// Copyright (c) 2012-2020 Wojciech Figat. All rights reserved.

// -----------------------------------------------------------------------------
// Original code from SharpDX project. https://github.com/sharpdx/SharpDX/
// Greetings to Alexandre Mutel. Original code published with the following license:
// -----------------------------------------------------------------------------
// Copyright (c) 2010-2014 SharpDX - Alexandre Mutel
// 
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
// 
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
// 
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.
// -----------------------------------------------------------------------------
// Original code from SlimMath project. http://code.google.com/p/slimmath/
// Greetings to SlimDX Group. Original code published with the following license:
// -----------------------------------------------------------------------------
/*
* Copyright (c) 2007-2011 SlimDX Group
* 
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
* 
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
* 
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/

using System;
using System.ComponentModel;
using System.Globalization;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;

namespace FlaxEngine
{
    [Serializable]
    [TypeConverter(typeof(TypeConverters.Vector2Converter))]
    partial struct Vector2 : IEquatable<Vector2>, IFormattable
    {
        private static readonly string _formatString = "X:{0:F2} Y:{1:F2}";

        /// <summary>
        /// The size of the <see cref="Vector2" /> type, in bytes.
        /// </summary>
        public static readonly int SizeInBytes = Marshal.SizeOf(typeof(Vector2));

        /// <summary>
        /// A <see cref="Vector2" /> with all of its components set to zero.
        /// </summary>
        public static readonly Vector2 Zero;

        /// <summary>
        /// The X unit <see cref="Vector2" /> (1, 0).
        /// </summary>
        public static readonly Vector2 UnitX = new Vector2(1.0f, 0.0f);

        /// <summary>
        /// The Y unit <see cref="Vector2" /> (0, 1).
        /// </summary>
        public static readonly Vector2 UnitY = new Vector2(0.0f, 1.0f);

        /// <summary>
        /// A <see cref="Vector2" /> with all of its components set to half.
        /// </summary>
        public static readonly Vector2 Half = new Vector2(0.5f, 0.5f);

        /// <summary>
        /// A <see cref="Vector2" /> with all of its components set to one.
        /// </summary>
        public static readonly Vector2 One = new Vector2(1.0f, 1.0f);

        /// <summary>
        /// A <see cref="Vector2" /> with all components equal to <see cref="float.MinValue"/>.
        /// </summary>
        public static readonly Vector2 Minimum = new Vector2(float.MinValue);

        /// <summary>
        /// A <see cref="Vector2" /> with all components equal to <see cref="float.MaxValue"/>.
        /// </summary>
        public static readonly Vector2 Maximum = new Vector2(float.MaxValue);

        /// <summary>
        /// Initializes a new instance of the <see cref="Vector2" /> struct.
        /// </summary>
        /// <param name="value">The value that will be assigned to all components.</param>
        public Vector2(float value)
        {
            X = value;
            Y = value;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="Vector2" /> struct.
        /// </summary>
        /// <param name="x">Initial value for the X component of the vector.</param>
        /// <param name="y">Initial value for the Y component of the vector.</param>
        public Vector2(float x, float y)
        {
            X = x;
            Y = y;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="Vector2" /> struct.
        /// </summary>
        /// <param name="value">A vector containing the values with which to initialize the X and Y components.</param>
        public Vector2(Vector3 value)
        {
            X = value.X;
            Y = value.Y;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="Vector2" /> struct.
        /// </summary>
        /// <param name="value">A vector containing the values with which to initialize the X and Y components.</param>
        public Vector2(Vector4 value)
        {
            X = value.X;
            Y = value.Y;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="Vector2" /> struct.
        /// </summary>
        /// <param name="values">
        /// The values to assign to the X and Y components of the vector. This must be an array with two
        /// elements.
        /// </param>
        /// <exception cref="ArgumentNullException">Thrown when <paramref name="values" /> is <c>null</c>.</exception>
        /// <exception cref="ArgumentOutOfRangeException">
        /// Thrown when <paramref name="values" /> contains more or less than two
        /// elements.
        /// </exception>
        public Vector2(float[] values)
        {
            if (values == null)
                throw new ArgumentNullException(nameof(values));
            if (values.Length != 2)
                throw new ArgumentOutOfRangeException(nameof(values), "There must be two and only two input values for Vector2.");

            X = values[0];
            Y = values[1];
        }

        /// <summary>
        /// Gets a value indicting whether this instance is normalized.
        /// </summary>
        public bool IsNormalized => Mathf.IsOne(X * X + Y * Y);

        /// <summary>
        /// Gets a value indicting whether this vector is zero
        /// </summary>
        public bool IsZero => Mathf.IsZero(X) && Mathf.IsZero(Y);

        /// <summary>
        /// Gets a minimum component value
        /// </summary>
        public float MinValue => Mathf.Min(X, Y);

        /// <summary>
        /// Gets a maximum component value
        /// </summary>
        public float MaxValue => Mathf.Max(X, Y);

        /// <summary>
        /// Gets an arithmetic average value of all vector components.
        /// </summary>
        public float AvgValue => (X + Y) * (1.0f / 2.0f);

        /// <summary>
        /// Gets a sum of the component values.
        /// </summary>
        public float ValuesSum => X + Y;

        /// <summary>
        /// Gets or sets the component at the specified index.
        /// </summary>
        /// <value>The value of the X or Y component, depending on the index.</value>
        /// <param name="index">The index of the component to access. Use 0 for the X component and 1 for the Y component.</param>
        /// <returns>The value of the component at the specified index.</returns>
        /// <exception cref="System.ArgumentOutOfRangeException">
        /// Thrown when the <paramref name="index" /> is out of the range [0,
        /// 1].
        /// </exception>
        public float this[int index]
        {
            get
            {
                switch (index)
                {
                case 0: return X;
                case 1: return Y;
                }

                throw new ArgumentOutOfRangeException(nameof(index), "Indices for Vector2 run from 0 to 1, inclusive.");
            }

            set
            {
                switch (index)
                {
                case 0:
                    X = value;
                    break;
                case 1:
                    Y = value;
                    break;
                default: throw new ArgumentOutOfRangeException(nameof(index), "Indices for Vector2 run from 0 to 1, inclusive.");
                }
            }
        }

        /// <summary>
        /// Calculates the length of the vector.
        /// </summary>
        /// <returns>The length of the vector.</returns>
        /// <remarks>
        /// <see cref="Vector2.LengthSquared" /> may be preferred when only the relative length is needed
        /// and speed is of the essence.
        /// </remarks>
        public float Length => (float)Math.Sqrt(X * X + Y * Y);

        /// <summary>
        /// Calculates the squared length of the vector.
        /// </summary>
        /// <returns>The squared length of the vector.</returns>
        /// <remarks>
        /// This method may be preferred to <see cref="Vector2.Length" /> when only a relative length is needed
        /// and speed is of the essence.
        /// </remarks>
        public float LengthSquared => X * X + Y * Y;

        /// <summary>
        /// Converts the vector into a unit vector.
        /// </summary>
        public void Normalize()
        {
            float length = Length;
            if (!Mathf.IsZero(length))
            {
                float inv = 1.0f / length;
                X *= inv;
                Y *= inv;
            }
        }

        /// <summary>
        /// Creates an array containing the elements of the vector.
        /// </summary>
        /// <returns>A two-element array containing the components of the vector.</returns>
        public float[] ToArray()
        {
            return new[]
            {
                X,
                Y
            };
        }

        /// <summary>
        /// Adds two vectors.
        /// </summary>
        /// <param name="left">The first vector to add.</param>
        /// <param name="right">The second vector to add.</param>
        /// <param name="result">When the method completes, contains the sum of the two vectors.</param>
        public static void Add(ref Vector2 left, ref Vector2 right, out Vector2 result)
        {
            result = new Vector2(left.X + right.X, left.Y + right.Y);
        }

        /// <summary>
        /// Adds two vectors.
        /// </summary>
        /// <param name="left">The first vector to add.</param>
        /// <param name="right">The second vector to add.</param>
        /// <returns>The sum of the two vectors.</returns>
        public static Vector2 Add(Vector2 left, Vector2 right)
        {
            return new Vector2(left.X + right.X, left.Y + right.Y);
        }

        /// <summary>
        /// Perform a component-wise addition
        /// </summary>
        /// <param name="left">The input vector</param>
        /// <param name="right">The scalar value to be added to elements</param>
        /// <param name="result">The vector with added scalar for each element.</param>
        public static void Add(ref Vector2 left, ref float right, out Vector2 result)
        {
            result = new Vector2(left.X + right, left.Y + right);
        }

        /// <summary>
        /// Perform a component-wise addition
        /// </summary>
        /// <param name="left">The input vector</param>
        /// <param name="right">The scalar value to be added to elements</param>
        /// <returns>The vector with added scalar for each element.</returns>
        public static Vector2 Add(Vector2 left, float right)
        {
            return new Vector2(left.X + right, left.Y + right);
        }

        /// <summary>
        /// Subtracts two vectors.
        /// </summary>
        /// <param name="left">The first vector to subtract.</param>
        /// <param name="right">The second vector to subtract.</param>
        /// <param name="result">When the method completes, contains the difference of the two vectors.</param>
        public static void Subtract(ref Vector2 left, ref Vector2 right, out Vector2 result)
        {
            result = new Vector2(left.X - right.X, left.Y - right.Y);
        }

        /// <summary>
        /// Subtracts two vectors.
        /// </summary>
        /// <param name="left">The first vector to subtract.</param>
        /// <param name="right">The second vector to subtract.</param>
        /// <returns>The difference of the two vectors.</returns>
        public static Vector2 Subtract(Vector2 left, Vector2 right)
        {
            return new Vector2(left.X - right.X, left.Y - right.Y);
        }

        /// <summary>
        /// Perform a component-wise subtraction
        /// </summary>
        /// <param name="left">The input vector</param>
        /// <param name="right">The scalar value to be subtracted from elements</param>
        /// <param name="result">The vector with subtracted scalar for each element.</param>
        public static void Subtract(ref Vector2 left, ref float right, out Vector2 result)
        {
            result = new Vector2(left.X - right, left.Y - right);
        }

        /// <summary>
        /// Perform a component-wise subtraction
        /// </summary>
        /// <param name="left">The input vector</param>
        /// <param name="right">The scalar value to be subtracted from elements</param>
        /// <returns>The vector with subtracted scalar for each element.</returns>
        public static Vector2 Subtract(Vector2 left, float right)
        {
            return new Vector2(left.X - right, left.Y - right);
        }

        /// <summary>
        /// Perform a component-wise subtraction
        /// </summary>
        /// <param name="left">The scalar value to be subtracted from elements</param>
        /// <param name="right">The input vector</param>
        /// <param name="result">The vector with subtracted scalar for each element.</param>
        public static void Subtract(ref float left, ref Vector2 right, out Vector2 result)
        {
            result = new Vector2(left - right.X, left - right.Y);
        }

        /// <summary>
        /// Perform a component-wise subtraction
        /// </summary>
        /// <param name="left">The scalar value to be subtracted from elements</param>
        /// <param name="right">The input vector</param>
        /// <returns>The vector with subtracted scalar for each element.</returns>
        public static Vector2 Subtract(float left, Vector2 right)
        {
            return new Vector2(left - right.X, left - right.Y);
        }

        /// <summary>
        /// Scales a vector by the given value.
        /// </summary>
        /// <param name="value">The vector to scale.</param>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <param name="result">When the method completes, contains the scaled vector.</param>
        public static void Multiply(ref Vector2 value, float scale, out Vector2 result)
        {
            result = new Vector2(value.X * scale, value.Y * scale);
        }

        /// <summary>
        /// Scales a vector by the given value.
        /// </summary>
        /// <param name="value">The vector to scale.</param>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <returns>The scaled vector.</returns>
        public static Vector2 Multiply(Vector2 value, float scale)
        {
            return new Vector2(value.X * scale, value.Y * scale);
        }

        /// <summary>
        /// Multiplies a vector with another by performing component-wise multiplication.
        /// </summary>
        /// <param name="left">The first vector to multiply.</param>
        /// <param name="right">The second vector to multiply.</param>
        /// <param name="result">When the method completes, contains the multiplied vector.</param>
        public static void Multiply(ref Vector2 left, ref Vector2 right, out Vector2 result)
        {
            result = new Vector2(left.X * right.X, left.Y * right.Y);
        }

        /// <summary>
        /// Multiplies a vector with another by performing component-wise multiplication.
        /// </summary>
        /// <param name="left">The first vector to multiply.</param>
        /// <param name="right">The second vector to multiply.</param>
        /// <returns>The multiplied vector.</returns>
        public static Vector2 Multiply(Vector2 left, Vector2 right)
        {
            return new Vector2(left.X * right.X, left.Y * right.Y);
        }

        /// <summary>
        /// Scales a vector by the given value.
        /// </summary>
        /// <param name="value">The vector to scale.</param>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <param name="result">When the method completes, contains the scaled vector.</param>
        public static void Divide(ref Vector2 value, float scale, out Vector2 result)
        {
            result = new Vector2(value.X / scale, value.Y / scale);
        }

        /// <summary>
        /// Scales a vector by the given value.
        /// </summary>
        /// <param name="value">The vector to scale.</param>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <returns>The scaled vector.</returns>
        public static Vector2 Divide(Vector2 value, float scale)
        {
            return new Vector2(value.X / scale, value.Y / scale);
        }

        /// <summary>
        /// Scales a vector by the given value.
        /// </summary>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <param name="value">The vector to scale.</param>
        /// <param name="result">When the method completes, contains the scaled vector.</param>
        public static void Divide(float scale, ref Vector2 value, out Vector2 result)
        {
            result = new Vector2(scale / value.X, scale / value.Y);
        }

        /// <summary>
        /// Scales a vector by the given value.
        /// </summary>
        /// <param name="value">The vector to scale.</param>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <returns>The scaled vector.</returns>
        public static Vector2 Divide(float scale, Vector2 value)
        {
            return new Vector2(scale / value.X, scale / value.Y);
        }

        /// <summary>
        /// Reverses the direction of a given vector.
        /// </summary>
        /// <param name="value">The vector to negate.</param>
        /// <param name="result">When the method completes, contains a vector facing in the opposite direction.</param>
        public static void Negate(ref Vector2 value, out Vector2 result)
        {
            result = new Vector2(-value.X, -value.Y);
        }

        /// <summary>
        /// Reverses the direction of a given vector.
        /// </summary>
        /// <param name="value">The vector to negate.</param>
        /// <returns>A vector facing in the opposite direction.</returns>
        public static Vector2 Negate(Vector2 value)
        {
            return new Vector2(-value.X, -value.Y);
        }

        /// <summary>
        /// Returns a <see cref="Vector2" /> containing the 2D Cartesian coordinates of a point specified in Barycentric
        /// coordinates relative to a 2D triangle.
        /// </summary>
        /// <param name="value1">A <see cref="Vector2" /> containing the 2D Cartesian coordinates of vertex 1 of the triangle.</param>
        /// <param name="value2">A <see cref="Vector2" /> containing the 2D Cartesian coordinates of vertex 2 of the triangle.</param>
        /// <param name="value3">A <see cref="Vector2" /> containing the 2D Cartesian coordinates of vertex 3 of the triangle.</param>
        /// <param name="amount1">
        /// Barycentric coordinate b2, which expresses the weighting factor toward vertex 2 (specified in
        /// <paramref name="value2" />).
        /// </param>
        /// <param name="amount2">
        /// Barycentric coordinate b3, which expresses the weighting factor toward vertex 3 (specified in
        /// <paramref name="value3" />).
        /// </param>
        /// <param name="result">When the method completes, contains the 2D Cartesian coordinates of the specified point.</param>
        public static void Barycentric(ref Vector2 value1, ref Vector2 value2, ref Vector2 value3, float amount1, float amount2, out Vector2 result)
        {
            result = new Vector2(value1.X + amount1 * (value2.X - value1.X) + amount2 * (value3.X - value1.X),
                                 value1.Y + amount1 * (value2.Y - value1.Y) + amount2 * (value3.Y - value1.Y));
        }

        /// <summary>
        /// Returns a <see cref="Vector2" /> containing the 2D Cartesian coordinates of a point specified in Barycentric
        /// coordinates relative to a 2D triangle.
        /// </summary>
        /// <param name="value1">A <see cref="Vector2" /> containing the 2D Cartesian coordinates of vertex 1 of the triangle.</param>
        /// <param name="value2">A <see cref="Vector2" /> containing the 2D Cartesian coordinates of vertex 2 of the triangle.</param>
        /// <param name="value3">A <see cref="Vector2" /> containing the 2D Cartesian coordinates of vertex 3 of the triangle.</param>
        /// <param name="amount1">
        /// Barycentric coordinate b2, which expresses the weighting factor toward vertex 2 (specified in
        /// <paramref name="value2" />).
        /// </param>
        /// <param name="amount2">
        /// Barycentric coordinate b3, which expresses the weighting factor toward vertex 3 (specified in
        /// <paramref name="value3" />).
        /// </param>
        /// <returns>A new <see cref="Vector2" /> containing the 2D Cartesian coordinates of the specified point.</returns>
        public static Vector2 Barycentric(Vector2 value1, Vector2 value2, Vector2 value3, float amount1, float amount2)
        {
            Vector2 result;
            Barycentric(ref value1, ref value2, ref value3, amount1, amount2, out result);
            return result;
        }

        /// <summary>
        /// Restricts a value to be within a specified range.
        /// </summary>
        /// <param name="value">The value to clamp.</param>
        /// <param name="min">The minimum value.</param>
        /// <param name="max">The maximum value.</param>
        /// <param name="result">When the method completes, contains the clamped value.</param>
        public static void Clamp(ref Vector2 value, ref Vector2 min, ref Vector2 max, out Vector2 result)
        {
            float x = value.X;
            x = x > max.X ? max.X : x;
            x = x < min.X ? min.X : x;

            float y = value.Y;
            y = y > max.Y ? max.Y : y;
            y = y < min.Y ? min.Y : y;

            result = new Vector2(x, y);
        }

        /// <summary>
        /// Restricts a value to be within a specified range.
        /// </summary>
        /// <param name="value">The value to clamp.</param>
        /// <param name="min">The minimum value.</param>
        /// <param name="max">The maximum value.</param>
        /// <returns>The clamped value.</returns>
        public static Vector2 Clamp(Vector2 value, Vector2 min, Vector2 max)
        {
            Vector2 result;
            Clamp(ref value, ref min, ref max, out result);
            return result;
        }

        /// <summary>
        /// Saturates this instance in the range [0,1]
        /// </summary>
        public void Saturate()
        {
            X = X < 0.0f ? 0.0f : X > 1.0f ? 1.0f : X;
            Y = Y < 0.0f ? 0.0f : Y > 1.0f ? 1.0f : Y;
        }

        /// <summary>
        /// Calculates the area of the triangle.
        /// </summary>
        /// <param name="v0">The first triangle vertex.</param>
        /// <param name="v1">The second triangle vertex.</param>
        /// <param name="v2">The third triangle vertex.</param>
        /// <returns>The triangle area.</returns>
        public static float TriangleArea(ref Vector2 v0, ref Vector2 v1, ref Vector2 v2)
        {
            return Mathf.Abs((v0.X * (v1.Y - v2.Y) + v1.X * (v2.Y - v0.Y) + v2.X * (v0.Y - v1.Y)) / 2);
        }

        /// <summary>
        /// Calculates the distance between two vectors.
        /// </summary>
        /// <param name="value1">The first vector.</param>
        /// <param name="value2">The second vector.</param>
        /// <param name="result">When the method completes, contains the distance between the two vectors.</param>
        /// <remarks>
        /// <see cref="Vector2.DistanceSquared(ref Vector2, ref Vector2, out float)" /> may be preferred when only the relative
        /// distance is needed
        /// and speed is of the essence.
        /// </remarks>
        public static void Distance(ref Vector2 value1, ref Vector2 value2, out float result)
        {
            float x = value1.X - value2.X;
            float y = value1.Y - value2.Y;

            result = (float)Math.Sqrt(x * x + y * y);
        }

        /// <summary>
        /// Calculates the distance between two vectors.
        /// </summary>
        /// <param name="value1">The first vector.</param>
        /// <param name="value2">The second vector.</param>
        /// <returns>The distance between the two vectors.</returns>
        /// <remarks>
        /// <see cref="Vector2.DistanceSquared(Vector2, Vector2)" /> may be preferred when only the relative distance is needed
        /// and speed is of the essence.
        /// </remarks>
        public static float Distance(Vector2 value1, Vector2 value2)
        {
            float x = value1.X - value2.X;
            float y = value1.Y - value2.Y;

            return (float)Math.Sqrt(x * x + y * y);
        }

        /// <summary>
        /// Calculates the distance between two vectors.
        /// </summary>
        /// <param name="value1">The first vector.</param>
        /// <param name="value2">The second vector.</param>
        /// <returns>The distance between the two vectors.</returns>
        /// <remarks>
        /// <see cref="Vector2.DistanceSquared(ref Vector2, ref Vector2, out float)" /> may be preferred when only the relative
        /// distance is needed
        /// and speed is of the essence.
        /// </remarks>
        public static float Distance(ref Vector2 value1, ref Vector2 value2)
        {
            float x = value1.X - value2.X;
            float y = value1.Y - value2.Y;

            return (float)Math.Sqrt(x * x + y * y);
        }

        /// <summary>
        /// Calculates the squared distance between two vectors.
        /// </summary>
        /// <param name="value1">The first vector.</param>
        /// <param name="value2">The second vector</param>
        /// <param name="result">When the method completes, contains the squared distance between the two vectors.</param>
        /// <remarks>
        /// Distance squared is the value before taking the square root.
        /// Distance squared can often be used in place of distance if relative comparisons are being made.
        /// For example, consider three points A, B, and C. To determine whether B or C is further from A,
        /// compare the distance between A and B to the distance between A and C. Calculating the two distances
        /// involves two square roots, which are computationally expensive. However, using distance squared
        /// provides the same information and avoids calculating two square roots.
        /// </remarks>
        public static void DistanceSquared(ref Vector2 value1, ref Vector2 value2, out float result)
        {
            float x = value1.X - value2.X;
            float y = value1.Y - value2.Y;

            result = x * x + y * y;
        }

        /// <summary>
        /// Calculates the squared distance between two vectors.
        /// </summary>
        /// <param name="value1">The first vector.</param>
        /// <param name="value2">The second vector</param>
        /// <returns>The squared distance between the two vectors.</returns>
        /// <remarks>
        /// Distance squared is the value before taking the square root.
        /// Distance squared can often be used in place of distance if relative comparisons are being made.
        /// For example, consider three points A, B, and C. To determine whether B or C is further from A,
        /// compare the distance between A and B to the distance between A and C. Calculating the two distances
        /// involves two square roots, which are computationally expensive. However, using distance squared
        /// provides the same information and avoids calculating two square roots.
        /// </remarks>
        public static float DistanceSquared(ref Vector2 value1, ref Vector2 value2)
        {
            float x = value1.X - value2.X;
            float y = value1.Y - value2.Y;

            return x * x + y * y;
        }

        /// <summary>
        /// Calculates the squared distance between two vectors.
        /// </summary>
        /// <param name="value1">The first vector.</param>
        /// <param name="value2">The second vector.</param>
        /// <returns>The squared distance between the two vectors.</returns>
        /// <remarks>
        /// Distance squared is the value before taking the square root.
        /// Distance squared can often be used in place of distance if relative comparisons are being made.
        /// For example, consider three points A, B, and C. To determine whether B or C is further from A,
        /// compare the distance between A and B to the distance between A and C. Calculating the two distances
        /// involves two square roots, which are computationally expensive. However, using distance squared
        /// provides the same information and avoids calculating two square roots.
        /// </remarks>
        public static float DistanceSquared(Vector2 value1, Vector2 value2)
        {
            float x = value1.X - value2.X;
            float y = value1.Y - value2.Y;

            return x * x + y * y;
        }

        /// <summary>
        /// Tests whether one vector is near another vector.
        /// </summary>
        /// <param name="left">The left vector.</param>
        /// <param name="right">The right vector.</param>
        /// <param name="epsilon">The epsilon.</param>
        /// <returns><c>true</c> if left and right are near, <c>false</c> otherwise</returns>
        public static bool NearEqual(Vector2 left, Vector2 right, float epsilon = Mathf.Epsilon)
        {
            return NearEqual(ref left, ref right, epsilon);
        }

        /// <summary>
        /// Tests whether one vector is near another vector.
        /// </summary>
        /// <param name="left">The left vector.</param>
        /// <param name="right">The right vector.</param>
        /// <param name="epsilon">The epsilon.</param>
        /// <returns><c>true</c> if left and right are near another, <c>false</c> otherwise</returns>
        public static bool NearEqual(ref Vector2 left, ref Vector2 right, float epsilon = Mathf.Epsilon)
        {
            return Mathf.WithinEpsilon(left.X, right.X, epsilon) &&
                   Mathf.WithinEpsilon(left.Y, right.Y, epsilon);
        }

        /// <summary>
        /// Calculates the dot product of two vectors.
        /// </summary>
        /// <param name="left">First source vector.</param>
        /// <param name="right">Second source vector.</param>
        /// <param name="result">When the method completes, contains the dot product of the two vectors.</param>
        public static void Dot(ref Vector2 left, ref Vector2 right, out float result)
        {
            result = left.X * right.X + left.Y * right.Y;
        }

        /// <summary>
        /// Calculates the dot product of two vectors.
        /// </summary>
        /// <param name="left">First source vector.</param>
        /// <param name="right">Second source vector.</param>
        /// <returns>The dot product of the two vectors.</returns>
        public static float Dot(ref Vector2 left, ref Vector2 right)
        {
            return left.X * right.X + left.Y * right.Y;
        }

        /// <summary>
        /// Calculates the dot product of two vectors.
        /// </summary>
        /// <param name="left">First source vector.</param>
        /// <param name="right">Second source vector.</param>
        /// <returns>The dot product of the two vectors.</returns>
        public static float Dot(Vector2 left, Vector2 right)
        {
            return left.X * right.X + left.Y * right.Y;
        }

        /// <summary>
        /// Calculates the cross product of two vectors.
        /// </summary>
        /// <param name="left">First source vector.</param>
        /// <param name="right">Second source vector.</param>
        /// <param name="result">When the method completes, contains the cross product of the two vectors.</param>
        public static void Cross(ref Vector2 left, ref Vector2 right, out float result)
        {
            result = left.X * right.Y - left.Y * right.X;
        }

        /// <summary>
        /// Calculates the cross product of two vectors.
        /// </summary>
        /// <param name="left">First source vector.</param>
        /// <param name="right">Second source vector.</param>
        /// <returns>The cross product of the two vectors.</returns>
        public static float Cross(ref Vector2 left, ref Vector2 right)
        {
            return left.X * right.Y - left.Y * right.X;
        }

        /// <summary>
        /// Calculates the cross product of two vectors.
        /// </summary>
        /// <param name="left">First source vector.</param>
        /// <param name="right">Second source vector.</param>
        /// <returns>The cross product of the two vectors.</returns>
        public static float Cross(Vector2 left, Vector2 right)
        {
            return left.X * right.Y - left.Y * right.X;
        }

        /// <summary>
        /// Converts the vector into a unit vector.
        /// </summary>
        /// <param name="value">The vector to normalize.</param>
        /// <param name="result">When the method completes, contains the normalized vector.</param>
        public static void Normalize(ref Vector2 value, out Vector2 result)
        {
            result = value;
            result.Normalize();
        }

        /// <summary>
        /// Converts the vector into a unit vector.
        /// </summary>
        /// <param name="value">The vector to normalize.</param>
        /// <returns>The normalized vector.</returns>
        public static Vector2 Normalize(Vector2 value)
        {
            value.Normalize();
            return value;
        }

        /// <summary>
        /// Returns the vector with components rounded to the nearest integer.
        /// </summary>
        /// <param name="v">The value.</param>
        /// <returns>The result.</returns>
        public static Vector2 Round(Vector2 v)
        {
            return new Vector2(Mathf.Round(v.X), Mathf.Round(v.Y));
        }

        /// <summary>
        /// Returns the vector with components containing the smallest integer greater to or equal to the original value.
        /// </summary>
        /// <param name="v">The value.</param>
        /// <returns>The result.</returns>
        public static Vector2 Ceil(Vector2 v)
        {
            return new Vector2(Mathf.Ceil(v.X), Mathf.Ceil(v.Y));
        }

        /// <summary>
        /// Breaks the components of the vector into an integral and a fractional part. Returns vector made of fractional parts.
        /// </summary>
        /// <param name="v">The value.</param>
        /// <returns>The result.</returns>
        public static Vector2 Mod(Vector2 v)
        {
            return new Vector2(v.X - (int)v.X, v.Y - (int)v.Y);
        }

        /// <summary>
        /// Performs a linear interpolation between two vectors.
        /// </summary>
        /// <param name="start">Start vector.</param>
        /// <param name="end">End vector.</param>
        /// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end" />.</param>
        /// <param name="result">When the method completes, contains the linear interpolation of the two vectors.</param>
        /// <remarks>
        /// Passing <paramref name="amount" /> a value of 0 will cause <paramref name="start" /> to be returned; a value of 1
        /// will cause <paramref name="end" /> to be returned.
        /// </remarks>
        public static void Lerp(ref Vector2 start, ref Vector2 end, float amount, out Vector2 result)
        {
            result.X = Mathf.Lerp(start.X, end.X, amount);
            result.Y = Mathf.Lerp(start.Y, end.Y, amount);
        }

        /// <summary>
        /// Performs a linear interpolation between two vectors.
        /// </summary>
        /// <param name="start">Start vector.</param>
        /// <param name="end">End vector.</param>
        /// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end" />.</param>
        /// <returns>The linear interpolation of the two vectors.</returns>
        /// <remarks>
        /// Passing <paramref name="amount" /> a value of 0 will cause <paramref name="start" /> to be returned; a value of 1
        /// will cause <paramref name="end" /> to be returned.
        /// </remarks>
        public static Vector2 Lerp(Vector2 start, Vector2 end, float amount)
        {
            Vector2 result;
            Lerp(ref start, ref end, amount, out result);
            return result;
        }

        /// <summary>
        /// Performs a linear interpolation between two vectors.
        /// </summary>
        /// <param name="start">Start vector.</param>
        /// <param name="end">End vector.</param>
        /// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end" />.</param>
        /// <param name="result">When the method completes, contains the linear interpolation of the two vectors.</param>
        /// <remarks>
        /// Passing <paramref name="amount" /> a value of 0 will cause <paramref name="start" /> to be returned; a value of 1
        /// will cause <paramref name="end" /> to be returned.
        /// </remarks>
        public static void Lerp(ref Vector2 start, ref Vector2 end, ref Vector2 amount, out Vector2 result)
        {
            result.X = Mathf.Lerp(start.X, end.X, amount.X);
            result.Y = Mathf.Lerp(start.Y, end.Y, amount.Y);
        }

        /// <summary>
        /// Performs a linear interpolation between two vectors.
        /// </summary>
        /// <param name="start">Start vector.</param>
        /// <param name="end">End vector.</param>
        /// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end" />.</param>
        /// <returns>The linear interpolation of the two vectors.</returns>
        /// <remarks>
        /// Passing <paramref name="amount" /> a value of 0 will cause <paramref name="start" /> to be returned; a value of 1
        /// will cause <paramref name="end" /> to be returned.
        /// </remarks>
        public static Vector2 Lerp(Vector2 start, Vector2 end, Vector2 amount)
        {
            Vector2 result;
            Lerp(ref start, ref end, ref amount, out result);
            return result;
        }

        /// <summary>
        /// Performs a cubic interpolation between two vectors.
        /// </summary>
        /// <param name="start">Start vector.</param>
        /// <param name="end">End vector.</param>
        /// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end" />.</param>
        /// <param name="result">When the method completes, contains the cubic interpolation of the two vectors.</param>
        public static void SmoothStep(ref Vector2 start, ref Vector2 end, float amount, out Vector2 result)
        {
            amount = Mathf.SmoothStep(amount);
            Lerp(ref start, ref end, amount, out result);
        }

        /// <summary>
        /// Performs a cubic interpolation between two vectors.
        /// </summary>
        /// <param name="start">Start vector.</param>
        /// <param name="end">End vector.</param>
        /// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end" />.</param>
        /// <returns>The cubic interpolation of the two vectors.</returns>
        public static Vector2 SmoothStep(Vector2 start, Vector2 end, float amount)
        {
            Vector2 result;
            SmoothStep(ref start, ref end, amount, out result);
            return result;
        }

        /// <summary>
        /// Performs a Hermite spline interpolation.
        /// </summary>
        /// <param name="value1">First source position vector.</param>
        /// <param name="tangent1">First source tangent vector.</param>
        /// <param name="value2">Second source position vector.</param>
        /// <param name="tangent2">Second source tangent vector.</param>
        /// <param name="amount">Weighting factor.</param>
        /// <param name="result">When the method completes, contains the result of the Hermite spline interpolation.</param>
        public static void Hermite(ref Vector2 value1, ref Vector2 tangent1, ref Vector2 value2, ref Vector2 tangent2, float amount, out Vector2 result)
        {
            float squared = amount * amount;
            float cubed = amount * squared;
            float part1 = 2.0f * cubed - 3.0f * squared + 1.0f;
            float part2 = -2.0f * cubed + 3.0f * squared;
            float part3 = cubed - 2.0f * squared + amount;
            float part4 = cubed - squared;

            result.X = value1.X * part1 + value2.X * part2 + tangent1.X * part3 + tangent2.X * part4;
            result.Y = value1.Y * part1 + value2.Y * part2 + tangent1.Y * part3 + tangent2.Y * part4;
        }

        /// <summary>
        /// Performs a Hermite spline interpolation.
        /// </summary>
        /// <param name="value1">First source position vector.</param>
        /// <param name="tangent1">First source tangent vector.</param>
        /// <param name="value2">Second source position vector.</param>
        /// <param name="tangent2">Second source tangent vector.</param>
        /// <param name="amount">Weighting factor.</param>
        /// <returns>The result of the Hermite spline interpolation.</returns>
        public static Vector2 Hermite(Vector2 value1, Vector2 tangent1, Vector2 value2, Vector2 tangent2, float amount)
        {
            Vector2 result;
            Hermite(ref value1, ref tangent1, ref value2, ref tangent2, amount, out result);
            return result;
        }

        /// <summary>
        /// Calculates the 2D vector perpendicular to the given 2D vector. The result is always rotated 90-degrees in a counter-clockwise direction for a 2D coordinate system where the positive Y axis goes up.
        /// </summary>
        /// <param name="inDirection">The input direction.</param>
        /// <returns>The result.</returns>
        public static Vector2 Perpendicular(Vector2 inDirection)
        {
            return new Vector2(-inDirection.Y, inDirection.X);
        }

        /// <summary>
        /// Calculates the 2D vector perpendicular to the given 2D vector. The result is always rotated 90-degrees in a counter-clockwise direction for a 2D coordinate system where the positive Y axis goes up.
        /// </summary>
        /// <param name="inDirection">The in direction.</param>
        /// <param name="result">When the method completes, contains the result of the calculation.</param>
        public static void Perpendicular(ref Vector2 inDirection, out Vector2 result)
        {
            result = new Vector2(-inDirection.Y, inDirection.X);
        }

        /// <summary>
        /// Performs a Catmull-Rom interpolation using the specified positions.
        /// </summary>
        /// <param name="value1">The first position in the interpolation.</param>
        /// <param name="value2">The second position in the interpolation.</param>
        /// <param name="value3">The third position in the interpolation.</param>
        /// <param name="value4">The fourth position in the interpolation.</param>
        /// <param name="amount">Weighting factor.</param>
        /// <param name="result">When the method completes, contains the result of the Catmull-Rom interpolation.</param>
        public static void CatmullRom(ref Vector2 value1, ref Vector2 value2, ref Vector2 value3, ref Vector2 value4, float amount, out Vector2 result)
        {
            float squared = amount * amount;
            float cubed = amount * squared;

            result.X = 0.5f * (2.0f * value2.X + (-value1.X + value3.X) * amount +
                               (2.0f * value1.X - 5.0f * value2.X + 4.0f * value3.X - value4.X) * squared +
                               (-value1.X + 3.0f * value2.X - 3.0f * value3.X + value4.X) * cubed);

            result.Y = 0.5f * (2.0f * value2.Y + (-value1.Y + value3.Y) * amount +
                               (2.0f * value1.Y - 5.0f * value2.Y + 4.0f * value3.Y - value4.Y) * squared +
                               (-value1.Y + 3.0f * value2.Y - 3.0f * value3.Y + value4.Y) * cubed);
        }

        /// <summary>
        /// Performs a Catmull-Rom interpolation using the specified positions.
        /// </summary>
        /// <param name="value1">The first position in the interpolation.</param>
        /// <param name="value2">The second position in the interpolation.</param>
        /// <param name="value3">The third position in the interpolation.</param>
        /// <param name="value4">The fourth position in the interpolation.</param>
        /// <param name="amount">Weighting factor.</param>
        /// <returns>A vector that is the result of the Catmull-Rom interpolation.</returns>
        public static Vector2 CatmullRom(Vector2 value1, Vector2 value2, Vector2 value3, Vector2 value4, float amount)
        {
            Vector2 result;
            CatmullRom(ref value1, ref value2, ref value3, ref value4, amount, out result);
            return result;
        }

        /// <summary>
        /// Returns a vector containing the largest components of the specified vectors.
        /// </summary>
        /// <param name="left">The first source vector.</param>
        /// <param name="right">The second source vector.</param>
        /// <param name="result">
        /// When the method completes, contains an new vector composed of the largest components of the source
        /// vectors.
        /// </param>
        public static void Max(ref Vector2 left, ref Vector2 right, out Vector2 result)
        {
            result.X = left.X > right.X ? left.X : right.X;
            result.Y = left.Y > right.Y ? left.Y : right.Y;
        }

        /// <summary>
        /// Returns a vector containing the largest components of the specified vectors.
        /// </summary>
        /// <param name="left">The first source vector.</param>
        /// <param name="right">The second source vector.</param>
        /// <returns>A vector containing the largest components of the source vectors.</returns>
        public static Vector2 Max(Vector2 left, Vector2 right)
        {
            Vector2 result;
            Max(ref left, ref right, out result);
            return result;
        }

        /// <summary>
        /// Returns a vector containing the smallest components of the specified vectors.
        /// </summary>
        /// <param name="left">The first source vector.</param>
        /// <param name="right">The second source vector.</param>
        /// <param name="result">
        /// When the method completes, contains an new vector composed of the smallest components of the
        /// source vectors.
        /// </param>
        public static void Min(ref Vector2 left, ref Vector2 right, out Vector2 result)
        {
            result.X = left.X < right.X ? left.X : right.X;
            result.Y = left.Y < right.Y ? left.Y : right.Y;
        }

        /// <summary>
        /// Returns a vector containing the smallest components of the specified vectors.
        /// </summary>
        /// <param name="left">The first source vector.</param>
        /// <param name="right">The second source vector.</param>
        /// <returns>A vector containing the smallest components of the source vectors.</returns>
        public static Vector2 Min(Vector2 left, Vector2 right)
        {
            Vector2 result;
            Min(ref left, ref right, out result);
            return result;
        }

        /// <summary>
        /// Returns the absolute value of a vector.
        /// </summary>
        /// <param name="v">The value.</param>
        /// <returns> A vector which components are less or equal to 0.</returns>
        public static Vector2 Abs(Vector2 v)
        {
            return new Vector2(Math.Abs(v.X), Math.Abs(v.Y));
        }

        /// <summary>
        /// Returns the reflection of a vector off a surface that has the specified normal.
        /// </summary>
        /// <param name="vector">The source vector.</param>
        /// <param name="normal">Normal of the surface.</param>
        /// <param name="result">When the method completes, contains the reflected vector.</param>
        /// <remarks>
        /// Reflect only gives the direction of a reflection off a surface, it does not determine
        /// whether the original vector was close enough to the surface to hit it.
        /// </remarks>
        public static void Reflect(ref Vector2 vector, ref Vector2 normal, out Vector2 result)
        {
            float dot = vector.X * normal.X + vector.Y * normal.Y;

            result.X = vector.X - 2.0f * dot * normal.X;
            result.Y = vector.Y - 2.0f * dot * normal.Y;
        }

        /// <summary>
        /// Returns the reflection of a vector off a surface that has the specified normal.
        /// </summary>
        /// <param name="vector">The source vector.</param>
        /// <param name="normal">Normal of the surface.</param>
        /// <returns>The reflected vector.</returns>
        /// <remarks>
        /// Reflect only gives the direction of a reflection off a surface, it does not determine
        /// whether the original vector was close enough to the surface to hit it.
        /// </remarks>
        public static Vector2 Reflect(Vector2 vector, Vector2 normal)
        {
            Vector2 result;
            Reflect(ref vector, ref normal, out result);
            return result;
        }

        /// <summary>
        /// Orthogonalizes a list of vectors.
        /// </summary>
        /// <param name="destination">The list of orthogonalized vectors.</param>
        /// <param name="source">The list of vectors to orthogonalize.</param>
        /// <remarks>
        /// <para>
        ///   Orthogonalization is the process of making all vectors orthogonal to each other. This
        ///   means that any given vector in the list will be orthogonal to any other given vector in the
        ///   list.
        /// </para>
        /// <para>
        ///   Because this method uses the modified Gram-Schmidt process, the resulting vectors
        ///   tend to be numerically unstable. The numeric stability decreases according to the vectors
        ///   position in the list so that the first vector is the most stable and the last vector is the
        ///   least stable.
        /// </para>
        /// </remarks>
        /// <exception cref="ArgumentNullException">
        /// Thrown when <paramref name="source" /> or <paramref name="destination" /> is
        /// <c>null</c>.
        /// </exception>
        /// <exception cref="ArgumentOutOfRangeException">
        /// Thrown when <paramref name="destination" /> is shorter in length than
        /// <paramref name="source" />.
        /// </exception>
        public static void Orthogonalize(Vector2[] destination, params Vector2[] source)
        {
            //Uses the modified Gram-Schmidt process.
            //q1 = m1
            //q2 = m2 - ((q1 ⋅ m2) / (q1 ⋅ q1)) * q1
            //q3 = m3 - ((q1 ⋅ m3) / (q1 ⋅ q1)) * q1 - ((q2 ⋅ m3) / (q2 ⋅ q2)) * q2
            //q4 = m4 - ((q1 ⋅ m4) / (q1 ⋅ q1)) * q1 - ((q2 ⋅ m4) / (q2 ⋅ q2)) * q2 - ((q3 ⋅ m4) / (q3 ⋅ q3)) * q3
            //q5 = ...

            if (source == null)
                throw new ArgumentNullException(nameof(source));
            if (destination == null)
                throw new ArgumentNullException(nameof(destination));
            if (destination.Length < source.Length)
                throw new ArgumentOutOfRangeException(nameof(destination), "The destination array must be of same length or larger length than the source array.");

            for (var i = 0; i < source.Length; ++i)
            {
                Vector2 newvector = source[i];

                for (var r = 0; r < i; ++r)
                    newvector -= Dot(destination[r], newvector) / Dot(destination[r], destination[r]) * destination[r];

                destination[i] = newvector;
            }
        }

        /// <summary>
        /// Orthonormalizes a list of vectors.
        /// </summary>
        /// <param name="destination">The list of orthonormalized vectors.</param>
        /// <param name="source">The list of vectors to orthonormalize.</param>
        /// <remarks>
        /// <para>
        ///   Orthonormalization is the process of making all vectors orthogonal to each
        ///   other and making all vectors of unit length. This means that any given vector will
        ///   be orthogonal to any other given vector in the list.
        /// </para>
        /// <para>
        ///   Because this method uses the modified Gram-Schmidt process, the resulting vectors
        ///   tend to be numerically unstable. The numeric stability decreases according to the vectors
        ///   position in the list so that the first vector is the most stable and the last vector is the
        ///   least stable.
        /// </para>
        /// </remarks>
        /// <exception cref="ArgumentNullException">
        /// Thrown when <paramref name="source" /> or <paramref name="destination" /> is
        /// <c>null</c>.
        /// </exception>
        /// <exception cref="ArgumentOutOfRangeException">
        /// Thrown when <paramref name="destination" /> is shorter in length than
        /// <paramref name="source" />.
        /// </exception>
        public static void Orthonormalize(Vector2[] destination, params Vector2[] source)
        {
            //Uses the modified Gram-Schmidt process.
            //Because we are making unit vectors, we can optimize the math for orthogonalization
            //and simplify the projection operation to remove the division.
            //q1 = m1 / |m1|
            //q2 = (m2 - (q1 ⋅ m2) * q1) / |m2 - (q1 ⋅ m2) * q1|
            //q3 = (m3 - (q1 ⋅ m3) * q1 - (q2 ⋅ m3) * q2) / |m3 - (q1 ⋅ m3) * q1 - (q2 ⋅ m3) * q2|
            //q4 = (m4 - (q1 ⋅ m4) * q1 - (q2 ⋅ m4) * q2 - (q3 ⋅ m4) * q3) / |m4 - (q1 ⋅ m4) * q1 - (q2 ⋅ m4) * q2 - (q3 ⋅ m4) * q3|
            //q5 = ...

            if (source == null)
                throw new ArgumentNullException(nameof(source));
            if (destination == null)
                throw new ArgumentNullException(nameof(destination));
            if (destination.Length < source.Length)
                throw new ArgumentOutOfRangeException(nameof(destination), "The destination array must be of same length or larger length than the source array.");

            for (var i = 0; i < source.Length; ++i)
            {
                Vector2 newvector = source[i];

                for (var r = 0; r < i; ++r)
                    newvector -= Dot(destination[r], newvector) * destination[r];

                newvector.Normalize();
                destination[i] = newvector;
            }
        }

        /// <summary>
        /// Transforms a 2D vector by the given <see cref="Quaternion" /> rotation.
        /// </summary>
        /// <param name="vector">The vector to rotate.</param>
        /// <param name="rotation">The <see cref="Quaternion" /> rotation to apply.</param>
        /// <param name="result">When the method completes, contains the transformed <see cref="Vector4" />.</param>
        public static void Transform(ref Vector2 vector, ref Quaternion rotation, out Vector2 result)
        {
            float x = rotation.X + rotation.X;
            float y = rotation.Y + rotation.Y;
            float z = rotation.Z + rotation.Z;
            float wz = rotation.W * z;
            float xx = rotation.X * x;
            float xy = rotation.X * y;
            float yy = rotation.Y * y;
            float zz = rotation.Z * z;

            result = new Vector2(vector.X * (1.0f - yy - zz) + vector.Y * (xy - wz), vector.X * (xy + wz) + vector.Y * (1.0f - xx - zz));
        }

        /// <summary>
        /// Transforms a 2D vector by the given <see cref="Quaternion" /> rotation.
        /// </summary>
        /// <param name="vector">The vector to rotate.</param>
        /// <param name="rotation">The <see cref="Quaternion" /> rotation to apply.</param>
        /// <returns>The transformed <see cref="Vector4" />.</returns>
        public static Vector2 Transform(Vector2 vector, Quaternion rotation)
        {
            Vector2 result;
            Transform(ref vector, ref rotation, out result);
            return result;
        }

        /// <summary>
        /// Transforms an array of vectors by the given <see cref="Quaternion" /> rotation.
        /// </summary>
        /// <param name="source">The array of vectors to transform.</param>
        /// <param name="rotation">The <see cref="Quaternion" /> rotation to apply.</param>
        /// <param name="destination">
        /// The array for which the transformed vectors are stored.
        /// This array may be the same array as <paramref name="source" />.
        /// </param>
        /// <exception cref="ArgumentNullException">
        /// Thrown when <paramref name="source" /> or <paramref name="destination" /> is
        /// <c>null</c>.
        /// </exception>
        /// <exception cref="ArgumentOutOfRangeException">
        /// Thrown when <paramref name="destination" /> is shorter in length than
        /// <paramref name="source" />.
        /// </exception>
        public static void Transform(Vector2[] source, ref Quaternion rotation, Vector2[] destination)
        {
            if (source == null)
                throw new ArgumentNullException(nameof(source));
            if (destination == null)
                throw new ArgumentNullException(nameof(destination));
            if (destination.Length < source.Length)
                throw new ArgumentOutOfRangeException(nameof(destination), "The destination array must be of same length or larger length than the source array.");

            float x = rotation.X + rotation.X;
            float y = rotation.Y + rotation.Y;
            float z = rotation.Z + rotation.Z;
            float wz = rotation.W * z;
            float xx = rotation.X * x;
            float xy = rotation.X * y;
            float yy = rotation.Y * y;
            float zz = rotation.Z * z;

            float num1 = 1.0f - yy - zz;
            float num2 = xy - wz;
            float num3 = xy + wz;
            float num4 = 1.0f - xx - zz;

            for (var i = 0; i < source.Length; ++i)
                destination[i] = new Vector2(
                    source[i].X * num1 + source[i].Y * num2,
                    source[i].X * num3 + source[i].Y * num4);
        }

        /// <summary>
        /// Transforms a 2D vector by the given <see cref="Matrix" />.
        /// </summary>
        /// <param name="vector">The source vector.</param>
        /// <param name="transform">The transformation <see cref="Matrix" />.</param>
        /// <param name="result">When the method completes, contains the transformed <see cref="Vector4" />.</param>
        public static void Transform(ref Vector2 vector, ref Matrix transform, out Vector4 result)
        {
            result = new Vector4(
                vector.X * transform.M11 + vector.Y * transform.M21 + transform.M41,
                vector.X * transform.M12 + vector.Y * transform.M22 + transform.M42,
                vector.X * transform.M13 + vector.Y * transform.M23 + transform.M43,
                vector.X * transform.M14 + vector.Y * transform.M24 + transform.M44);
        }

        /// <summary>
        /// Transforms a 2D vector by the given <see cref="Matrix" />.
        /// </summary>
        /// <param name="vector">The source vector.</param>
        /// <param name="transform">The transformation <see cref="Matrix" />.</param>
        /// <returns>The transformed <see cref="Vector4" />.</returns>
        public static Vector4 Transform(Vector2 vector, Matrix transform)
        {
            Vector4 result;
            Transform(ref vector, ref transform, out result);
            return result;
        }

        /// <summary>
        /// Transforms an array of 2D vectors by the given <see cref="Matrix" />.
        /// </summary>
        /// <param name="source">The array of vectors to transform.</param>
        /// <param name="transform">The transformation <see cref="Matrix" />.</param>
        /// <param name="destination">The array for which the transformed vectors are stored.</param>
        /// <exception cref="ArgumentNullException">
        /// Thrown when <paramref name="source" /> or <paramref name="destination" /> is
        /// <c>null</c>.
        /// </exception>
        /// <exception cref="ArgumentOutOfRangeException">
        /// Thrown when <paramref name="destination" /> is shorter in length than
        /// <paramref name="source" />.
        /// </exception>
        public static void Transform(Vector2[] source, ref Matrix transform, Vector4[] destination)
        {
            if (source == null)
                throw new ArgumentNullException(nameof(source));
            if (destination == null)
                throw new ArgumentNullException(nameof(destination));
            if (destination.Length < source.Length)
                throw new ArgumentOutOfRangeException(nameof(destination), "The destination array must be of same length or larger length than the source array.");

            for (var i = 0; i < source.Length; ++i)
                Transform(ref source[i], ref transform, out destination[i]);
        }

        /// <summary>
        /// Performs a coordinate transformation using the given <see cref="Matrix" />.
        /// </summary>
        /// <param name="coordinate">The coordinate vector to transform.</param>
        /// <param name="transform">The transformation <see cref="Matrix" />.</param>
        /// <param name="result">When the method completes, contains the transformed coordinates.</param>
        /// <remarks>
        /// A coordinate transform performs the transformation with the assumption that the w component
        /// is one. The four dimensional vector obtained from the transformation operation has each
        /// component in the vector divided by the w component. This forces the w component to be one and
        /// therefore makes the vector homogeneous. The homogeneous vector is often preferred when working
        /// with coordinates as the w component can safely be ignored.
        /// </remarks>
        public static void TransformCoordinate(ref Vector2 coordinate, ref Matrix transform, out Vector2 result)
        {
            var vector = new Vector4
            {
                X = coordinate.X * transform.M11 + coordinate.Y * transform.M21 + transform.M41,
                Y = coordinate.X * transform.M12 + coordinate.Y * transform.M22 + transform.M42,
                Z = coordinate.X * transform.M13 + coordinate.Y * transform.M23 + transform.M43,
                W = 1f / (coordinate.X * transform.M14 + coordinate.Y * transform.M24 + transform.M44)
            };

            result = new Vector2(vector.X * vector.W, vector.Y * vector.W);
        }

        /// <summary>
        /// Performs a coordinate transformation using the given <see cref="Matrix" />.
        /// </summary>
        /// <param name="coordinate">The coordinate vector to transform.</param>
        /// <param name="transform">The transformation <see cref="Matrix" />.</param>
        /// <returns>The transformed coordinates.</returns>
        /// <remarks>
        /// A coordinate transform performs the transformation with the assumption that the w component
        /// is one. The four dimensional vector obtained from the transformation operation has each
        /// component in the vector divided by the w component. This forces the w component to be one and
        /// therefore makes the vector homogeneous. The homogeneous vector is often preferred when working
        /// with coordinates as the w component can safely be ignored.
        /// </remarks>
        public static Vector2 TransformCoordinate(Vector2 coordinate, Matrix transform)
        {
            Vector2 result;
            TransformCoordinate(ref coordinate, ref transform, out result);
            return result;
        }

        /// <summary>
        /// Performs a coordinate transformation on an array of vectors using the given <see cref="Matrix" />.
        /// </summary>
        /// <param name="source">The array of coordinate vectors to transform.</param>
        /// <param name="transform">The transformation <see cref="Matrix" />.</param>
        /// <param name="destination">
        /// The array for which the transformed vectors are stored.
        /// This array may be the same array as <paramref name="source" />.
        /// </param>
        /// <exception cref="ArgumentNullException">
        /// Thrown when <paramref name="source" /> or <paramref name="destination" /> is
        /// <c>null</c>.
        /// </exception>
        /// <exception cref="ArgumentOutOfRangeException">
        /// Thrown when <paramref name="destination" /> is shorter in length than
        /// <paramref name="source" />.
        /// </exception>
        /// <remarks>
        /// A coordinate transform performs the transformation with the assumption that the w component
        /// is one. The four dimensional vector obtained from the transformation operation has each
        /// component in the vector divided by the w component. This forces the w component to be one and
        /// therefore makes the vector homogeneous. The homogeneous vector is often preferred when working
        /// with coordinates as the w component can safely be ignored.
        /// </remarks>
        public static void TransformCoordinate(Vector2[] source, ref Matrix transform, Vector2[] destination)
        {
            if (source == null)
                throw new ArgumentNullException(nameof(source));
            if (destination == null)
                throw new ArgumentNullException(nameof(destination));
            if (destination.Length < source.Length)
                throw new ArgumentOutOfRangeException(nameof(destination), "The destination array must be of same length or larger length than the source array.");

            for (var i = 0; i < source.Length; ++i)
                TransformCoordinate(ref source[i], ref transform, out destination[i]);
        }

        /// <summary>
        /// Performs a normal transformation using the given <see cref="Matrix" />.
        /// </summary>
        /// <param name="normal">The normal vector to transform.</param>
        /// <param name="transform">The transformation <see cref="Matrix" />.</param>
        /// <param name="result">When the method completes, contains the transformed normal.</param>
        /// <remarks>
        /// A normal transform performs the transformation with the assumption that the w component
        /// is zero. This causes the fourth row and fourth column of the matrix to be unused. The
        /// end result is a vector that is not translated, but all other transformation properties
        /// apply. This is often preferred for normal vectors as normals purely represent direction
        /// rather than location because normal vectors should not be translated.
        /// </remarks>
        public static void TransformNormal(ref Vector2 normal, ref Matrix transform, out Vector2 result)
        {
            result = new Vector2(
                normal.X * transform.M11 + normal.Y * transform.M21,
                normal.X * transform.M12 + normal.Y * transform.M22);
        }

        /// <summary>
        /// Performs a normal transformation using the given <see cref="Matrix" />.
        /// </summary>
        /// <param name="normal">The normal vector to transform.</param>
        /// <param name="transform">The transformation <see cref="Matrix" />.</param>
        /// <returns>The transformed normal.</returns>
        /// <remarks>
        /// A normal transform performs the transformation with the assumption that the w component
        /// is zero. This causes the fourth row and fourth column of the matrix to be unused. The
        /// end result is a vector that is not translated, but all other transformation properties
        /// apply. This is often preferred for normal vectors as normals purely represent direction
        /// rather than location because normal vectors should not be translated.
        /// </remarks>
        public static Vector2 TransformNormal(Vector2 normal, Matrix transform)
        {
            Vector2 result;
            TransformNormal(ref normal, ref transform, out result);
            return result;
        }

        /// <summary>
        /// Performs a normal transformation on an array of vectors using the given <see cref="Matrix" />.
        /// </summary>
        /// <param name="source">The array of normal vectors to transform.</param>
        /// <param name="transform">The transformation <see cref="Matrix" />.</param>
        /// <param name="destination">
        /// The array for which the transformed vectors are stored.
        /// This array may be the same array as <paramref name="source" />.
        /// </param>
        /// <exception cref="ArgumentNullException">
        /// Thrown when <paramref name="source" /> or <paramref name="destination" /> is
        /// <c>null</c>.
        /// </exception>
        /// <exception cref="ArgumentOutOfRangeException">
        /// Thrown when <paramref name="destination" /> is shorter in length than
        /// <paramref name="source" />.
        /// </exception>
        /// <remarks>
        /// A normal transform performs the transformation with the assumption that the w component
        /// is zero. This causes the fourth row and fourth column of the matrix to be unused. The
        /// end result is a vector that is not translated, but all other transformation properties
        /// apply. This is often preferred for normal vectors as normals purely represent direction
        /// rather than location because normal vectors should not be translated.
        /// </remarks>
        public static void TransformNormal(Vector2[] source, ref Matrix transform, Vector2[] destination)
        {
            if (source == null)
                throw new ArgumentNullException(nameof(source));
            if (destination == null)
                throw new ArgumentNullException(nameof(destination));
            if (destination.Length < source.Length)
                throw new ArgumentOutOfRangeException(nameof(destination), "The destination array must be of same length or larger length than the source array.");

            for (var i = 0; i < source.Length; ++i)
                TransformNormal(ref source[i], ref transform, out destination[i]);
        }

        /// <summary>
        /// Adds two vectors.
        /// </summary>
        /// <param name="left">The first vector to add.</param>
        /// <param name="right">The second vector to add.</param>
        /// <returns>The sum of the two vectors.</returns>
        public static Vector2 operator +(Vector2 left, Vector2 right)
        {
            return new Vector2(left.X + right.X, left.Y + right.Y);
        }

        /// <summary>
        /// Multiplies a vector with another by performing component-wise multiplication equivalent to
        /// <see cref="Multiply(ref Vector2,ref Vector2,out Vector2)" />.
        /// </summary>
        /// <param name="left">The first vector to multiply.</param>
        /// <param name="right">The second vector to multiply.</param>
        /// <returns>The multiplication of the two vectors.</returns>
        public static Vector2 operator *(Vector2 left, Vector2 right)
        {
            return new Vector2(left.X * right.X, left.Y * right.Y);
        }

        /// <summary>
        /// Assert a vector (return it unchanged).
        /// </summary>
        /// <param name="value">The vector to assert (unchanged).</param>
        /// <returns>The asserted (unchanged) vector.</returns>
        public static Vector2 operator +(Vector2 value)
        {
            return value;
        }

        /// <summary>
        /// Subtracts two vectors.
        /// </summary>
        /// <param name="left">The first vector to subtract.</param>
        /// <param name="right">The second vector to subtract.</param>
        /// <returns>The difference of the two vectors.</returns>
        public static Vector2 operator -(Vector2 left, Vector2 right)
        {
            return new Vector2(left.X - right.X, left.Y - right.Y);
        }

        /// <summary>
        /// Reverses the direction of a given vector.
        /// </summary>
        /// <param name="value">The vector to negate.</param>
        /// <returns>A vector facing in the opposite direction.</returns>
        public static Vector2 operator -(Vector2 value)
        {
            return new Vector2(-value.X, -value.Y);
        }

        /// <summary>
        /// Scales a vector by the given value.
        /// </summary>
        /// <param name="value">The vector to scale.</param>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <returns>The scaled vector.</returns>
        public static Vector2 operator *(float scale, Vector2 value)
        {
            return new Vector2(value.X * scale, value.Y * scale);
        }

        /// <summary>
        /// Scales a vector by the given value.
        /// </summary>
        /// <param name="value">The vector to scale.</param>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <returns>The scaled vector.</returns>
        public static Vector2 operator *(Vector2 value, float scale)
        {
            return new Vector2(value.X * scale, value.Y * scale);
        }

        /// <summary>
        /// Scales a vector by the given value.
        /// </summary>
        /// <param name="value">The vector to scale.</param>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <returns>The scaled vector.</returns>
        public static Vector2 operator /(Vector2 value, float scale)
        {
            return new Vector2(value.X / scale, value.Y / scale);
        }

        /// <summary>
        /// Scales a vector by the given value.
        /// </summary>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <param name="value">The vector to scale.</param>
        /// <returns>The scaled vector.</returns>
        public static Vector2 operator /(float scale, Vector2 value)
        {
            return new Vector2(scale / value.X, scale / value.Y);
        }

        /// <summary>
        /// Scales a vector by the given value.
        /// </summary>
        /// <param name="value">The vector to scale.</param>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <returns>The scaled vector.</returns>
        public static Vector2 operator /(Vector2 value, Vector2 scale)
        {
            return new Vector2(value.X / scale.X, value.Y / scale.Y);
        }

        /// <summary>
        /// Remainder of value divided by scale.
        /// </summary>
        /// <param name="value">The vector to scale.</param>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <returns>The remained vector.</returns>
        public static Vector2 operator %(Vector2 value, float scale)
        {
            return new Vector2(value.X % scale, value.Y % scale);
        }

        /// <summary>
        /// Remainder of value divided by scale.
        /// </summary>
        /// <param name="value">The amount by which to scale the vector.</param>
        /// <param name="scale">The vector to scale.</param>
        /// <returns>The remained vector.</returns>
        public static Vector2 operator %(float value, Vector2 scale)
        {
            return new Vector2(value % scale.X, value % scale.Y);
        }

        /// <summary>
        /// Remainder of value divided by scale.
        /// </summary>
        /// <param name="value">The vector to scale.</param>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <returns>The remained vector.</returns>
        public static Vector2 operator %(Vector2 value, Vector2 scale)
        {
            return new Vector2(value.X % scale.X, value.Y % scale.Y);
        }

        /// <summary>
        /// Perform a component-wise addition
        /// </summary>
        /// <param name="value">The input vector.</param>
        /// <param name="scalar">The scalar value to be added on elements</param>
        /// <returns>The vector with added scalar for each element.</returns>
        public static Vector2 operator +(Vector2 value, float scalar)
        {
            return new Vector2(value.X + scalar, value.Y + scalar);
        }

        /// <summary>
        /// Perform a component-wise addition
        /// </summary>
        /// <param name="value">The input vector.</param>
        /// <param name="scalar">The scalar value to be added on elements</param>
        /// <returns>The vector with added scalar for each element.</returns>
        public static Vector2 operator +(float scalar, Vector2 value)
        {
            return new Vector2(scalar + value.X, scalar + value.Y);
        }

        /// <summary>
        /// Perform a component-wise subtraction
        /// </summary>
        /// <param name="value">The input vector.</param>
        /// <param name="scalar">The scalar value to be subtracted from elements</param>
        /// <returns>The vector with subtracted scalar from each element.</returns>
        public static Vector2 operator -(Vector2 value, float scalar)
        {
            return new Vector2(value.X - scalar, value.Y - scalar);
        }

        /// <summary>
        /// Perform a component-wise subtraction
        /// </summary>
        /// <param name="value">The input vector.</param>
        /// <param name="scalar">The scalar value to be subtracted from elements</param>
        /// <returns>The vector with subtracted scalar from each element.</returns>
        public static Vector2 operator -(float scalar, Vector2 value)
        {
            return new Vector2(scalar - value.X, scalar - value.Y);
        }

        /// <summary>
        /// Tests for equality between two objects.
        /// </summary>
        /// <param name="left">The first value to compare.</param>
        /// <param name="right">The second value to compare.</param>
        /// <returns>
        /// <c>true</c> if <paramref name="left" /> has the same value as <paramref name="right" />; otherwise,
        /// <c>false</c>.
        /// </returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static bool operator ==(Vector2 left, Vector2 right)
        {
            return left.Equals(ref right);
        }

        /// <summary>
        /// Tests for inequality between two objects.
        /// </summary>
        /// <param name="left">The first value to compare.</param>
        /// <param name="right">The second value to compare.</param>
        /// <returns>
        /// <c>true</c> if <paramref name="left" /> has a different value than <paramref name="right" />; otherwise,
        /// <c>false</c>.
        /// </returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static bool operator !=(Vector2 left, Vector2 right)
        {
            return !left.Equals(ref right);
        }

        /// <summary>
        /// Performs an explicit conversion from <see cref="Vector2" /> to <see cref="Vector3" />.
        /// </summary>
        /// <param name="value">The value.</param>
        /// <returns>The result of the conversion.</returns>
        public static explicit operator Vector3(Vector2 value)
        {
            return new Vector3(value, 0.0f);
        }

        /// <summary>
        /// Performs an explicit conversion from <see cref="Vector2" /> to <see cref="Vector4" />.
        /// </summary>
        /// <param name="value">The value.</param>
        /// <returns>The result of the conversion.</returns>
        public static explicit operator Vector4(Vector2 value)
        {
            return new Vector4(value, 0.0f, 0.0f);
        }

        /// <summary>
        /// Returns a <see cref="System.String" /> that represents this instance.
        /// </summary>
        /// <returns>
        /// A <see cref="System.String" /> that represents this instance.
        /// </returns>
        public override string ToString()
        {
            return string.Format(CultureInfo.CurrentCulture, "X:{0} Y:{1}", X, Y);
        }

        /// <summary>
        /// Returns a <see cref="System.String" /> that represents this instance.
        /// </summary>
        /// <param name="format">The format.</param>
        /// <returns>
        /// A <see cref="System.String" /> that represents this instance.
        /// </returns>
        public string ToString(string format)
        {
            if (format == null)
                return ToString();

            return string.Format(CultureInfo.CurrentCulture, _formatString, X.ToString(format, CultureInfo.CurrentCulture), Y.ToString(format, CultureInfo.CurrentCulture));
        }

        /// <summary>
        /// Returns a <see cref="System.String" /> that represents this instance.
        /// </summary>
        /// <param name="formatProvider">The format provider.</param>
        /// <returns>
        /// A <see cref="System.String" /> that represents this instance.
        /// </returns>
        public string ToString(IFormatProvider formatProvider)
        {
            return string.Format(formatProvider, _formatString, X, Y);
        }

        /// <summary>
        /// Returns a <see cref="System.String" /> that represents this instance.
        /// </summary>
        /// <param name="format">The format.</param>
        /// <param name="formatProvider">The format provider.</param>
        /// <returns>
        /// A <see cref="System.String" /> that represents this instance.
        /// </returns>
        public string ToString(string format, IFormatProvider formatProvider)
        {
            if (format == null)
                return ToString(formatProvider);

            return string.Format(formatProvider, _formatString, X.ToString(format, formatProvider), Y.ToString(format, formatProvider));
        }

        /// <summary>
        /// Returns a hash code for this instance.
        /// </summary>
        /// <returns>
        /// A hash code for this instance, suitable for use in hashing algorithms and data structures like a hash table.
        /// </returns>
        public override int GetHashCode()
        {
            unchecked
            {
                return (X.GetHashCode() * 397) ^ Y.GetHashCode();
            }
        }

        /// <summary>
        /// Determines whether the specified <see cref="Vector2" /> is equal to this instance.
        /// </summary>
        /// <param name="other">The <see cref="Vector2" /> to compare with this instance.</param>
        /// <returns>
        /// <c>true</c> if the specified <see cref="Vector2" /> is equal to this instance; otherwise, <c>false</c>.
        /// </returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public bool Equals(ref Vector2 other)
        {
            return Mathf.NearEqual(other.X, X) && Mathf.NearEqual(other.Y, Y);
        }

        /// <summary>
        /// Determines whether the specified <see cref="Vector2"/> are equal.
        /// </summary>
        public static bool Equals(ref Vector2 a, ref Vector2 b)
        {
            return Mathf.NearEqual(a.X, b.X) && Mathf.NearEqual(a.Y, b.Y);
        }

        /// <summary>
        /// Determines whether the specified <see cref="Vector2" /> is equal to this instance.
        /// </summary>
        /// <param name="other">The <see cref="Vector2" /> to compare with this instance.</param>
        /// <returns>
        /// <c>true</c> if the specified <see cref="Vector2" /> is equal to this instance; otherwise, <c>false</c>.
        /// </returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public bool Equals(Vector2 other)
        {
            return Equals(ref other);
        }

        /// <summary>
        /// Determines whether the specified <see cref="System.Object" /> is equal to this instance.
        /// </summary>
        /// <param name="value">The <see cref="System.Object" /> to compare with this instance.</param>
        /// <returns>
        /// <c>true</c> if the specified <see cref="System.Object" /> is equal to this instance; otherwise, <c>false</c>.
        /// </returns>
        public override bool Equals(object value)
        {
            if (!(value is Vector2))
                return false;

            var strongValue = (Vector2)value;
            return Equals(ref strongValue);
        }
    }
}
