using System;

namespace Assistance {

	public struct Point {

		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() <= Geometry.precision*Geometry.precision; }

		public double lenSqr()

			{ return x*x + y*y; }

		public double len()

			{ return Math.Sqrt(lenSqr()); }

		public Point normalize() {

			double l = len();

			return l > Geometry.precision*Geometry.precision ? this/l : this;

		}

		public Point rotate(double angle) {

			double s = Math.Sin(angle);

			double c = Math.Cos(angle);

			return new Point(c*x - s*y, s*x + c*y);

		}

	}

}