public class Point extends Complex{

  public Point() {
    x = 0.0;
    y = 0.0;
  }

  public Point(double xVal, double yVal) {
    x = xVal;
    y = yVal;
    if (x == 1.0/0.0 || x == -1.0/0.0 || x == Double.NaN
     || y == 1.0/0.0 || y == -1.0/0.0 || y == Double.NaN) {
      System.out.println("  Point undefined: "+this);
      Point Q = null;
      Q.x = 3.0;
    }
  }

  public String toString() {
    return "("+x+","+y+")";
  }

 /* Reflect the point A through this point B to get the returned point C.
  * The rule for computing A thru B (as complex numbers) is:		|
  *
  *            B - t A	         where t = (1+BB')/2, and
  * A |> B = -----------               B' is the complex
  *           t -  A B'                conjugate of B
  */
  public Point reflect (Point A) {
    double t = (1.0 + this.normSquared()) / 2.0;
    // compute the numerator as  B - t * A
    Complex numerator = this.minus(A.times(t));
    // compute the denominator as  t - A * B'
    Complex denominator = Complex.subtract(t, A.times(this.conjugate())) ;
    Complex C = numerator.over(denominator) ;
    return new Point(C.x,C.y);
  }

} // Point