CypherCore/Source/Framework/GameMath/Vector2.cs

/*
 * Copyright (C) 2012-2019 CypherCore <http://github.com/CypherCore>
 * Copyright (C) 2003-2004  Eran Kampf	eran@ekampf.com	http://www.ekampf.com
 * 
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Diagnostics;
using System.Runtime.InteropServices;
using System.Text.RegularExpressions;

namespace Framework.GameMath
{
    /// <summary>
    /// Represents 2-Dimentional vector of single-precision floating point numbers.
    /// </summary>
    [Serializable]
    [StructLayout(LayoutKind.Sequential)]
    [TypeConverter(typeof(Vector2FConverter))]
    public struct Vector2 : ICloneable
    {
        #region Private fields
        private float _x;
        private float _y;
        #endregion

        #region Constructors
        /// <summary>
        /// Initializes a new instance of the <see cref="Vector2"/> class with the specified coordinates.
        /// </summary>
        /// <param name="x">The vector's X coordinate.</param>
        /// <param name="y">The vector's Y coordinate.</param>
        public Vector2(float x, float y)
        {
            _x = x;
            _y = y;
        }
        /// <summary>
        /// Initializes a new instance of the <see cref="Vector2"/> class with the specified coordinates.
        /// </summary>
        /// <param name="coordinates">An array containing the coordinate parameters.</param>
        public Vector2(float[] coordinates)
        {
            Debug.Assert(coordinates != null);
            Debug.Assert(coordinates.Length >= 2);

            _x = coordinates[0];
            _y = coordinates[1];
        }
        /// <summary>
        /// Initializes a new instance of the <see cref="Vector2"/> class with the specified coordinates.
        /// </summary>
        /// <param name="coordinates">An array containing the coordinate parameters.</param>
        public Vector2(List<float> coordinates)
        {
            Debug.Assert(coordinates != null);
            Debug.Assert(coordinates.Count >= 2);

            _x = coordinates[0];
            _y = coordinates[1];
        }
        /// <summary>
        /// Initializes a new instance of the <see cref="Vector2"/> class using coordinates from a given <see cref="Vector2"/> instance.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> to get the coordinates from.</param>
        public Vector2(Vector2 vector)
        {
            _x = vector.X;
            _y = vector.Y;
        }
        #endregion

        #region Constants
        /// <summary>
        /// 4-Dimentional single-precision floating point zero vector.
        /// </summary>
        public static readonly Vector2 Zero = new Vector2(0.0f, 0.0f);
        /// <summary>
        /// 4-Dimentional single-precision floating point X-Axis vector.
        /// </summary>
        public static readonly Vector2 XAxis = new Vector2(1.0f, 0.0f);
        /// <summary>
        /// 4-Dimentional single-precision floating point Y-Axis vector.
        /// </summary>
        public static readonly Vector2 YAxis = new Vector2(0.0f, 1.0f);
        #endregion

        #region Public properties
        /// <summary>
        /// Gets or sets the x-coordinate of this vector.
        /// </summary>
        /// <value>The x-coordinate of this vector.</value>
        public float X
        {
            get { return _x; }
            set { _x = value; }
        }
        /// <summary>
        /// Gets or sets the y-coordinate of this vector.
        /// </summary>
        /// <value>The y-coordinate of this vector.</value>
        public float Y
        {
            get { return _y; }
            set { _y = value; }
        }
        #endregion

        #region ICloneable Members
        /// <summary>
        /// Creates an exact copy of this <see cref="Vector2"/> object.
        /// </summary>
        /// <returns>The <see cref="Vector2"/> object this method creates, cast as an object.</returns>
        object ICloneable.Clone()
        {
            return new Vector2(this);
        }
        /// <summary>
        /// Creates an exact copy of this <see cref="Vector2"/> object.
        /// </summary>
        /// <returns>The <see cref="Vector2"/> object this method creates.</returns>
        public Vector2 Clone()
        {
            return new Vector2(this);
        }
        #endregion

        #region Public Static Parse Methods
        /// <summary>
        /// Converts the specified string to its <see cref="Vector2"/> equivalent.
        /// </summary>
        /// <param name="value">A string representation of a <see cref="Vector2"/>.</param>
        /// <returns>A <see cref="Vector2"/> that represents the vector specified by the <paramref name="value"/> parameter.</returns>
        public static Vector2 Parse(string value)
        {
            Regex r = new Regex(@"\((?<x>.*),(?<y>.*)\)", RegexOptions.Singleline);
            Match m = r.Match(value);
            if (m.Success)
            {
                return new Vector2(
                    float.Parse(m.Result("${x}")),
                    float.Parse(m.Result("${y}"))
                    );
            }
            else
            {
                throw new Exception("Unsuccessful Match.");
            }
        }
        /// <summary>
        /// Converts the specified string to its <see cref="Vector2"/> equivalent.
        /// A return value indicates whether the conversion succeeded or failed.
        /// </summary>
        /// <param name="value">A string representation of a <see cref="Vector2"/>.</param>
        /// <param name="result">
        /// When this method returns, if the conversion succeeded,
        /// contains a <see cref="Vector2"/> representing the vector specified by <paramref name="value"/>.
        /// </param>
        /// <returns><see langword="true"/> if value was converted successfully; otherwise, <see langword="false"/>.</returns>
        public static bool TryParse(string value, out Vector2 result)
        {
            Regex r = new Regex(@"\((?<x>.*),(?<y>.*)\)", RegexOptions.Singleline);
            Match m = r.Match(value);
            if (m.Success)
            {
                result = new Vector2(
                    float.Parse(m.Result("${x}")),
                    float.Parse(m.Result("${y}"))
                    );

                return true;
            }

            result = Vector2.Zero;
            return false;
        }
        #endregion

        #region Public Static Vector Arithmetics
        /// <summary>
        /// Adds two vectors.
        /// </summary>
        /// <param name="left">A <see cref="Vector2"/> instance.</param>
        /// <param name="right">A <see cref="Vector2"/> instance.</param>
        /// <returns>A new <see cref="Vector2"/> instance containing the sum.</returns>
        public static Vector2 Add(Vector2 left, Vector2 right)
        {
            return new Vector2(left.X + right.X, left.Y + right.Y);
        }
        /// <summary>
        /// Adds a vector and a scalar.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A single-precision floating-point number.</param>
        /// <returns>A new <see cref="Vector2"/> instance containing the sum.</returns>
        public static Vector2 Add(Vector2 vector, float scalar)
        {
            return new Vector2(vector.X + scalar, vector.Y + scalar);
        }
        /// <summary>
        /// Adds two vectors and put the result in the third vector.
        /// </summary>
        /// <param name="left">A <see cref="Vector2"/> instance.</param>
        /// <param name="right">A <see cref="Vector2"/> instance</param>
        /// <param name="result">A <see cref="Vector2"/> instance to hold the result.</param>
        public static void Add(Vector2 left, Vector2 right, ref Vector2 result)
        {
            result.X = left.X + right.X;
            result.Y = left.Y + right.Y;
        }
        /// <summary>
        /// Adds a vector and a scalar and put the result into another vector.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A single-precision floating-point number.</param>
        /// <param name="result">A <see cref="Vector2"/> instance to hold the result.</param>
        public static void Add(Vector2 vector, float scalar, ref Vector2 result)
        {
            result.X = vector.X + scalar;
            result.Y = vector.Y + scalar;
        }
        /// <summary>
        /// Subtracts a vector from a vector.
        /// </summary>
        /// <param name="left">A <see cref="Vector2"/> instance.</param>
        /// <param name="right">A <see cref="Vector2"/> instance.</param>
        /// <returns>A new <see cref="Vector2"/> instance containing the difference.</returns>
        /// <remarks>
        ///	result[i] = left[i] - right[i].
        /// </remarks>
        public static Vector2 Subtract(Vector2 left, Vector2 right)
        {
            return new Vector2(left.X - right.X, left.Y - right.Y);
        }
        /// <summary>
        /// Subtracts a scalar from a vector.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A single-precision floating-point number.</param>
        /// <returns>A new <see cref="Vector2"/> instance containing the difference.</returns>
        /// <remarks>
        /// result[i] = vector[i] - scalar
        /// </remarks>
        public static Vector2 Subtract(Vector2 vector, float scalar)
        {
            return new Vector2(vector.X - scalar, vector.Y - scalar);
        }
        /// <summary>
        /// Subtracts a vector from a scalar.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A single-precision floating-point number.</param>
        /// <returns>A new <see cref="Vector2"/> instance containing the difference.</returns>
        /// <remarks>
        /// result[i] = scalar - vector[i]
        /// </remarks>
        public static Vector2 Subtract(float scalar, Vector2 vector)
        {
            return new Vector2(scalar - vector.X, scalar - vector.Y);
        }
        /// <summary>
        /// Subtracts a vector from a second vector and puts the result into a third vector.
        /// </summary>
        /// <param name="left">A <see cref="Vector2"/> instance.</param>
        /// <param name="right">A <see cref="Vector2"/> instance</param>
        /// <param name="result">A <see cref="Vector2"/> instance to hold the result.</param>
        /// <remarks>
        ///	result[i] = left[i] - right[i].
        /// </remarks>
        public static void Subtract(Vector2 left, Vector2 right, ref Vector2 result)
        {
            result.X = left.X - right.X;
            result.Y = left.Y - right.Y;
        }
        /// <summary>
        /// Subtracts a vector from a scalar and put the result into another vector.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A single-precision floating-point number.</param>
        /// <param name="result">A <see cref="Vector2"/> instance to hold the result.</param>
        /// <remarks>
        /// result[i] = vector[i] - scalar
        /// </remarks>
        public static void Subtract(Vector2 vector, float scalar, ref Vector2 result)
        {
            result.X = vector.X - scalar;
            result.Y = vector.Y - scalar;
        }
        /// <summary>
        /// Subtracts a scalar from a vector and put the result into another vector.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A single-precision floating-point number.</param>
        /// <param name="result">A <see cref="Vector2"/> instance to hold the result.</param>
        /// <remarks>
        /// result[i] = scalar - vector[i]
        /// </remarks>
        public static void Subtract(float scalar, Vector2 vector, ref Vector2 result)
        {
            result.X = scalar - vector.X;
            result.Y = scalar - vector.Y;
        }
        /// <summary>
        /// Divides a vector by another vector.
        /// </summary>
        /// <param name="left">A <see cref="Vector2"/> instance.</param>
        /// <param name="right">A <see cref="Vector2"/> instance.</param>
        /// <returns>A new <see cref="Vector2"/> containing the quotient.</returns>
        /// <remarks>
        ///	result[i] = left[i] / right[i].
        /// </remarks>
        public static Vector2 Divide(Vector2 left, Vector2 right)
        {
            return new Vector2(left.X / right.X, left.Y / right.Y);
        }
        /// <summary>
        /// Divides a vector by a scalar.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A scalar</param>
        /// <returns>A new <see cref="Vector2"/> containing the quotient.</returns>
        /// <remarks>
        /// result[i] = vector[i] / scalar;
        /// </remarks>
        public static Vector2 Divide(Vector2 vector, float scalar)
        {
            return new Vector2(vector.X / scalar, vector.Y / scalar);
        }
        /// <summary>
        /// Divides a scalar by a vector.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A scalar</param>
        /// <returns>A new <see cref="Vector2"/> containing the quotient.</returns>
        /// <remarks>
        /// result[i] = scalar / vector[i]
        /// </remarks>
        public static Vector2 Divide(float scalar, Vector2 vector)
        {
            return new Vector2(scalar / vector.X, scalar / vector.Y);
        }
        /// <summary>
        /// Divides a vector by another vector.
        /// </summary>
        /// <param name="left">A <see cref="Vector2"/> instance.</param>
        /// <param name="right">A <see cref="Vector2"/> instance.</param>
        /// <param name="result">A <see cref="Vector2"/> instance to hold the result.</param>
        /// <remarks>
        /// result[i] = left[i] / right[i]
        /// </remarks>
        public static void Divide(Vector2 left, Vector2 right, ref Vector2 result)
        {
            result.X = left.X / right.X;
            result.Y = left.Y / right.Y;
        }
        /// <summary>
        /// Divides a vector by a scalar.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A scalar</param>
        /// <param name="result">A <see cref="Vector2"/> instance to hold the result.</param>
        /// <remarks>
        /// result[i] = vector[i] / scalar
        /// </remarks>
        public static void Divide(Vector2 vector, float scalar, ref Vector2 result)
        {
            result.X = vector.X / scalar;
            result.Y = vector.Y / scalar;
        }
        /// <summary>
        /// Divides a scalar by a vector.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A scalar</param>
        /// <param name="result">A <see cref="Vector2"/> instance to hold the result.</param>
        /// <remarks>
        /// result[i] = scalar / vector[i]
        /// </remarks>
        public static void Divide(float scalar, Vector2 vector, ref Vector2 result)
        {
            result.X = scalar / vector.X;
            result.Y = scalar / vector.Y;
        }
        /// <summary>
        /// Multiplies a vector by a scalar.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A single-precision floating-point number.</param>
        /// <returns>A new <see cref="Vector2"/> containing the result.</returns>
        public static Vector2 Multiply(Vector2 vector, float scalar)
        {
            return new Vector2(vector.X * scalar, vector.Y * scalar);
        }
        /// <summary>
        /// Multiplies a vector by a scalar and put the result in another vector.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A single-precision floating-point number.</param>
        /// <param name="result">A <see cref="Vector2"/> instance to hold the result.</param>
        public static void Multiply(Vector2 vector, float scalar, ref Vector2 result)
        {
            result.X = vector.X * scalar;
            result.Y = vector.Y * scalar;
        }
        /// <summary>
        /// Calculates the dot product of two vectors.
        /// </summary>
        /// <param name="left">A <see cref="Vector2"/> instance.</param>
        /// <param name="right">A <see cref="Vector2"/> instance.</param>
        /// <returns>The dot product value.</returns>
        public static float DotProduct(Vector2 left, Vector2 right)
        {
            return (left.X * right.X) + (left.Y * right.Y);
        }
        /// <summary>
        /// Calculates the Kross product of two vectors.
        /// </summary>
        /// <param name="left">A <see cref="Vector2"/> instance.</param>
        /// <param name="right">A <see cref="Vector2"/> instance.</param>
        /// <returns>The Kross product value.</returns>
        /// <remarks>
        /// <p>
        /// The Kross product is defined as:
        /// Kross(u,v) = u.X*v.Y - u.Y*v.X.
        /// </p>
        /// <p>
        /// The operation is related to the cross product in 3D given by (x0, y0, 0) X (x1, y1, 0) = (0, 0, Kross((x0, y0), (x1, y1))).
        /// The operation has the property that Kross(u, v) = -Kross(v, u).
        /// </p>
        /// </remarks>
        public static float KrossProduct(Vector2 left, Vector2 right)
        {
            return (left.X * right.Y) - (left.Y * right.X);
        }
        /// <summary>
        /// Negates a vector.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <returns>A new <see cref="Vector2"/> instance containing the negated values.</returns>
        public static Vector2 Negate(Vector2 vector)
        {
            return new Vector2(-vector.X, -vector.Y);
        }
        /// <summary>
        /// Tests whether two vectors are approximately equal using default tolerance value.
        /// </summary>
        /// <param name="left">A <see cref="Vector2"/> instance.</param>
        /// <param name="right">A <see cref="Vector2"/> instance.</param>
        /// <returns><see langword="true"/> if the two vectors are approximately equal; otherwise, <see langword="false"/>.</returns>
        public static bool ApproxEqual(Vector2 left, Vector2 right)
        {
            return ApproxEqual(left, right, MathFunctions.Epsilon);
        }
        /// <summary>
        /// Tests whether two vectors are approximately equal given a tolerance value.
        /// </summary>
        /// <param name="left">A <see cref="Vector2"/> instance.</param>
        /// <param name="right">A <see cref="Vector2"/> instance.</param>
        /// <param name="tolerance">The tolerance value used to test approximate equality.</param>
        /// <returns><see langword="true"/> if the two vectors are approximately equal; otherwise, <see langword="false"/>.</returns>
        public static bool ApproxEqual(Vector2 left, Vector2 right, float tolerance)
        {
            return
                (
                (System.Math.Abs(left.X - right.X) <= tolerance) &&
                (System.Math.Abs(left.Y - right.Y) <= tolerance)
                );
        }
        #endregion

        #region Public Methods
        /// <summary>
        /// Scale the vector so that its length is 1.
        /// </summary>
        public void Normalize()
        {
            float length = GetLength();
            if (length == 0)
            {
                throw new DivideByZeroException("Trying to normalize a vector with length of zero.");
            }

            _x /= length;
            _y /= length;
        }
        /// <summary>
        /// Calculates the length of the vector.
        /// </summary>
        /// <returns>Returns the length of the vector. (Sqrt(X*X + Y*Y))</returns>
        public float GetLength()
        {
            return (float)System.Math.Sqrt(_x * _x + _y * _y);
        }
        /// <summary>
        /// Calculates the squared length of the vector.
        /// </summary>
        /// <returns>Returns the squared length of the vector. (X*X + Y*Y)</returns>
        public float GetLengthSquared()
        {
            return (_x * _x + _y * _y);
        }
        /// <summary>
        /// Clamps vector values to zero using a given tolerance value.
        /// </summary>
        /// <param name="tolerance">The tolerance to use.</param>
        /// <remarks>
        /// The vector values that are close to zero within the given tolerance are set to zero.
        /// </remarks>
        public void ClampZero(float tolerance)
        {
            _x = MathFunctions.Clamp(_x, 0, tolerance);
            _y = MathFunctions.Clamp(_y, 0, tolerance);
        }
        /// <summary>
        /// Clamps vector values to zero using the default tolerance value.
        /// </summary>
        /// <remarks>
        /// The vector values that are close to zero within the given tolerance are set to zero.
        /// The tolerance value used is <see cref="MathFunctions.Epsilon"/>
        /// </remarks>
        public void ClampZero()
        {
            _x = MathFunctions.Clamp(_x, 0);
            _y = MathFunctions.Clamp(_y, 0);
        }
        #endregion

        #region System.Object Overrides
        /// <summary>
        /// Returns the hashcode for this instance.
        /// </summary>
        /// <returns>A 32-bit signed integer hash code.</returns>
        public override int GetHashCode()
        {
            return _x.GetHashCode() ^ _y.GetHashCode();
        }
        /// <summary>
        /// Returns a value indicating whether this instance is equal to
        /// the specified object.
        /// </summary>
        /// <param name="obj">An object to compare to this instance.</param>
        /// <returns><see langword="true"/> if <paramref name="obj"/> is a <see cref="Vector2"/> and has the same values as this instance; otherwise, <see langword="false"/>.</returns>
        public override bool Equals(object obj)
        {
            if (obj is Vector2)
            {
                Vector2 v = (Vector2)obj;
                return (_x == v.X) && (_y == v.Y);
            }
            return false;
        }
        /// <summary>
        /// Returns a string representation of this object.
        /// </summary>
        /// <returns>A string representation of this object.</returns>
        public override string ToString()
        {
            return $"({_x}, {_y})";
        }
        #endregion

        #region Comparison Operators
        /// <summary>
        /// Tests whether two specified vectors are equal.
        /// </summary>
        /// <param name="left">A <see cref="Vector2"/> instance.</param>
        /// <param name="right">A <see cref="Vector2"/> instance.</param>
        /// <returns><see langword="true"/> if the two vectors are equal; otherwise, <see langword="false"/>.</returns>
        public static bool operator ==(Vector2 left, Vector2 right)
        {
            return ValueType.Equals(left, right);
        }
        /// <summary>
        /// Tests whether two specified vectors are not equal.
        /// </summary>
        /// <param name="left">A <see cref="Vector2"/> instance.</param>
        /// <param name="right">A <see cref="Vector2"/> instance.</param>
        /// <returns><see langword="true"/> if the two vectors are not equal; otherwise, <see langword="false"/>.</returns>
        public static bool operator !=(Vector2 left, Vector2 right)
        {
            return !ValueType.Equals(left, right);
        }

        /// <summary>
        /// Tests if a vector's components are greater than another vector's components.
        /// </summary>
        /// <param name="left">A <see cref="Vector2"/> instance.</param>
        /// <param name="right">A <see cref="Vector2"/> instance.</param>
        /// <returns><see langword="true"/> if the left-hand vector's components are greater than the right-hand vector's component; otherwise, <see langword="false"/>.</returns>
        public static bool operator >(Vector2 left, Vector2 right)
        {
            return (
                (left._x > right._x) &&
                (left._y > right._y));
        }
        /// <summary>
        /// Tests if a vector's components are smaller than another vector's components.
        /// </summary>
        /// <param name="left">A <see cref="Vector2"/> instance.</param>
        /// <param name="right">A <see cref="Vector2"/> instance.</param>
        /// <returns><see langword="true"/> if the left-hand vector's components are smaller than the right-hand vector's component; otherwise, <see langword="false"/>.</returns>
        public static bool operator <(Vector2 left, Vector2 right)
        {
            return (
                (left._x < right._x) &&
                (left._y < right._y));
        }
        /// <summary>
        /// Tests if a vector's components are greater or equal than another vector's components.
        /// </summary>
        /// <param name="left">A <see cref="Vector2"/> instance.</param>
        /// <param name="right">A <see cref="Vector2"/> instance.</param>
        /// <returns><see langword="true"/> if the left-hand vector's components are greater or equal than the right-hand vector's component; otherwise, <see langword="false"/>.</returns>
        public static bool operator >=(Vector2 left, Vector2 right)
        {
            return (
                (left._x >= right._x) &&
                (left._y >= right._y));
        }
        /// <summary>
        /// Tests if a vector's components are smaller or equal than another vector's components.
        /// </summary>
        /// <param name="left">A <see cref="Vector2"/> instance.</param>
        /// <param name="right">A <see cref="Vector2"/> instance.</param>
        /// <returns><see langword="true"/> if the left-hand vector's components are smaller or equal than the right-hand vector's component; otherwise, <see langword="false"/>.</returns>
        public static bool operator <=(Vector2 left, Vector2 right)
        {
            return (
                (left._x <= right._x) &&
                (left._y <= right._y));
        }
        #endregion

        #region Unary Operators
        /// <summary>
        /// Negates the values of the given vector.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <returns>A new <see cref="Vector2"/> instance containing the negated values.</returns>
        public static Vector2 operator -(Vector2 vector)
        {
            return Vector2.Negate(vector);
        }
        #endregion

        #region Binary Operators
        /// <summary>
        /// Adds two vectors.
        /// </summary>
        /// <param name="left">A <see cref="Vector2"/> instance.</param>
        /// <param name="right">A <see cref="Vector2"/> instance.</param>
        /// <returns>A new <see cref="Vector2"/> instance containing the sum.</returns>
        public static Vector2 operator +(Vector2 left, Vector2 right)
        {
            return Vector2.Add(left, right);
        }
        /// <summary>
        /// Adds a vector and a scalar.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A single-precision floating-point number.</param>
        /// <returns>A new <see cref="Vector2"/> instance containing the sum.</returns>
        public static Vector2 operator +(Vector2 vector, float scalar)
        {
            return Vector2.Add(vector, scalar);
        }
        /// <summary>
        /// Adds a vector and a scalar.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A single-precision floating-point number.</param>
        /// <returns>A new <see cref="Vector2"/> instance containing the sum.</returns>
        public static Vector2 operator +(float scalar, Vector2 vector)
        {
            return Vector2.Add(vector, scalar);
        }
        /// <summary>
        /// Subtracts a vector from a vector.
        /// </summary>
        /// <param name="left">A <see cref="Vector2"/> instance.</param>
        /// <param name="right">A <see cref="Vector2"/> instance.</param>
        /// <returns>A new <see cref="Vector2"/> instance containing the difference.</returns>
        /// <remarks>
        ///	result[i] = left[i] - right[i].
        /// </remarks>
        public static Vector2 operator -(Vector2 left, Vector2 right)
        {
            return Vector2.Subtract(left, right);
        }
        /// <summary>
        /// Subtracts a scalar from a vector.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A single-precision floating-point number.</param>
        /// <returns>A new <see cref="Vector2"/> instance containing the difference.</returns>
        /// <remarks>
        /// result[i] = vector[i] - scalar
        /// </remarks>
        public static Vector2 operator -(Vector2 vector, float scalar)
        {
            return Vector2.Subtract(vector, scalar);
        }
        /// <summary>
        /// Subtracts a vector from a scalar.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A single-precision floating-point number.</param>
        /// <returns>A new <see cref="Vector2"/> instance containing the difference.</returns>
        /// <remarks>
        /// result[i] = scalar - vector[i]
        /// </remarks>
        public static Vector2 operator -(float scalar, Vector2 vector)
        {
            return Vector2.Subtract(scalar, vector);
        }
        /// <summary>
        /// Multiplies a vector by a scalar.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A single-precision floating-point number.</param>
        /// <returns>A new <see cref="Vector2"/> containing the result.</returns>
        public static Vector2 operator *(Vector2 vector, float scalar)
        {
            return Vector2.Multiply(vector, scalar);
        }
        /// <summary>
        /// Multiplies a vector by a scalar.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A single-precision floating-point number.</param>
        /// <returns>A new <see cref="Vector2"/> containing the result.</returns>
        public static Vector2 operator *(float scalar, Vector2 vector)
        {
            return Vector2.Multiply(vector, scalar);
        }
        /// <summary>
        /// Divides a vector by a scalar.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A scalar</param>
        /// <returns>A new <see cref="Vector2"/> containing the quotient.</returns>
        /// <remarks>
        /// result[i] = vector[i] / scalar;
        /// </remarks>
        public static Vector2 operator /(Vector2 vector, float scalar)
        {
            return Vector2.Divide(vector, scalar);
        }
        /// <summary>
        /// Divides a scalar by a vector.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <param name="scalar">A scalar</param>
        /// <returns>A new <see cref="Vector2"/> containing the quotient.</returns>
        /// <remarks>
        /// result[i] = scalar / vector[i]
        /// </remarks>
        public static Vector2 operator /(float scalar, Vector2 vector)
        {
            return Vector2.Divide(scalar, vector);
        }
        #endregion

        #region Array Indexing Operator
        /// <summary>
        /// Indexer ( [x, y] ).
        /// </summary>
        public float this[int index]
        {
            get
            {
                switch (index)
                {
                    case 0:
                        return _x;
                    case 1:
                        return _y;
                    default:
                        throw new IndexOutOfRangeException();
                }
            }
            set
            {
                switch (index)
                {
                    case 0:
                        _x = value;
                        break;
                    case 1:
                        _y = value;
                        break;
                    default:
                        throw new IndexOutOfRangeException();
                }
            }

        }
        #endregion

        #region Conversion Operators
        /// <summary>
        /// Converts the vector to an array of single-precision floating point values.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <returns>An array of single-precision floating point values.</returns>
        public static explicit operator float[] (Vector2 vector)
        {
            float[] array = new float[2];
            array[0] = vector.X;
            array[1] = vector.Y;
            return array;
        }
        /// <summary>
        /// Converts the vector to a <see cref="System.Collections.Generic.List{T}"/> of single-precision floating point values.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <returns>A <see cref="System.Collections.Generic.List{T}"/> of single-precision floating point values.</returns>
        public static explicit operator List<float>(Vector2 vector)
        {
            List<float> list = new List<float>();
            list.Add(vector.X);
            list.Add(vector.Y);

            return list;
        }
        /// <summary>
        /// Converts the vector to a <see cref="System.Collections.Generic.LinkedList{T}"/> of single-precision floating point values.
        /// </summary>
        /// <param name="vector">A <see cref="Vector2"/> instance.</param>
        /// <returns>A <see cref="System.Collections.Generic.LinkedList{T}"/> of single-precision floating point values.</returns>
        public static explicit operator LinkedList<float>(Vector2 vector)
        {
            LinkedList<float> list = new LinkedList<float>();
            list.AddLast(vector.X);
            list.AddLast(vector.Y);

            return list;
        }
        #endregion
    }

    #region Vector2FConverter class
    /// <summary>
    /// Converts a <see cref="Vector2"/> to and from string representation.
    /// </summary>
    public class Vector2FConverter : ExpandableObjectConverter
    {
        /// <summary>
        /// Returns whether this converter can convert an object of the given type to the type of this converter, using the specified context.
        /// </summary>
        /// <param name="context">An <see cref="ITypeDescriptorContext"/> that provides a format context.</param>
        /// <param name="sourceType">A <see cref="Type"/> that represents the type you want to convert from.</param>
        /// <returns><b>true</b> if this converter can perform the conversion; otherwise, <b>false</b>.</returns>
        public override bool CanConvertFrom(ITypeDescriptorContext context, Type sourceType)
        {
            if (sourceType == typeof(string))
                return true;

            return base.CanConvertFrom(context, sourceType);
        }
        /// <summary>
        /// Returns whether this converter can convert the object to the specified type, using the specified context.
        /// </summary>
        /// <param name="context">An <see cref="ITypeDescriptorContext"/> that provides a format context.</param>
        /// <param name="destinationType">A <see cref="Type"/> that represents the type you want to convert to.</param>
        /// <returns><b>true</b> if this converter can perform the conversion; otherwise, <b>false</b>.</returns>
        public override bool CanConvertTo(ITypeDescriptorContext context, Type destinationType)
        {
            if (destinationType == typeof(string))
                return true;

            return base.CanConvertTo(context, destinationType);
        }
        /// <summary>
        /// Converts the given value object to the specified type, using the specified context and culture information.
        /// </summary>
        /// <param name="context">An <see cref="ITypeDescriptorContext"/> that provides a format context.</param>
        /// <param name="culture">A <see cref="System.Globalization.CultureInfo"/> object. If a null reference (Nothing in Visual Basic) is passed, the current culture is assumed.</param>
        /// <param name="value">The <see cref="Object"/> to convert.</param>
        /// <param name="destinationType">The Type to convert the <paramref name="value"/> parameter to.</param>
        /// <returns>An <see cref="Object"/> that represents the converted value.</returns>
        public override object ConvertTo(ITypeDescriptorContext context, System.Globalization.CultureInfo culture, object value, Type destinationType)
        {
            if ((destinationType == typeof(string)) && (value is Vector2))
            {
                Vector2 v = (Vector2)value;
                return v.ToString();
            }

            return base.ConvertTo(context, culture, value, destinationType);
        }
        /// <summary>
        /// Converts the given object to the type of this converter, using the specified context and culture information.
        /// </summary>
        /// <param name="context">An <see cref="ITypeDescriptorContext"/> that provides a format context.</param>
        /// <param name="culture">The <see cref="System.Globalization.CultureInfo"/> to use as the current culture. </param>
        /// <param name="value">The <see cref="Object"/> to convert.</param>
        /// <returns>An <see cref="Object"/> that represents the converted value.</returns>
        public override object ConvertFrom(ITypeDescriptorContext context, System.Globalization.CultureInfo culture, object value)
        {
            if (value.GetType() == typeof(string))
            {
                return Vector2.Parse((string)value);
            }

            return base.ConvertFrom(context, culture, value);
        }

        /// <summary>
        /// Returns whether this object supports a standard set of values that can be picked from a list.
        /// </summary>
        /// <param name="context">An <see cref="ITypeDescriptorContext"/> that provides a format context.</param>
        /// <returns><b>true</b> if <see cref="GetStandardValues"/> should be called to find a common set of values the object supports; otherwise, <b>false</b>.</returns>
        public override bool GetStandardValuesSupported(ITypeDescriptorContext context)
        {
            return true;
        }

        /// <summary>
        /// Returns a collection of standard values for the data type this type converter is designed for when provided with a format context.
        /// </summary>
        /// <param name="context">An <see cref="ITypeDescriptorContext"/> that provides a format context that can be used to extract additional information about the environment from which this converter is invoked. This parameter or properties of this parameter can be a null reference.</param>
        /// <returns>A <see cref="TypeConverter.StandardValuesCollection"/> that holds a standard set of valid values, or a null reference (Nothing in Visual Basic) if the data type does not support a standard set of values.</returns>
        public override System.ComponentModel.TypeConverter.StandardValuesCollection GetStandardValues(ITypeDescriptorContext context)
        {
            StandardValuesCollection svc =
                new StandardValuesCollection(new object[3] { Vector2.Zero, Vector2.XAxis, Vector2.YAxis });

            return svc;
        }
    }
    #endregion
}