package cse1030.drawing;

public class Spiro {

  /**
   * The greatest common divisor of two positive integers computed using the
   * Euclidean algorithm.
   * 
   * @param p
   *          an integer greater than zero
   * @param q
   *          an integer greater than zero
   * @return the greatest common divisor of <code>p</code> and <code>q</code>
   */
  private static int gcd(int p, int q) {
    while (p != q) {
      if (p > q) {
        p = p - q;
      } else {
        q = q - p;
      }
    }
    return p;
  }

  /**
   * Computes the number of times that the innermost circle must travel around
   * the fixed circle to complete the hypotrochoid pattern. The innermost circle
   * has radius <code>p / q</code> and the fixed circle has radius
   * <code>1</code>.
   * 
   * @param p
   *          together with <code>q</code> defines the radius of the innermost
   *          circle
   * @param q
   *          together with <code>p</code> defines the radius of the innermost
   *          circle
   * @return the number of times that the innermost circle must travel around
   *         the fixed circle for a complete hypotrochoid
   */
  public static int numberOfRevolutions(int p, int q) {
    if (p <= 0) {
      throw new IllegalArgumentException("p must be greater than zero");
    }
    if (q <= 0) {
      throw new IllegalArgumentException("q must be greater than zero");
    }
    int g = Spiro.gcd(p, q);
    return (p / g);
  }

  /**
   * Draws a hypotrochoid using the command line arguments to define the
   * parameters of the hypotrochoid.
   * 
   * @param args
   *          requires 3 arguments (an <code>int</code>, an <code>int</code>,
   *          and a <code>double</code>.
   *          <p>
   *          The first two parameters, <code>P</code> and <code>Q</code>,
   *          define the radius, <code>r</code>, of the inner circle (
   *          <code>r = P / Q</code>). The second parameter, <code>H</code>,
   *          defines the distance from the center of the inner circle to
   *          the tip of the pencil.
   */
  public static void main(String[] args) {
    final int P = Integer.parseInt(args[0]);
    final int Q = Integer.parseInt(args[1]);
    final double H = Double.parseDouble(args[2]);
    final int N = Spiro.numberOfRevolutions(P, Q);

    // here is how you draw an IPoint2D 
    IPoint2D point = new IPoint2D(0., 0.);
    SimpleDrawing.drawPoint(point);
    
    // YOUR CODE SHOULD GO AFTER THIS COMMENT



  }

}