#region License

/* MoonWorks - Game Development Framework
 * Copyright 2022 Evan Hemsley
 */

/* Derived from code by Ethan Lee (Copyright 2009-2021).
 * Released under the Microsoft Public License.
 * See fna.LICENSE for details.

 * Derived from code by the Mono.Xna Team (Copyright 2006).
 * Released under the MIT License. See monoxna.LICENSE for details.
 */

#endregion

#region Using Statements
using System;
using System.Diagnostics;

#endregion

namespace MoonWorks.Math.Fixed
{
	/// <summary>
	/// An efficient mathematical representation for three dimensional fixed point rotations.
	/// </summary>
	[Serializable]
	[DebuggerDisplay("{DebugDisplayString,nq}")]
	public struct Quaternion : IEquatable<Quaternion>
	{
		#region Public Static Properties

		/// <summary>
		/// Returns a quaternion representing no rotation.
		/// </summary>
		public static Quaternion Identity
		{
			get
			{
				return identity;
			}
		}

		#endregion

		#region Internal Properties

		internal string DebugDisplayString
		{
			get
			{
				if (this == Quaternion.Identity)
				{
					return "Identity";
				}

				return string.Concat(
					X.ToString(), " ",
					Y.ToString(), " ",
					Z.ToString(), " ",
					W.ToString()
				);
			}
		}

		#endregion

		#region Public Fields

		/// <summary>
		/// The x coordinate of this <see cref="Quaternion"/>.
		/// </summary>
		public Fix64 X;

		/// <summary>
		/// The y coordinate of this <see cref="Quaternion"/>.
		/// </summary>
		public Fix64 Y;

		/// <summary>
		/// The z coordinate of this <see cref="Quaternion"/>.
		/// </summary>
		public Fix64 Z;

		/// <summary>
		/// The rotation component of this <see cref="Quaternion"/>.
		/// </summary>
		public Fix64 W;

		#endregion

		#region Private Static Variables

		private static readonly Quaternion identity = new Quaternion(0, 0, 0, 1);

		#endregion

		#region Public Constructors

		/// <summary>
		/// Constructs a quaternion with X, Y, Z and W from four values.
		/// </summary>
		/// <param name="x">The x coordinate in 3d-space.</param>
		/// <param name="y">The y coordinate in 3d-space.</param>
		/// <param name="z">The z coordinate in 3d-space.</param>
		/// <param name="w">The rotation component.</param>
		public Quaternion(int x, int y, int z, int w)
		{
			X = new Fix64(x);
			Y = new Fix64(y);
			Z = new Fix64(z);
			W = new Fix64(w);
		}

        public Quaternion(Fix64 x, Fix64 y, Fix64 z, Fix64 w)
        {
			X = x;
			Y = y;
			Z = z;
			W = w;
		}

		/// <summary>
		/// Constructs a quaternion with X, Y, Z from <see cref="Vector3"/> and rotation component from a scalar.
		/// </summary>
		/// <param name="value">The x, y, z coordinates in 3d-space.</param>
		/// <param name="w">The rotation component.</param>
		public Quaternion(Vector3 vectorPart, Fix64 scalarPart)
		{
			X = vectorPart.X;
			Y = vectorPart.Y;
			Z = vectorPart.Z;
			W = scalarPart;
		}

		#endregion

		#region Public Methods

		/// <summary>
		/// Transforms this quaternion into its conjugated version.
		/// </summary>
		public void Conjugate()
		{
			X = -X;
			Y = -Y;
			Z = -Z;
		}

		/// <summary>
		/// Compares whether current instance is equal to specified <see cref="Object"/>.
		/// </summary>
		/// <param name="obj">The <see cref="Object"/> to compare.</param>
		/// <returns><c>true</c> if the instances are equal; <c>false</c> otherwise.</returns>
		public override bool Equals(object obj)
		{
			return (obj is Quaternion) && Equals((Quaternion) obj);
		}

		/// <summary>
		/// Compares whether current instance is equal to specified <see cref="Quaternion"/>.
		/// </summary>
		/// <param name="other">The <see cref="Quaternion"/> to compare.</param>
		/// <returns><c>true</c> if the instances are equal; <c>false</c> otherwise.</returns>
		public bool Equals(Quaternion other)
		{
			return (X == other.X &&
					Y == other.Y &&
					Z == other.Z &&
					W == other.W);
		}

		/// <summary>
		/// Gets the hash code of this <see cref="Quaternion"/>.
		/// </summary>
		/// <returns>Hash code of this <see cref="Quaternion"/>.</returns>
		public override int GetHashCode()
		{
			return (
				this.X.GetHashCode() +
				this.Y.GetHashCode() +
				this.Z.GetHashCode() +
				this.W.GetHashCode()
			);
		}

		/// <summary>
		/// Returns the magnitude of the quaternion components.
		/// </summary>
		/// <returns>The magnitude of the quaternion components.</returns>
		public Fix64 Length()
		{
			Fix64 num = (
				(this.X * this.X) +
				(this.Y * this.Y) +
				(this.Z * this.Z) +
				(this.W * this.W)
			);
			return (Fix64) Fix64.Sqrt(num);
		}

		/// <summary>
		/// Returns the squared magnitude of the quaternion components.
		/// </summary>
		/// <returns>The squared magnitude of the quaternion components.</returns>
		public Fix64 LengthSquared()
		{
			return (
				(this.X * this.X) +
				(this.Y * this.Y) +
				(this.Z * this.Z) +
				(this.W * this.W)
			);
		}

		/// <summary>
		/// Scales the quaternion magnitude to unit length.
		/// </summary>
		public void Normalize()
		{
			Fix64 num = Fix64.One / (Fix64.Sqrt(
				(X * X) +
				(Y * Y) +
				(Z * Z) +
				(W * W)
			));
			this.X *= num;
			this.Y *= num;
			this.Z *= num;
			this.W *= num;
		}

		/// <summary>
		/// Returns a <see cref="String"/> representation of this <see cref="Quaternion"/> in the format:
		/// {X:[<see cref="X"/>] Y:[<see cref="Y"/>] Z:[<see cref="Z"/>] W:[<see cref="W"/>]}
		/// </summary>
		/// <returns>A <see cref="String"/> representation of this <see cref="Quaternion"/>.</returns>
		public override string ToString()
		{
			return (
				"{X:" + X.ToString() +
				" Y:" + Y.ToString() +
				" Z:" + Z.ToString() +
				" W:" + W.ToString() +
				"}"
			);
		}

		#endregion

		#region Public Static Methods

		/// <summary>
		/// Creates a new <see cref="Quaternion"/> that contains the sum of two quaternions.
		/// </summary>
		/// <param name="quaternion1">Source <see cref="Quaternion"/>.</param>
		/// <param name="quaternion2">Source <see cref="Quaternion"/>.</param>
		/// <returns>The result of the quaternion addition.</returns>
		public static Quaternion Add(Quaternion quaternion1, Quaternion quaternion2)
		{
			Quaternion quaternion;
			Add(ref quaternion1, ref quaternion2, out quaternion);
			return quaternion;
		}

		/// <summary>
		/// Creates a new <see cref="Quaternion"/> that contains the sum of two quaternions.
		/// </summary>
		/// <param name="quaternion1">Source <see cref="Quaternion"/>.</param>
		/// <param name="quaternion2">Source <see cref="Quaternion"/>.</param>
		/// <param name="result">The result of the quaternion addition as an output parameter.</param>
		public static void Add(
			ref Quaternion quaternion1,
			ref Quaternion quaternion2,
			out Quaternion result
		)
		{
			result.X = quaternion1.X + quaternion2.X;
			result.Y = quaternion1.Y + quaternion2.Y;
			result.Z = quaternion1.Z + quaternion2.Z;
			result.W = quaternion1.W + quaternion2.W;
		}

		/// <summary>
		/// Creates a new <see cref="Quaternion"/> that contains concatenation between two quaternion.
		/// </summary>
		/// <param name="value1">The first <see cref="Quaternion"/> to concatenate.</param>
		/// <param name="value2">The second <see cref="Quaternion"/> to concatenate.</param>
		/// <returns>The result of rotation of <paramref name="value1"/> followed by <paramref name="value2"/> rotation.</returns>
		public static Quaternion Concatenate(Quaternion value1, Quaternion value2)
		{
			Quaternion quaternion;
			Concatenate(ref value1, ref value2, out quaternion);
			return quaternion;
		}

		/// <summary>
		/// Creates a new <see cref="Quaternion"/> that contains concatenation between two quaternion.
		/// </summary>
		/// <param name="value1">The first <see cref="Quaternion"/> to concatenate.</param>
		/// <param name="value2">The second <see cref="Quaternion"/> to concatenate.</param>
		/// <param name="result">The result of rotation of <paramref name="value1"/> followed by <paramref name="value2"/> rotation as an output parameter.</param>
		public static void Concatenate(
			ref Quaternion value1,
			ref Quaternion value2,
			out Quaternion result
		)
		{
			Fix64 x1 = value1.X;
			Fix64 y1 = value1.Y;
			Fix64 z1 = value1.Z;
			Fix64 w1 = value1.W;

			Fix64 x2 = value2.X;
			Fix64 y2 = value2.Y;
			Fix64 z2 = value2.Z;
			Fix64 w2 = value2.W;

			result.X = ((x2 * w1) + (x1 * w2)) + ((y2 * z1) - (z2 * y1));
			result.Y = ((y2 * w1) + (y1 * w2)) + ((z2 * x1) - (x2 * z1));
			result.Z = ((z2 * w1) + (z1 * w2)) + ((x2 * y1) - (y2 * x1));
			result.W = (w2 * w1) - (((x2 * x1) + (y2 * y1)) + (z2 * z1));
		}

		/// <summary>
		/// Creates a new <see cref="Quaternion"/> that contains conjugated version of the specified quaternion.
		/// </summary>
		/// <param name="value">The quaternion which values will be used to create the conjugated version.</param>
		/// <returns>The conjugate version of the specified quaternion.</returns>
		public static Quaternion Conjugate(Quaternion value)
		{
			return new Quaternion(-value.X, -value.Y, -value.Z, value.W);
		}

		/// <summary>
		/// Creates a new <see cref="Quaternion"/> that contains conjugated version of the specified quaternion.
		/// </summary>
		/// <param name="value">The quaternion which values will be used to create the conjugated version.</param>
		/// <param name="result">The conjugated version of the specified quaternion as an output parameter.</param>
		public static void Conjugate(ref Quaternion value, out Quaternion result)
		{
			result.X = -value.X;
			result.Y = -value.Y;
			result.Z = -value.Z;
			result.W = value.W;
		}

		/// <summary>
		/// Creates a new <see cref="Quaternion"/> from the specified axis and angle.
		/// </summary>
		/// <param name="axis">The axis of rotation.</param>
		/// <param name="angle">The angle in radians.</param>
		/// <returns>The new quaternion builded from axis and angle.</returns>
		public static Quaternion CreateFromAxisAngle(Vector3 axis, Fix64 angle)
		{
			Quaternion quaternion;
			CreateFromAxisAngle(ref axis, angle, out quaternion);
			return quaternion;
		}

		/// <summary>
		/// Creates a new <see cref="Quaternion"/> from the specified axis and angle.
		/// </summary>
		/// <param name="axis">The axis of rotation.</param>
		/// <param name="angle">The angle in radians.</param>
		/// <param name="result">The new quaternion builded from axis and angle as an output parameter.</param>
		public static void CreateFromAxisAngle(
			ref Vector3 axis,
			Fix64 angle,
			out Quaternion result
		)
		{
			Fix64 half = angle / new Fix64(2);
			Fix64 sin = Fix64.Sin(half);
			Fix64 cos = Fix64.Cos(half);
			result.X = axis.X * sin;
			result.Y = axis.Y * sin;
			result.Z = axis.Z * sin;
			result.W = cos;
		}

		/// <summary>
		/// Creates a new <see cref="Quaternion"/> from the specified <see cref="Matrix4x4"/>.
		/// </summary>
		/// <param name="matrix">The rotation matrix.</param>
		/// <returns>A quaternion composed from the rotation part of the matrix.</returns>
		public static Quaternion CreateFromRotationMatrix(Matrix4x4 matrix)
		{
			Quaternion quaternion;
			CreateFromRotationMatrix(ref matrix, out quaternion);
			return quaternion;
		}

		/// <summary>
		/// Creates a new <see cref="Quaternion"/> from the specified <see cref="Matrix4x4"/>.
		/// </summary>
		/// <param name="matrix">The rotation matrix.</param>
		/// <param name="result">A quaternion composed from the rotation part of the matrix as an output parameter.</param>
		public static void CreateFromRotationMatrix(ref Matrix4x4 matrix, out Quaternion result)
		{
			Fix64 sqrt;
			Fix64 half;
			Fix64 scale = matrix.M11 + matrix.M22 + matrix.M33;
			Fix64 two = new Fix64(2);

			if (scale > Fix64.Zero)
			{
				sqrt = Fix64.Sqrt(scale + Fix64.One);
				result.W = sqrt / two;
				sqrt = Fix64.One / (sqrt * two);

				result.X = (matrix.M23 - matrix.M32) * sqrt;
				result.Y = (matrix.M31 - matrix.M13) * sqrt;
				result.Z = (matrix.M12 - matrix.M21) * sqrt;
			}
			else if ((matrix.M11 >= matrix.M22) && (matrix.M11 >= matrix.M33))
			{
				sqrt = Fix64.Sqrt(Fix64.One + matrix.M11 - matrix.M22 - matrix.M33);
				half = Fix64.One / (sqrt * two);

				result.X = sqrt / two;
				result.Y = (matrix.M12 + matrix.M21) * half;
				result.Z = (matrix.M13 + matrix.M31) * half;
				result.W = (matrix.M23 - matrix.M32) * half;
			}
			else if (matrix.M22 > matrix.M33)
			{
				sqrt = Fix64.Sqrt(Fix64.One + matrix.M22 - matrix.M11 - matrix.M33);
				half = Fix64.One / (sqrt * two);

				result.X = (matrix.M21 + matrix.M12) * half;
				result.Y = sqrt / two;
				result.Z = (matrix.M32 + matrix.M23) * half;
				result.W = (matrix.M31 - matrix.M13) * half;
			}
			else
			{
				sqrt = Fix64.Sqrt(Fix64.One + matrix.M33 - matrix.M11 - matrix.M22);
				half = Fix64.One / (sqrt * two);

				result.X = (matrix.M31 + matrix.M13) * half;
				result.Y = (matrix.M32 + matrix.M23) * half;
				result.Z = sqrt / two;
				result.W = (matrix.M12 - matrix.M21) * half;
			}
		}

		/// <summary>
		/// Creates a new <see cref="Quaternion"/> from the specified yaw, pitch and roll angles.
		/// </summary>
		/// <param name="yaw">Yaw around the y axis in radians.</param>
		/// <param name="pitch">Pitch around the x axis in radians.</param>
		/// <param name="roll">Roll around the z axis in radians.</param>
		/// <returns>A new quaternion from the concatenated yaw, pitch, and roll angles.</returns>
		public static Quaternion CreateFromYawPitchRoll(Fix64 yaw, Fix64 pitch, Fix64 roll)
		{
			Quaternion quaternion;
			CreateFromYawPitchRoll(yaw, pitch, roll, out quaternion);
			return quaternion;
		}

		/// <summary>
		/// Creates a new <see cref="Quaternion"/> from the specified yaw, pitch and roll angles.
		/// </summary>
		/// <param name="yaw">Yaw around the y axis in radians.</param>
		/// <param name="pitch">Pitch around the x axis in radians.</param>
		/// <param name="roll">Roll around the z axis in radians.</param>
		/// <param name="result">A new quaternion from the concatenated yaw, pitch, and roll angles as an output parameter.</param>
		public static void CreateFromYawPitchRoll(
			Fix64 yaw,
			Fix64 pitch,
			Fix64 roll,
			out Quaternion result)
		{
			Fix64 two = new Fix64(2);
			Fix64 halfRoll = roll / two;;
			Fix64 sinRoll = Fix64.Sin(halfRoll);
			Fix64 cosRoll = Fix64.Cos(halfRoll);
			Fix64 halfPitch = pitch / two;
			Fix64 sinPitch = Fix64.Sin(halfPitch);
			Fix64 cosPitch = Fix64.Cos(halfPitch);
			Fix64 halfYaw = yaw / two;
			Fix64 sinYaw = Fix64.Sin(halfYaw);
			Fix64 cosYaw = Fix64.Cos(halfYaw);
			result.X = ((cosYaw * sinPitch) * cosRoll) + ((sinYaw * cosPitch) * sinRoll);
			result.Y = ((sinYaw * cosPitch) * cosRoll) - ((cosYaw * sinPitch) * sinRoll);
			result.Z = ((cosYaw * cosPitch) * sinRoll) - ((sinYaw * sinPitch) * cosRoll);
			result.W = ((cosYaw * cosPitch) * cosRoll) + ((sinYaw * sinPitch) * sinRoll);
		}

		/// <summary>
		/// Divides a <see cref="Quaternion"/> by the other <see cref="Quaternion"/>.
		/// </summary>
		/// <param name="quaternion1">Source <see cref="Quaternion"/>.</param>
		/// <param name="quaternion2">Divisor <see cref="Quaternion"/>.</param>
		/// <returns>The result of dividing the quaternions.</returns>
		public static Quaternion Divide(Quaternion quaternion1, Quaternion quaternion2)
		{
			Quaternion quaternion;
			Divide(ref quaternion1, ref quaternion2, out quaternion);
			return quaternion;
		}

		/// <summary>
		/// Divides a <see cref="Quaternion"/> by the other <see cref="Quaternion"/>.
		/// </summary>
		/// <param name="quaternion1">Source <see cref="Quaternion"/>.</param>
		/// <param name="quaternion2">Divisor <see cref="Quaternion"/>.</param>
		/// <param name="result">The result of dividing the quaternions as an output parameter.</param>
		public static void Divide(
			ref Quaternion quaternion1,
			ref Quaternion quaternion2,
			out Quaternion result
		)
		{
			Fix64 x = quaternion1.X;
			Fix64 y = quaternion1.Y;
			Fix64 z = quaternion1.Z;
			Fix64 w = quaternion1.W;
			Fix64 num14 = (
				(quaternion2.X * quaternion2.X) +
				(quaternion2.Y * quaternion2.Y) +
				(quaternion2.Z * quaternion2.Z) +
				(quaternion2.W * quaternion2.W)
			);
			Fix64 num5 = Fix64.One / num14;
			Fix64 num4 = -quaternion2.X * num5;
			Fix64 num3 = -quaternion2.Y * num5;
			Fix64 num2 = -quaternion2.Z * num5;
			Fix64 num = quaternion2.W * num5;
			Fix64 num13 = (y * num2) - (z * num3);
			Fix64 num12 = (z * num4) - (x * num2);
			Fix64 num11 = (x * num3) - (y * num4);
			Fix64 num10 = ((x * num4) + (y * num3)) + (z * num2);
			result.X = ((x * num) + (num4 * w)) + num13;
			result.Y = ((y * num) + (num3 * w)) + num12;
			result.Z = ((z * num) + (num2 * w)) + num11;
			result.W = (w * num) - num10;
		}

		/// <summary>
		/// Returns a dot product of two quaternions.
		/// </summary>
		/// <param name="quaternion1">The first quaternion.</param>
		/// <param name="quaternion2">The second quaternion.</param>
		/// <returns>The dot product of two quaternions.</returns>
		public static Fix64 Dot(Quaternion quaternion1, Quaternion quaternion2)
		{
			return (
				(quaternion1.X * quaternion2.X) +
				(quaternion1.Y * quaternion2.Y) +
				(quaternion1.Z * quaternion2.Z) +
				(quaternion1.W * quaternion2.W)
			);
		}

		/// <summary>
		/// Returns a dot product of two quaternions.
		/// </summary>
		/// <param name="quaternion1">The first quaternion.</param>
		/// <param name="quaternion2">The second quaternion.</param>
		/// <param name="result">The dot product of two quaternions as an output parameter.</param>
		public static void Dot(
			ref Quaternion quaternion1,
			ref Quaternion quaternion2,
			out Fix64 result
		)
		{
			result = (
				(quaternion1.X * quaternion2.X) +
				(quaternion1.Y * quaternion2.Y) +
				(quaternion1.Z * quaternion2.Z) +
				(quaternion1.W * quaternion2.W)
			);
		}

		/// <summary>
		/// Returns the inverse quaternion which represents the opposite rotation.
		/// </summary>
		/// <param name="quaternion">Source <see cref="Quaternion"/>.</param>
		/// <returns>The inverse quaternion.</returns>
		public static Quaternion Inverse(Quaternion quaternion)
		{
			Quaternion inverse;
			Inverse(ref quaternion, out inverse);
			return inverse;
		}

		/// <summary>
		/// Returns the inverse quaternion which represents the opposite rotation.
		/// </summary>
		/// <param name="quaternion">Source <see cref="Quaternion"/>.</param>
		/// <param name="result">The inverse quaternion as an output parameter.</param>
		public static void Inverse(ref Quaternion quaternion, out Quaternion result)
		{
			Fix64 num2 = (
				(quaternion.X * quaternion.X) +
				(quaternion.Y * quaternion.Y) +
				(quaternion.Z * quaternion.Z) +
				(quaternion.W * quaternion.W)
			);
			Fix64 num = Fix64.One / num2;
			result.X = -quaternion.X * num;
			result.Y = -quaternion.Y * num;
			result.Z = -quaternion.Z * num;
			result.W = quaternion.W * num;
		}

		/// <summary>
		/// Creates a new <see cref="Quaternion"/> that contains subtraction of one <see cref="Quaternion"/> from another.
		/// </summary>
		/// <param name="quaternion1">Source <see cref="Quaternion"/>.</param>
		/// <param name="quaternion2">Source <see cref="Quaternion"/>.</param>
		/// <returns>The result of the quaternion subtraction.</returns>
		public static Quaternion Subtract(Quaternion quaternion1, Quaternion quaternion2)
		{
			Quaternion quaternion;
			Subtract(ref quaternion1, ref quaternion2, out quaternion);
			return quaternion;
		}

		/// <summary>
		/// Creates a new <see cref="Quaternion"/> that contains subtraction of one <see cref="Quaternion"/> from another.
		/// </summary>
		/// <param name="quaternion1">Source <see cref="Quaternion"/>.</param>
		/// <param name="quaternion2">Source <see cref="Quaternion"/>.</param>
		/// <param name="result">The result of the quaternion subtraction as an output parameter.</param>
		public static void Subtract(
			ref Quaternion quaternion1,
			ref Quaternion quaternion2,
			out Quaternion result
		)
		{
			result.X = quaternion1.X - quaternion2.X;
			result.Y = quaternion1.Y - quaternion2.Y;
			result.Z = quaternion1.Z - quaternion2.Z;
			result.W = quaternion1.W - quaternion2.W;
		}

		/// <summary>
		/// Creates a new <see cref="Quaternion"/> that contains a multiplication of two quaternions.
		/// </summary>
		/// <param name="quaternion1">Source <see cref="Quaternion"/>.</param>
		/// <param name="quaternion2">Source <see cref="Quaternion"/>.</param>
		/// <returns>The result of the quaternion multiplication.</returns>
		public static Quaternion Multiply(Quaternion quaternion1, Quaternion quaternion2)
		{
			Quaternion quaternion;
			Multiply(ref quaternion1, ref quaternion2, out quaternion);
			return quaternion;
		}

		/// <summary>
		/// Creates a new <see cref="Quaternion"/> that contains a multiplication of <see cref="Quaternion"/> and a scalar.
		/// </summary>
		/// <param name="quaternion1">Source <see cref="Quaternion"/>.</param>
		/// <param name="scaleFactor">Scalar value.</param>
		/// <returns>The result of the quaternion multiplication with a scalar.</returns>
		public static Quaternion Multiply(Quaternion quaternion1, Fix64 scaleFactor)
		{
			Quaternion quaternion;
			Multiply(ref quaternion1, scaleFactor, out quaternion);
			return quaternion;
		}

		/// <summary>
		/// Creates a new <see cref="Quaternion"/> that contains a multiplication of two quaternions.
		/// </summary>
		/// <param name="quaternion1">Source <see cref="Quaternion"/>.</param>
		/// <param name="quaternion2">Source <see cref="Quaternion"/>.</param>
		/// <param name="result">The result of the quaternion multiplication as an output parameter.</param>
		public static void Multiply(
			ref Quaternion quaternion1,
			ref Quaternion quaternion2,
			out Quaternion result
		)
		{
			Fix64 x = quaternion1.X;
			Fix64 y = quaternion1.Y;
			Fix64 z = quaternion1.Z;
			Fix64 w = quaternion1.W;
			Fix64 num4 = quaternion2.X;
			Fix64 num3 = quaternion2.Y;
			Fix64 num2 = quaternion2.Z;
			Fix64 num = quaternion2.W;
			Fix64 num12 = (y * num2) - (z * num3);
			Fix64 num11 = (z * num4) - (x * num2);
			Fix64 num10 = (x * num3) - (y * num4);
			Fix64 num9 = ((x * num4) + (y * num3)) + (z * num2);
			result.X = ((x * num) + (num4 * w)) + num12;
			result.Y = ((y * num) + (num3 * w)) + num11;
			result.Z = ((z * num) + (num2 * w)) + num10;
			result.W = (w * num) - num9;
		}

		/// <summary>
		/// Creates a new <see cref="Quaternion"/> that contains a multiplication of <see cref="Quaternion"/> and a scalar.
		/// </summary>
		/// <param name="quaternion1">Source <see cref="Quaternion"/>.</param>
		/// <param name="scaleFactor">Scalar value.</param>
		/// <param name="result">The result of the quaternion multiplication with a scalar as an output parameter.</param>
		public static void Multiply(
			ref Quaternion quaternion1,
			Fix64 scaleFactor,
			out Quaternion result
		)
		{
			result.X = quaternion1.X * scaleFactor;
			result.Y = quaternion1.Y * scaleFactor;
			result.Z = quaternion1.Z * scaleFactor;
			result.W = quaternion1.W * scaleFactor;
		}

		/// <summary>
		/// Flips the sign of the all the quaternion components.
		/// </summary>
		/// <param name="quaternion">Source <see cref="Quaternion"/>.</param>
		/// <returns>The result of the quaternion negation.</returns>
		public static Quaternion Negate(Quaternion quaternion)
		{
			return new Quaternion(
				-quaternion.X,
				-quaternion.Y,
				-quaternion.Z,
				-quaternion.W
			);
		}

		/// <summary>
		/// Flips the sign of the all the quaternion components.
		/// </summary>
		/// <param name="quaternion">Source <see cref="Quaternion"/>.</param>
		/// <param name="result">The result of the quaternion negation as an output parameter.</param>
		public static void Negate(ref Quaternion quaternion, out Quaternion result)
		{
			result.X = -quaternion.X;
			result.Y = -quaternion.Y;
			result.Z = -quaternion.Z;
			result.W = -quaternion.W;
		}

		/// <summary>
		/// Scales the quaternion magnitude to unit length.
		/// </summary>
		/// <param name="quaternion">Source <see cref="Quaternion"/>.</param>
		/// <returns>The unit length quaternion.</returns>
		public static Quaternion Normalize(Quaternion quaternion)
		{
			Quaternion quaternion2;
			Normalize(ref quaternion, out quaternion2);
			return quaternion2;
		}

		/// <summary>
		/// Scales the quaternion magnitude to unit length.
		/// </summary>
		/// <param name="quaternion">Source <see cref="Quaternion"/>.</param>
		/// <param name="result">The unit length quaternion an output parameter.</param>
		public static void Normalize(ref Quaternion quaternion, out Quaternion result)
		{
			Fix64 num = Fix64.One / (Fix64.Sqrt(
				(quaternion.X * quaternion.X) +
				(quaternion.Y * quaternion.Y) +
				(quaternion.Z * quaternion.Z) +
				(quaternion.W * quaternion.W)
			));
			result.X = quaternion.X * num;
			result.Y = quaternion.Y * num;
			result.Z = quaternion.Z * num;
			result.W = quaternion.W * num;
		}

		public static Quaternion LookAt(in Vector3 forward, in Vector3 up)
		{
			Matrix4x4 orientation = Matrix4x4.Identity;
			orientation.Forward = forward;
			orientation.Right = Vector3.Normalize(Vector3.Cross(forward, up));
			orientation.Up = Vector3.Cross(orientation.Right, forward);

			return Quaternion.CreateFromRotationMatrix(orientation);
		}

		#endregion

		#region Public Static Operator Overloads

		/// <summary>
		/// Adds two quaternions.
		/// </summary>
		/// <param name="quaternion1">Source <see cref="Quaternion"/> on the left of the add sign.</param>
		/// <param name="quaternion2">Source <see cref="Quaternion"/> on the right of the add sign.</param>
		/// <returns>Sum of the vectors.</returns>
		public static Quaternion operator +(Quaternion quaternion1, Quaternion quaternion2)
		{
			Quaternion quaternion;
			Add(ref quaternion1, ref quaternion2, out quaternion);
			return quaternion;
		}

		/// <summary>
		/// Divides a <see cref="Quaternion"/> by the other <see cref="Quaternion"/>.
		/// </summary>
		/// <param name="quaternion1">Source <see cref="Quaternion"/> on the left of the div sign.</param>
		/// <param name="quaternion2">Divisor <see cref="Quaternion"/> on the right of the div sign.</param>
		/// <returns>The result of dividing the quaternions.</returns>
		public static Quaternion operator /(Quaternion quaternion1, Quaternion quaternion2)
		{
			Quaternion quaternion;
			Divide(ref quaternion1, ref quaternion2, out quaternion);
			return quaternion;
		}

		/// <summary>
		/// Compares whether two <see cref="Quaternion"/> instances are equal.
		/// </summary>
		/// <param name="quaternion1"><see cref="Quaternion"/> instance on the left of the equal sign.</param>
		/// <param name="quaternion2"><see cref="Quaternion"/> instance on the right of the equal sign.</param>
		/// <returns><c>true</c> if the instances are equal; <c>false</c> otherwise.</returns>
		public static bool operator ==(Quaternion quaternion1, Quaternion quaternion2)
		{
			return quaternion1.Equals(quaternion2);
		}

		/// <summary>
		/// Compares whether two <see cref="Quaternion"/> instances are not equal.
		/// </summary>
		/// <param name="quaternion1"><see cref="Quaternion"/> instance on the left of the not equal sign.</param>
		/// <param name="quaternion2"><see cref="Quaternion"/> instance on the right of the not equal sign.</param>
		/// <returns><c>true</c> if the instances are not equal; <c>false</c> otherwise.</returns>
		public static bool operator !=(Quaternion quaternion1, Quaternion quaternion2)
		{
			return !quaternion1.Equals(quaternion2);
		}

		/// <summary>
		/// Multiplies two quaternions.
		/// </summary>
		/// <param name="quaternion1">Source <see cref="Quaternion"/> on the left of the mul sign.</param>
		/// <param name="quaternion2">Source <see cref="Quaternion"/> on the right of the mul sign.</param>
		/// <returns>Result of the quaternions multiplication.</returns>
		public static Quaternion operator *(Quaternion quaternion1, Quaternion quaternion2)
		{
			Quaternion quaternion;
			Multiply(ref quaternion1, ref quaternion2, out quaternion);
			return quaternion;
		}

		/// <summary>
		/// Multiplies the components of quaternion by a scalar.
		/// </summary>
		/// <param name="quaternion1">Source <see cref="Vector3"/> on the left of the mul sign.</param>
		/// <param name="scaleFactor">Scalar value on the right of the mul sign.</param>
		/// <returns>Result of the quaternion multiplication with a scalar.</returns>
		public static Quaternion operator *(Quaternion quaternion1, Fix64 scaleFactor)
		{
			Quaternion quaternion;
			Multiply(ref quaternion1, scaleFactor, out quaternion);
			return quaternion;
		}

		/// <summary>
		/// Subtracts a <see cref="Quaternion"/> from a <see cref="Quaternion"/>.
		/// </summary>
		/// <param name="quaternion1">Source <see cref="Vector3"/> on the left of the sub sign.</param>
		/// <param name="quaternion2">Source <see cref="Vector3"/> on the right of the sub sign.</param>
		/// <returns>Result of the quaternion subtraction.</returns>
		public static Quaternion operator -(Quaternion quaternion1, Quaternion quaternion2)
		{
			Quaternion quaternion;
			Subtract(ref quaternion1, ref quaternion2, out quaternion);
			return quaternion;
		}

		/// <summary>
		/// Flips the sign of the all the quaternion components.
		/// </summary>
		/// <param name="quaternion">Source <see cref="Quaternion"/> on the right of the sub sign.</param>
		/// <returns>The result of the quaternion negation.</returns>
		public static Quaternion operator -(Quaternion quaternion)
		{
			Quaternion quaternion2;
			Negate(ref quaternion, out quaternion2);
			return quaternion2;
		}

		#endregion
	}
}