RAGECOOP-V/Core/CompactVectors/LQuaternion.cs

using System;
using System.Collections.Generic;
using System.Globalization;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using GTA.Math;

namespace RageCoop.Core.CompactVectors
{
    internal struct LQuaternion : IEquatable<LQuaternion>
    {
        /// <summary>
        /// Gets or sets the X component of the quaternion.
        /// </summary>
        /// <value>The X component of the quaternion.</value>
        public float X;

        /// <summary>
        /// Gets or sets the Y component of the quaternion.
        /// </summary>
        /// <value>The Y component of the quaternion.</value>
        public float Y;

        /// <summary>
        /// Gets or sets the Z component of the quaternion.
        /// </summary>
        /// <value>The Z component of the quaternion.</value>
        public float Z;

        /// <summary>
        /// Gets or sets the W component of the quaternion.
        /// </summary>
        /// <value>The W component of the quaternion.</value>
        public float W;

        /// <summary>
        /// Initializes a new instance of the <see cref="LQuaternion"/> structure.
        /// </summary>
        /// <param name="x">The X component of the quaternion.</param>
        /// <param name="y">The Y component of the quaternion.</param>
        /// <param name="z">The Z component of the quaternion.</param>
        /// <param name="w">The W component of the quaternion.</param>
        public LQuaternion(float x, float y, float z, float w) : this()
        {
            X = x;
            Y = y;
            Z = z;
            W = w;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="LQuaternion"/> structure.
        /// </summary>
        /// <param name="axis">The axis of rotation.</param>
        /// <param name="angle">The angle of rotation in radians.</param>
        public LQuaternion(Vector3 axis, float angle) : this()
        {
            axis = Vector3.Normalize(axis);

            float half = angle * 0.5f;
            float sin = (float)(System.Math.Sin((double)(half)));
            float cos = (float)(System.Math.Cos((double)(half)));

            X = axis.X * sin;
            Y = axis.Y * sin;
            Z = axis.Z * sin;
            W = cos;
        }

        /// <summary>
        /// A <see cref="LQuaternion"/> with all of its components set to zero.
        /// </summary>
        public static LQuaternion Zero => new LQuaternion();

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

        /// <summary>
        /// The identity <see cref="LQuaternion"/> (0, 0, 0, 1).
        /// </summary>
        public static LQuaternion Identity => new LQuaternion(0.0f, 0.0f, 0.0f, 1.0f);

        /// <summary>
        /// Gets the axis components of the quaternion.
        /// </summary>
        public Vector3 Axis
        {
            get
            {
                if (Length() != 1.0f)
                {
                    return Vector3.Zero;
                }

                float length = 1.0f - (W * W);
                if (length == 0f)
                {
                    return Vector3.UnitX;
                }

                float inv = 1.0f / (float)System.Math.Sqrt(length);
                return new Vector3(X * inv, Y * inv, Z * inv);
            }
        }

        /// <summary>
        /// Gets the angle of the quaternion.
        /// </summary>
        public float Angle => ((System.Math.Abs(W) <= 1.0f) ? 2.0f * (float)(System.Math.Acos(W)) : 0.0f);

        /// <summary>
        /// Calculates the length of the quaternion.
        /// </summary>
        /// <returns>The length of the quaternion.</returns>
        public float Length() => (float)System.Math.Sqrt((X * X) + (Y * Y) + (Z * Z) + (W * W));

        /// <summary>
        /// Calculates the squared length of the quaternion.
        /// </summary>
        /// <returns>The squared length of the quaternion.</returns>
        public float LengthSquared() => (X * X) + (Y * Y) + (Z * Z) + (W * W);

        /// <summary>
        /// Converts the quaternion into a unit quaternion.
        /// </summary>
        public void Normalize()
        {
            float length = Length();
            if (length != 0f)
            {
                float inverse = 1.0f / length;
                X *= inverse;
                Y *= inverse;
                Z *= inverse;
                W *= inverse;
            }
        }

        /// <summary>
        /// Conjugates the quaternion.
        /// </summary>
        public void Conjugate()
        {
            X = -X;
            Y = -Y;
            Z = -Z;
        }

        /// <summary>
        /// Conjugates and renormalizes the quaternion.
        /// </summary>
        public void Invert()
        {
            float lengthSq = LengthSquared();
            if (lengthSq != 0f)
            {
                lengthSq = 1.0f / lengthSq;

                X = -X * lengthSq;
                Y = -Y * lengthSq;
                Z = -Z * lengthSq;
                W = W * lengthSq;
            }
        }

        /// <summary>
        /// Reverses the direction of a given quaternion.
        /// </summary>
        /// <param name="quaternion">The quaternion to negate.</param>
        /// <returns>A quaternion facing in the opposite direction.</returns>
        public static LQuaternion Negate(LQuaternion quaternion)
        {
            LQuaternion result = Zero;
            result.X = -quaternion.X;
            result.Y = -quaternion.Y;
            result.Z = -quaternion.Z;
            result.W = -quaternion.W;
            return result;
        }

        /// <summary>
        /// Adds two quaternions.
        /// </summary>
        /// <param name="left">The first quaternion to add.</param>
        /// <param name="right">The second quaternion to add.</param>
        /// <returns>The sum of the two quaternions.</returns>
        public static LQuaternion Add(LQuaternion left, LQuaternion right)
        {
            LQuaternion result = Zero;
            result.X = left.X + right.X;
            result.Y = left.Y + right.Y;
            result.Z = left.Z + right.Z;
            result.W = left.W + right.W;
            return result;
        }

        /// <summary>
        /// Subtracts two quaternions.
        /// </summary>
        /// <param name="left">The first quaternion to subtract.</param>
        /// <param name="right">The second quaternion to subtract.</param>
        /// <returns>The difference of the two quaternions.</returns>
        public static LQuaternion Subtract(LQuaternion left, LQuaternion right)
        {
            LQuaternion result = Zero;
            result.X = left.X - right.X;
            result.Y = left.Y - right.Y;
            result.Z = left.Z - right.Z;
            result.W = left.W - right.W;
            return result;
        }

        /// <summary>
        /// Multiplies two Quaternions together.
        /// </summary>
        /// <param name="left">The Quaternion on the left side of the multiplication.</param>
        /// <param name="right">The Quaternion on the right side of the multiplication.</param>
        /// <returns>The result of the multiplication.</returns>
        public static LQuaternion Multiply(LQuaternion left, LQuaternion right)
        {
            LQuaternion quaternion;
            float lx = left.X;
            float ly = left.Y;
            float lz = left.Z;
            float lw = left.W;
            float rx = right.X;
            float ry = right.Y;
            float rz = right.Z;
            float rw = right.W;

            quaternion.X = (lx * rw + rx * lw) + (ly * rz) - (lz * ry);
            quaternion.Y = (ly * rw + ry * lw) + (lz * rx) - (lx * rz);
            quaternion.Z = (lz * rw + rz * lw) + (lx * ry) - (ly * rx);
            quaternion.W = (lw * rw) - (lx * rx + ly * ry + lz * rz);

            return quaternion;
        }

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

        /// <summary>
        /// Divides a quaternion by another.
        /// </summary>
        /// <param name="left">The first quaternion to divide.</param>
        /// <param name="right">The second quaternion to divide.</param>
        /// <returns>The divided quaternion.</returns>
        public static LQuaternion Divide(LQuaternion left, LQuaternion right)
        {
            return Multiply(left, Invert(right));
        }

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

        /// <summary>
        /// Creates the conjugate of a specified Quaternion.
        /// </summary>
        /// <param name="value">The Quaternion of which to return the conjugate.</param>
        /// <returns>A new Quaternion that is the conjugate of the specified one.</returns>
        public static LQuaternion Conjugate(LQuaternion value)
        {
            LQuaternion ans;

            ans.X = -value.X;
            ans.Y = -value.Y;
            ans.Z = -value.Z;
            ans.W = value.W;

            return ans;
        }

        /// <summary>
        /// Conjugates and renormalizes the quaternion.
        /// </summary>
        /// <param name="quaternion">The quaternion to conjugate and re-normalize.</param>
        /// <returns>The conjugated and renormalized quaternion.</returns>
        public static LQuaternion Invert(LQuaternion quaternion)
        {
            LQuaternion result = Zero;
            float lengthSq = 1.0f / ((quaternion.X * quaternion.X) + (quaternion.Y * quaternion.Y) + (quaternion.Z * quaternion.Z) + (quaternion.W * quaternion.W));

            result.X = -quaternion.X * lengthSq;
            result.Y = -quaternion.Y * lengthSq;
            result.Z = -quaternion.Z * lengthSq;
            result.W = quaternion.W * lengthSq;

            return result;
        }

        /// <summary>
        /// Calculates the dot product of two quaternions.
        /// </summary>
        /// <param name="left">First source quaternion.</param>
        /// <param name="right">Second source quaternion.</param>
        /// <returns>The dot product of the two quaternions.</returns>
        public static float Dot(LQuaternion left, LQuaternion right) => (left.X * right.X) + (left.Y * right.Y) + (left.Z * right.Z) + (left.W * right.W);

        /// <summary>
        /// Performs a linear interpolation between two quaternion.
        /// </summary>
        /// <param name="start">Start quaternion.</param>
        /// <param name="end">End quaternion.</param>
        /// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end"/>.</param>
        /// <returns>The linear interpolation of the two quaternions.</returns>
        /// <remarks>
        /// This method performs the linear interpolation based on the following formula.
        /// <code>start + (end - start) * amount</code>
        /// 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 LQuaternion Lerp(LQuaternion start, LQuaternion end, float amount)
        {
            LQuaternion result = Zero;
            float inverse = 1.0f - amount;
            float dot = (start.X * end.X) + (start.Y * end.Y) + (start.Z * end.Z) + (start.W * end.W);

            if (dot >= 0.0f)
            {
                result.X = (inverse * start.X) + (amount * end.X);
                result.Y = (inverse * start.Y) + (amount * end.Y);
                result.Z = (inverse * start.Z) + (amount * end.Z);
                result.W = (inverse * start.W) + (amount * end.W);
            }
            else
            {
                result.X = (inverse * start.X) - (amount * end.X);
                result.Y = (inverse * start.Y) - (amount * end.Y);
                result.Z = (inverse * start.Z) - (amount * end.Z);
                result.W = (inverse * start.W) - (amount * end.W);
            }

            float invLength = 1.0f / result.Length();

            result.X *= invLength;
            result.Y *= invLength;
            result.Z *= invLength;
            result.W *= invLength;

            return result;
        }

        /// <summary>
        /// Interpolates between two quaternions, using spherical linear interpolation..
        /// </summary>
        /// <param name="start">Start quaternion.</param>
        /// <param name="end">End quaternion.</param>
        /// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end"/>.</param>
        /// <returns>The spherical linear interpolation of the two quaternions.</returns>
        public static LQuaternion Slerp(LQuaternion start, LQuaternion end, float amount)
        {
            LQuaternion result = Zero;
            float kEpsilon = (float)(1.192093E-07);
            float opposite;
            float inverse;
            float dot = Dot(start, end);

            if (System.Math.Abs(dot) > (1.0f - kEpsilon))
            {
                inverse = 1.0f - amount;
                opposite = amount * System.Math.Sign(dot);
            }
            else
            {
                float acos = (float)System.Math.Acos(System.Math.Abs(dot));
                float invSin = (float)(1.0 / System.Math.Sin(acos));

                inverse = (float)(System.Math.Sin((1.0f - amount) * acos) * invSin);
                opposite = (float)(System.Math.Sin(amount * acos) * invSin * System.Math.Sign(dot));
            }

            result.X = (inverse * start.X) + (opposite * end.X);
            result.Y = (inverse * start.Y) + (opposite * end.Y);
            result.Z = (inverse * start.Z) + (opposite * end.Z);
            result.W = (inverse * start.W) + (opposite * end.W);

            return result;
        }

        /// <summary>
        /// Interpolates between two quaternions, using spherical linear interpolation. The parameter /t/ is not clamped.
        /// </summary>
        /// <param name="a"></param>
        /// <param name="b"></param>
        /// <param name="t"></param>
        public static LQuaternion SlerpUnclamped(LQuaternion a, LQuaternion b, float t)
        {
            if (a.LengthSquared() == 0.0f)
            {
                if (b.LengthSquared() == 0.0f)
                {
                    return Identity;
                }
                return b;
            }
            else if (b.LengthSquared() == 0.0f)
            {
                return a;
            }


            float cosHalfAngle = a.W * b.W + Vector3.Dot(a.Axis, b.Axis);

            if (cosHalfAngle >= 1.0f || cosHalfAngle <= -1.0f)
            {
                return a;
            }
            else if (cosHalfAngle < 0.0f)
            {
                b.X = -b.X;
                b.Y = -b.Y;
                b.Z = -b.Z;
                b.W = -b.W;
                cosHalfAngle = -cosHalfAngle;
            }

            float blendA;
            float blendB;
            if (cosHalfAngle < 0.99f)
            {
                float halfAngle = (float)System.Math.Acos(cosHalfAngle);
                float sinHalfAngle = (float)System.Math.Sin(halfAngle);
                float oneOverSinHalfAngle = 1.0f / sinHalfAngle;
                blendA = (float)System.Math.Sin(halfAngle * (1.0f - t)) * oneOverSinHalfAngle;
                blendB = (float)System.Math.Sin(halfAngle * t) * oneOverSinHalfAngle;
            }
            else
            {
                blendA = 1.0f - t;
                blendB = t;
            }

            LQuaternion result = new LQuaternion(blendA * a.Axis + blendB * b.Axis, blendA * a.W + blendB * b.W);
            if (result.LengthSquared() > 0.0f)
            {
                return Normalize(result);
            }
            else
            {
                return Identity;
            }
        }

        /// <summary>
        /// Creates a rotation with the specified <paramref name="forward"/> and <see cref="Vector3.WorldUp"/> directions.
        /// </summary>
        public static LQuaternion LookRotation(Vector3 forward) => LookRotation(forward, Vector3.WorldUp);
        /// <summary>
        /// Creates a rotation with the specified <paramref name="forward"/> and <paramref name="up"/> directions.
        /// </summary>
        public static LQuaternion LookRotation(Vector3 forward, Vector3 up) => DirectionVectors(Vector3.Cross(forward, up), forward, up);

        /// <summary>
        /// Creates a rotation which rotates from fromDirection to toDirection.
        /// </summary>
        public static LQuaternion FromToRotation(Vector3 fromDirection, Vector3 toDirection)
        {
            float NormAB = (float)(System.Math.Sqrt(fromDirection.LengthSquared() * fromDirection.LengthSquared()));

            float w = NormAB + Vector3.Dot(fromDirection, toDirection);
            LQuaternion Result;

            if (w >= 1e-6f * NormAB)
            {
                Result = new LQuaternion(Vector3.Cross(fromDirection, toDirection), w);
            }
            else
            {
                w = 0.0f;
                Result = System.Math.Abs(fromDirection.X) > System.Math.Abs(fromDirection.Y)
                    ? new LQuaternion(-fromDirection.Z, 0.0f, fromDirection.X, w)
                    : new LQuaternion(0.0f, -fromDirection.Z, fromDirection.Y, w);
            }

            Result.Normalize();
            return Result;
        }

        /// <summary>
        /// Rotates a rotation from towards to.
        /// </summary>
        /// <param name="from">From Quaternion.</param>
        /// <param name="to">To Quaternion.</param>
        /// <param name ="maxDegreesDelta"></param>
        public static LQuaternion RotateTowards(LQuaternion from, LQuaternion to, float maxDegreesDelta)
        {
            float angle = AngleBetween(from, to);
            if (angle == 0.0f)
            {
                return to;
            }
            float t = System.Math.Min(1.0f, maxDegreesDelta / angle);
            return SlerpUnclamped(from, to, t);
        }

        /// <summary>
        /// Returns the angle in degrees between two rotations a and b.
        /// </summary>
        /// <param name="a">The first quaternion to calculate angle.</param>
        /// <param name="b">The second quaternion to calculate angle.</param>
        /// <returns>The angle in degrees between two rotations a and b.</returns>
        public static float AngleBetween(LQuaternion a, LQuaternion b)
        {
            float dot = Dot(a, b);
            return (float)((System.Math.Acos(System.Math.Min(System.Math.Abs(dot), 1.0f)) * 2.0 * (180.0f / System.Math.PI)));
        }

        /// <summary>
        /// Returns a rotation that rotates z degrees around the z axis, x degrees around the x axis, and y degrees around the y axis (in that order).
        /// </summary>
        /// <param name="zaxis">Z degrees.</param>
        /// <param name ="xaxis">X degrees.</param>
        /// <param name ="yaxis">Y degrees.</param>
        public static LQuaternion Euler(float zaxis, float xaxis, float yaxis)
        {
            float Deg2Rad = (float)((System.Math.PI / 180.0));
            return RotationYawPitchRoll(zaxis * Deg2Rad, xaxis * Deg2Rad, yaxis * Deg2Rad);
        }

        /// <summary>
        /// Returns a rotation that rotates z degrees around the z axis, x degrees around the x axis, and y degrees around the y axis (in that order).
        /// </summary>
        /// <param name="euler">Euler angles in degrees. euler.X = around X axis, euler.Y = around Y axis, euler.Z = around Z axis</param>
        public static LQuaternion Euler(Vector3 euler)
        {
            Vector3 eulerRad = euler * (float)((System.Math.PI / 180.0));
            return RotationYawPitchRoll(eulerRad.Z, eulerRad.X, eulerRad.Y);
        }

        /// <summary>
        /// Creates a quaternion given a rotation and an axis.
        /// </summary>
        /// <param name="axis">The axis of rotation.</param>
        /// <param name="angle">The angle of rotation in radians.</param>
        /// <returns>The newly created quaternion.</returns>
        public static LQuaternion RotationAxis(Vector3 axis, float angle)
        {
            LQuaternion result = Zero;

            axis = Vector3.Normalize(axis);

            float half = angle * 0.5f;
            float sin = (float)(System.Math.Sin((double)(half)));
            float cos = (float)(System.Math.Cos((double)(half)));

            result.X = axis.X * sin;
            result.Y = axis.Y * sin;
            result.Z = axis.Z * sin;
            result.W = cos;

            return result;
        }

        /// <summary>
        /// Creates a quaternion given a rotation matrix.
        /// </summary>
        /// <param name="matrix">The rotation matrix.</param>
        /// <returns>The newly created quaternion.</returns>
        public static LQuaternion RotationMatrix(Matrix matrix)
        {
            LQuaternion result = Zero;
            float sqrt;
            float half;
            float scale = matrix.M11 + matrix.M22 + matrix.M33;

            if (scale > 0.0f)
            {
                sqrt = (float)System.Math.Sqrt(scale + 1.0f);
                result.W = sqrt * 0.5f;
                sqrt = 0.5f / sqrt;

                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 = (float)System.Math.Sqrt(1.0f + matrix.M11 - matrix.M22 - matrix.M33);
                half = 0.5f / sqrt;

                result.X = 0.5f * sqrt;
                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 = (float)System.Math.Sqrt(1.0f + matrix.M22 - matrix.M11 - matrix.M33);
                half = 0.5f / sqrt;

                result.X = (matrix.M21 + matrix.M12) * half;
                result.Y = 0.5f * sqrt;
                result.Z = (matrix.M32 + matrix.M23) * half;
                result.W = (matrix.M31 - matrix.M13) * half;
            }
            else
            {
                sqrt = (float)System.Math.Sqrt(1.0f + matrix.M33 - matrix.M11 - matrix.M22);
                half = 0.5f / sqrt;

                result.X = (matrix.M31 + matrix.M13) * half;
                result.Y = (matrix.M32 + matrix.M23) * half;
                result.Z = 0.5f * sqrt;
                result.W = (matrix.M12 - matrix.M21) * half;
            }

            return result;
        }

        /// <summary>
        /// Creates a Quaternion from the given yaw, pitch, and roll, in radians.
        /// </summary>
        /// <param name="yaw">The yaw angle, in radians, around the Z-axis.</param>
        /// <param name="pitch">The pitch angle, in radians, around the X-axis.</param>
        /// <param name="roll">The roll angle, in radians, around the Y-axis.</param>
        /// <returns>The newly created quaternion.</returns>
        public static LQuaternion RotationYawPitchRoll(float yaw, float pitch, float roll)
        {
            LQuaternion result = Zero;

            float halfYaw = yaw * 0.5f;
            float sinYaw = (float)(System.Math.Sin((double)(halfYaw)));
            float cosYaw = (float)(System.Math.Cos((double)(halfYaw)));
            float halfPitch = pitch * 0.5f;
            float sinPitch = (float)(System.Math.Sin((double)(halfPitch)));
            float cosPitch = (float)(System.Math.Cos((double)(halfPitch)));
            float halfRoll = roll * 0.5f;
            float sinRoll = (float)(System.Math.Sin((double)(halfRoll)));
            float cosRoll = (float)(System.Math.Cos((double)(halfRoll)));

            result.X = (cosRoll * sinPitch * cosYaw) + (sinRoll * cosPitch * sinYaw);
            result.Y = (sinRoll * cosPitch * cosYaw) - (cosRoll * sinPitch * sinYaw);
            result.Z = (cosRoll * cosPitch * sinYaw) - (sinRoll * sinPitch * cosYaw);
            result.W = (cosRoll * cosPitch * cosYaw) + (sinRoll * sinPitch * sinYaw);

            return result;
        }

        /// <summary>
        /// Creates a Quaternion from the given relative x, y, z axis
        /// </summary>
        /// The Vectors need to be perpendicular to each other
        /// <param name="rightVector">Relative X axis</param>
        /// <param name="forwardVector">Relative Y axis</param>
        /// <param name="upVector">Relative Z axis</param>
        /// <returns>The newly created quaternion.</returns>
        public static LQuaternion DirectionVectors(Vector3 rightVector, Vector3 forwardVector, Vector3 upVector)
        {
            rightVector.Normalize();
            forwardVector.Normalize();
            upVector.Normalize();

            Matrix rotationMatrix = new Matrix();
            rotationMatrix[0, 0] = rightVector.X;
            rotationMatrix[0, 1] = rightVector.Y;
            rotationMatrix[0, 2] = rightVector.Z;

            rotationMatrix[1, 0] = forwardVector.X;
            rotationMatrix[1, 1] = forwardVector.Y;
            rotationMatrix[1, 2] = forwardVector.Z;

            rotationMatrix[2, 0] = upVector.X;
            rotationMatrix[2, 1] = upVector.Y;
            rotationMatrix[2, 2] = upVector.Z;

            return RotationMatrix(rotationMatrix);
        }

        /// <summary>
        /// Get direction vectors from the given quaternion
        /// </summary>
        /// <param name="quaternion">The quaternion</param>
        /// <param name="rightVector">RightVector = relative x axis</param>
        /// <param name="forwardVector">ForwardVector = relative y axis</param>
        /// <param name="upVector">UpVector = relative z axis</param>
        public static void GetDirectionVectors(LQuaternion quaternion, out Vector3 rightVector, out Vector3 forwardVector, out Vector3 upVector)
        {
            quaternion.Normalize();
            rightVector = quaternion * Vector3.WorldEast;
            forwardVector = quaternion * Vector3.WorldNorth;
            upVector = quaternion * Vector3.WorldUp;
        }

        /// <summary>
        /// Reverses the direction of a given quaternion.
        /// </summary>
        /// <param name="quaternion">The quaternion to negate.</param>
        /// <returns>A quaternion facing in the opposite direction.</returns>
        public static LQuaternion operator -(LQuaternion quaternion)
        {
            LQuaternion result = Zero;
            result.X = -quaternion.X;
            result.Y = -quaternion.Y;
            result.Z = -quaternion.Z;
            result.W = -quaternion.W;
            return result;
        }

        /// <summary>
        /// Adds two quaternions.
        /// </summary>
        /// <param name="left">The first quaternion to add.</param>
        /// <param name="right">The second quaternion to add.</param>
        /// <returns>The sum of the two quaternions.</returns>
        public static LQuaternion operator +(LQuaternion left, LQuaternion right)
        {
            LQuaternion result = Zero;
            result.X = left.X + right.X;
            result.Y = left.Y + right.Y;
            result.Z = left.Z + right.Z;
            result.W = left.W + right.W;
            return result;
        }

        /// <summary>
        /// Subtracts two quaternions.
        /// </summary>
        /// <param name="left">The first quaternion to subtract.</param>
        /// <param name="right">The second quaternion to subtract.</param>
        /// <returns>The difference of the two quaternions.</returns>
        public static LQuaternion operator -(LQuaternion left, LQuaternion right)
        {
            LQuaternion result = Zero;
            result.X = left.X - right.X;
            result.Y = left.Y - right.Y;
            result.Z = left.Z - right.Z;
            result.W = left.W - right.W;
            return result;
        }

        /// <summary>
        /// Multiplies a quaternion by another.
        /// </summary>
        /// <param name="left">The first quaternion to multiply.</param>
        /// <param name="right">The second quaternion to multiply.</param>
        /// <returns>The multiplied quaternion.</returns>
        public static LQuaternion operator *(LQuaternion left, LQuaternion right)
        {
            LQuaternion quaternion = Zero;
            float lx = left.X;
            float ly = left.Y;
            float lz = left.Z;
            float lw = left.W;
            float rx = right.X;
            float ry = right.Y;
            float rz = right.Z;
            float rw = right.W;

            quaternion.X = (lx * rw + rx * lw) + (ly * rz) - (lz * ry);
            quaternion.Y = (ly * rw + ry * lw) + (lz * rx) - (lx * rz);
            quaternion.Z = (lz * rw + rz * lw) + (lx * ry) - (ly * rx);
            quaternion.W = (lw * rw) - (lx * rx + ly * ry + lz * rz);

            return quaternion;
        }

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

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

        /// <summary>
        /// Divides a Quaternion by another Quaternion.
        /// </summary>
        /// <param name="left">The source Quaternion.</param>
        /// <param name="right">The divisor.</param>
        /// <returns>The result of the division.</returns>
        public static LQuaternion operator /(LQuaternion left, LQuaternion right)
        {
            LQuaternion quaternion = Zero;

            float lx = left.X;
            float ly = left.Y;
            float lz = left.Z;
            float lw = left.W;

            // Inverse part.
            float ls = right.X * right.X + right.Y * right.Y +
                       right.Z * right.Z + right.W * right.W;
            float invNorm = 1.0f / ls;

            float rx = -right.X * invNorm;
            float ry = -right.Y * invNorm;
            float rz = -right.Z * invNorm;
            float rw = right.W * invNorm;

            // Multiply part.
            quaternion.X = (lx * rw + rx * lw) + (ly * rz) - (lz * ry);
            quaternion.Y = (ly * rw + ry * lw) + (lz * rx) - (lx * rz);
            quaternion.Z = (lz * rw + rz * lw) + (lx * ry) - (ly * rx);
            quaternion.W = (lw * rw) - (lx * rx + ly * ry + lz * rz);

            return quaternion;
        }

        /// <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><see langword="true" /> if <paramref name="left"/> has the same value as <paramref name="right"/>; otherwise, <see langword="false" />.</returns>
        public static bool operator ==(LQuaternion left, LQuaternion right) => Equals(left, 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><see langword="true" /> if <paramref name="left"/> has a different value than <paramref name="right"/>; otherwise, <see langword="false" />.</returns>
        public static bool operator !=(LQuaternion left, LQuaternion right) => !Equals(left, right);

        #region RotateTransformOperators

        /// <summary>
        /// Rotates the point with rotation.
        /// </summary>
        /// <param name="rotation">The quaternion to rotate the vector.</param>
        /// <param name="point">The vector to be rotated.</param>
        /// <returns>The vector after rotation.</returns>
        public static Vector3 operator *(LQuaternion rotation, Vector3 point)
        {
            float q0 = rotation.W;
            float q0Square = rotation.W * rotation.W;
            Vector3 q = new Vector3(rotation.X, rotation.Y, rotation.Z);
            return ((q0Square - q.LengthSquared()) * point) + (2 * Vector3.Dot(q, point) * q) + (2 * q0 * Vector3.Cross(q, point));
        }

        /// <summary>
        /// Rotates the point with rotation.
        /// </summary>
        /// <param name="rotation">The quaternion to rotate the vector.</param>
        /// <param name="point">The vector to be rotated.</param>
        /// <returns>The vector after rotation.</returns>
        public static Vector3 RotateTransform(LQuaternion rotation, Vector3 point) => rotation * point;

        /// <summary>
        /// Rotates the point with rotation.
        /// </summary>
        /// <param name="rotation">The quaternion to rotate the vector.</param>
        /// <param name="point">The vector to be rotated.</param>
        /// <param name="center">The vector representing the origin of the new coordinate system.</param>
        /// <returns>The vector after rotation in the original coordinate system.</returns>
        public static Vector3 RotateTransform(LQuaternion rotation, Vector3 point, Vector3 center)
        {
            Vector3 PointNewCenter = Vector3.Subtract(point, center);
            Vector3 TransformedPoint = RotateTransform(rotation, PointNewCenter);
            return Vector3.Add(TransformedPoint, center);
        }

        /// <summary>
        /// Rotates the point with rotation.
        /// </summary>
        /// <param name="point">The vector to be rotated.</param>
        /// <returns>The vector after rotation.</returns>
        public Vector3 RotateTransform(Vector3 point) => RotateTransform(this, point);

        /// <summary>
        /// Rotates the point with rotation.
        /// </summary>
        /// <param name="point">The vector to be rotated.</param>
        /// <param name="center">The vector representing the origin of the new coordinate system.</param>
        /// <returns>The vector after rotation in the original coordinate system.</returns>
        public Vector3 RotateTransform(Vector3 point, Vector3 center) => RotateTransform(this, point, center);

        #endregion RotateTransformOperators

        /// <summary>
        /// Converts the value of the object to its equivalent string representation.
        /// </summary>
        /// <returns>The string representation of the value of this instance.</returns>
        public override string ToString()
        {
            return String.Format(CultureInfo.CurrentCulture, "X:{0} Y:{1} Z:{2} W:{3}", X.ToString(), Y.ToString(), Z.ToString(), W.ToString());
        }

        /// <summary>
        /// Converts the value of the object to its equivalent string representation.
        /// </summary>
        /// <param name="format">The format.</param>
        /// <returns>The string representation of the value of this instance.</returns>
        public string ToString(string format)
        {
            return String.Format(CultureInfo.InvariantCulture, "X:{0} Y:{1} Z:{2} W:{3}", X.ToString(format), Y.ToString(format), Z.ToString(format), W.ToString(format));
        }

        /// <summary>
        /// Returns the hash code for this instance.
        /// </summary>
        /// <returns>A 32-bit signed integer hash code.</returns>
        public override int GetHashCode() => X.GetHashCode() + Y.GetHashCode() + Z.GetHashCode() + W.GetHashCode();

        /// <summary>
        /// Returns a value that indicates whether the current instance is equal to a specified object.
        /// </summary>
        /// <param name="obj">Object to make the comparison with.</param>
        /// <returns><see langword="true" /> if the current instance is equal to the specified object; <see langword="false" /> otherwise.</returns>
        public override bool Equals(object obj)
        {
            if (obj == null || obj.GetType() != GetType())
            {
                return false;
            }

            return Equals((LQuaternion)obj);
        }

        /// <summary>
        /// Returns a value that indicates whether the current instance is equal to the specified object.
        /// </summary>
        /// <param name="other">Object to make the comparison with.</param>
        /// <returns><see langword="true" /> if the current instance is equal to the specified object; <see langword="false" /> otherwise.</returns>
        public bool Equals(LQuaternion other) => (X == other.X && Y == other.Y && Z == other.Z && W == other.W);

        public static implicit operator Quaternion(LQuaternion q) => new(q.X, q.Y, q.Z, q.W);
        public static implicit operator LQuaternion(Quaternion q) => new(q.X, q.Y, q.Z, q.W);
    }
}