using System;

namespace Assistance {
	public struct Point {
		public static readonly double precision = 0.01;

		public double x;
		public double y;

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

		public static Point operator+ (Point a, Point b) {
			return new Point(a.x + b.x, a.y + b.y);
		}

		public static Point operator- (Point a, Point b) {
			return new Point(a.x - b.x, a.y - b.y);
		}

		public static Point operator* (Point a, double b) {
			return new Point(a.x*b, a.y*b);
		}

		public static Point operator* (double b, Point a) {
			return a*b;
		}

		public static Point operator/ (Point a, double b) {
			return new Point(a.x/b, a.y/b);
		}

		public static double dot(Point a, Point b) {
			return a.x*b.x + a.y*b.y;
		}

		public bool isEqual(Point other) {
			return (this - other).lenSqr() <= precision*precision;
		}

		public double lenSqr() {
			return x*x + y*y;
		}

		public double len() {
			return Math.Sqrt(lenSqr());
		}

		public Point normalize() {
			double l = len();
			return l > precision*precision*precision ? this/l : this;
		}

		public System.Drawing.PointF toFloat() {
			return new System.Drawing.PointF((float)x, (float)y);
		}

		public System.Drawing.Point toInt() {
			return new System.Drawing.Point((int)Math.Floor(x), (int)Math.Floor(y));
		}
	}
}