Point.java

class Point {

	final int x;
	final int y;

	public Point(int x, int y) {
		this.x = x;
		this.y = y;
	}

	public Point scale(double scale) {
		return new Point((int) (x * scale), (int) (y* scale));
	}

	public Point normalizeVs(Point center) {
		return new Point(x - center.x, y - center.y);
	}
	
	public int distance(Point to) {
		return (int) sqrt((x - to.x) * (x -to.x) + (y - to.y) * (y - to.y));
	}

	static int det(Point p1, Point p2) {
		return p1.x * p2.y - p1.y * p2.x;
	}

	
	@Override
	public String toString() {
		
		return x + "-" + y;
	}

	public Point add(Point vector) {
		return new Point(x + vector.x, y + vector.y);
	}

	/**
	 * @param p1
	 * @param p2
	 * @param q1
	 * @param q2
	 * @return angle in degrees between vector [p1->p2] and [q1->q2] in range (-180, 180)
	 */
	public static float angle(Point p1, Point p2, Point q1, Point q2) {
		Point w1 = p2.normalizeVs(p1);
		Point w2 = q2.normalizeVs(q1);
		float radian = (float) (atan2(w1.y, w1.x) - atan2(w2.y, w2.x));
		if (radian < - PI) radian += 2 * PI;
		return (float) (radian / (PI/180));
	}
	
	public static float angle(Point p1, Point p2, Point p3) {
		return angle(p1, p2, p2, p3);
	}
	
	
	public static float angle(Point p1, Point p2) {
		Point w1 = p2.normalizeVs(p1);
		return angle(w1);
	}
	
	/**
	 * @param w1
	 * @return angle in degrees between vector w1 and axis x in range (-180, 180)
	 */
	public static float angle(Point w1) {
		float radian = (float) atan2(w1.y, w1.x);
		if (radian < - PI) radian += 2 * PI;
		return (float) (radian / (PI/180));
	}

	public static Point rotate(Point p1, Point p2, int angle) {
		Point w1 = p2.normalizeVs(p1);
		float radian = (float) toRadians(angle);
		int x = (int) (w1.x * cos(radian) - w1.y * sin(radian));
	    int y = (int)(w1.x * sin(radian) + w1.y * cos(radian)) ;
		return p1.add(new Point(x, y));
	}


}