a2 = new Point2D(3,1); //center of second ellipse

        interactionPoints(a1, a2, ellipse);

    }
}