// Copyright (c) 2012-2024 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.Globalization;
using System.Runtime.CompilerServices;

namespace FlaxEngine
{
    partial struct Matrix : IEquatable<Matrix>, IFormattable
    {
        /// <summary>
        /// The size of the <see cref="Matrix" /> type, in bytes.
        /// </summary>
        public static readonly int SizeInBytes = 4 * 4 * sizeof(float);

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

        /// <summary>
        /// The identity <see cref="Matrix" />.
        /// </summary>
        public static readonly Matrix Identity = new Matrix
        {
            M11 = 1.0f,
            M22 = 1.0f,
            M33 = 1.0f,
            M44 = 1.0f
        };

        /// <summary>
        /// Value at row 1 column 1 of the matrix.
        /// </summary>
        public float M11;

        /// <summary>
        /// Value at row 1 column 2 of the matrix.
        /// </summary>
        public float M12;

        /// <summary>
        /// Value at row 1 column 3 of the matrix.
        /// </summary>
        public float M13;

        /// <summary>
        /// Value at row 1 column 4 of the matrix.
        /// </summary>
        public float M14;

        /// <summary>
        /// Value at row 2 column 1 of the matrix.
        /// </summary>
        public float M21;

        /// <summary>
        /// Value at row 2 column 2 of the matrix.
        /// </summary>
        public float M22;

        /// <summary>
        /// Value at row 2 column 3 of the matrix.
        /// </summary>
        public float M23;

        /// <summary>
        /// Value at row 2 column 4 of the matrix.
        /// </summary>
        public float M24;

        /// <summary>
        /// Value at row 3 column 1 of the matrix.
        /// </summary>
        public float M31;

        /// <summary>
        /// Value at row 3 column 2 of the matrix.
        /// </summary>
        public float M32;

        /// <summary>
        /// Value at row 3 column 3 of the matrix.
        /// </summary>
        public float M33;

        /// <summary>
        /// Value at row 3 column 4 of the matrix.
        /// </summary>
        public float M34;

        /// <summary>
        /// Value at row 4 column 1 of the matrix.
        /// </summary>
        public float M41;

        /// <summary>
        /// Value at row 4 column 2 of the matrix.
        /// </summary>
        public float M42;

        /// <summary>
        /// Value at row 4 column 3 of the matrix.
        /// </summary>
        public float M43;

        /// <summary>
        /// Value at row 4 column 4 of the matrix.
        /// </summary>
        public float M44;

        /// <summary>
        /// Gets or sets the up <see cref="Float3" /> of the matrix; that is M21, M22, and M23.
        /// </summary>
        public Float3 Up
        {
            get => new Float3(M21, M22, M23);
            set
            {
                M21 = value.X;
                M22 = value.Y;
                M23 = value.Z;
            }
        }

        /// <summary>
        /// Gets or sets the down <see cref="Float3" /> of the matrix; that is -M21, -M22, and -M23.
        /// </summary>
        public Float3 Down
        {
            get => new Float3(-M21, -M22, -M23);
            set
            {
                M21 = -value.X;
                M22 = -value.Y;
                M23 = -value.Z;
            }
        }

        /// <summary>
        /// Gets or sets the right <see cref="Float3" /> of the matrix; that is M11, M12, and M13.
        /// </summary>
        public Float3 Right
        {
            get => new Float3(M11, M12, M13);
            set
            {
                M11 = value.X;
                M12 = value.Y;
                M13 = value.Z;
            }
        }

        /// <summary>
        /// Gets or sets the left <see cref="Float3" /> of the matrix; that is -M11, -M12, and -M13.
        /// </summary>
        public Float3 Left
        {
            get => new Float3(-M11, -M12, -M13);
            set
            {
                M11 = -value.X;
                M12 = -value.Y;
                M13 = -value.Z;
            }
        }

        /// <summary>
        /// Gets or sets the forward <see cref="Float3" /> of the matrix; that is -M31, -M32, and -M33.
        /// </summary>
        public Float3 Forward
        {
            get => new Float3(-M31, -M32, -M33);
            set
            {
                M31 = -value.X;
                M32 = -value.Y;
                M33 = -value.Z;
            }
        }

        /// <summary>
        /// Gets or sets the backward <see cref="Float3" /> of the matrix; that is M31, M32, and M33.
        /// </summary>
        public Float3 Backward
        {
            get => new Float3(M31, M32, M33);
            set
            {
                M31 = value.X;
                M32 = value.Y;
                M33 = value.Z;
            }
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="Matrix" /> struct.
        /// </summary>
        /// <param name="value">The value that will be assigned to all components.</param>
        public Matrix(float value)
        {
            M11 = M12 = M13 = M14 = M21 = M22 = M23 = M24 = M31 = M32 = M33 = M34 = M41 = M42 = M43 = M44 = value;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="Matrix" /> struct.
        /// </summary>
        /// <param name="m11">The value to assign at row 1 column 1 of the matrix.</param>
        /// <param name="m12">The value to assign at row 1 column 2 of the matrix.</param>
        /// <param name="m13">The value to assign at row 1 column 3 of the matrix.</param>
        /// <param name="m14">The value to assign at row 1 column 4 of the matrix.</param>
        /// <param name="m21">The value to assign at row 2 column 1 of the matrix.</param>
        /// <param name="m22">The value to assign at row 2 column 2 of the matrix.</param>
        /// <param name="m23">The value to assign at row 2 column 3 of the matrix.</param>
        /// <param name="m24">The value to assign at row 2 column 4 of the matrix.</param>
        /// <param name="m31">The value to assign at row 3 column 1 of the matrix.</param>
        /// <param name="m32">The value to assign at row 3 column 2 of the matrix.</param>
        /// <param name="m33">The value to assign at row 3 column 3 of the matrix.</param>
        /// <param name="m34">The value to assign at row 3 column 4 of the matrix.</param>
        /// <param name="m41">The value to assign at row 4 column 1 of the matrix.</param>
        /// <param name="m42">The value to assign at row 4 column 2 of the matrix.</param>
        /// <param name="m43">The value to assign at row 4 column 3 of the matrix.</param>
        /// <param name="m44">The value to assign at row 4 column 4 of the matrix.</param>
        public Matrix(float m11, float m12, float m13, float m14,
                      float m21, float m22, float m23, float m24,
                      float m31, float m32, float m33, float m34,
                      float m41, float m42, float m43, float m44)
        {
            M11 = m11;
            M12 = m12;
            M13 = m13;
            M14 = m14;
            M21 = m21;
            M22 = m22;
            M23 = m23;
            M24 = m24;
            M31 = m31;
            M32 = m32;
            M33 = m33;
            M34 = m34;
            M41 = m41;
            M42 = m42;
            M43 = m43;
            M44 = m44;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="Matrix" /> struct.
        /// </summary>
        /// <param name="values">The values to assign to the components of the matrix. This must be an array with sixteen 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 sixteen
        /// elements.
        /// </exception>
        public Matrix(float[] values)
        {
            if (values == null)
                throw new ArgumentNullException(nameof(values));
            if (values.Length != 16)
                throw new ArgumentOutOfRangeException(nameof(values), "There must be sixteen and only sixteen input values for Matrix.");

            M11 = values[0];
            M12 = values[1];
            M13 = values[2];
            M14 = values[3];

            M21 = values[4];
            M22 = values[5];
            M23 = values[6];
            M24 = values[7];

            M31 = values[8];
            M32 = values[9];
            M33 = values[10];
            M34 = values[11];

            M41 = values[12];
            M42 = values[13];
            M43 = values[14];
            M44 = values[15];
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="Matrix" /> struct.
        /// </summary>
        /// <param name="m">The rotation/scale matrix.</param>
        public Matrix(Matrix3x3 m)
        {
            M11 = m.M11;
            M12 = m.M12;
            M13 = m.M13;
            M14 = 0;
            M21 = m.M21;
            M22 = m.M22;
            M23 = m.M23;
            M24 = 0;
            M31 = m.M31;
            M32 = m.M32;
            M33 = m.M33;
            M34 = 0;
            M41 = 0;
            M42 = 0;
            M43 = 0;
            M44 = 1;
        }

        /// <summary>
        /// Gets or sets the first row in the matrix; that is M11, M12, M13, and M14.
        /// </summary>
        public Float4 Row1
        {
            get => new Float4(M11, M12, M13, M14);
            set
            {
                M11 = value.X;
                M12 = value.Y;
                M13 = value.Z;
                M14 = value.W;
            }
        }

        /// <summary>
        /// Gets or sets the second row in the matrix; that is M21, M22, M23, and M24.
        /// </summary>
        public Float4 Row2
        {
            get => new Float4(M21, M22, M23, M24);
            set
            {
                M21 = value.X;
                M22 = value.Y;
                M23 = value.Z;
                M24 = value.W;
            }
        }

        /// <summary>
        /// Gets or sets the third row in the matrix; that is M31, M32, M33, and M34.
        /// </summary>
        public Float4 Row3
        {
            get => new Float4(M31, M32, M33, M34);
            set
            {
                M31 = value.X;
                M32 = value.Y;
                M33 = value.Z;
                M34 = value.W;
            }
        }

        /// <summary>
        /// Gets or sets the fourth row in the matrix; that is M41, M42, M43, and M44.
        /// </summary>
        public Float4 Row4
        {
            get => new Float4(M41, M42, M43, M44);
            set
            {
                M41 = value.X;
                M42 = value.Y;
                M43 = value.Z;
                M44 = value.W;
            }
        }

        /// <summary>
        /// Gets or sets the first column in the matrix; that is M11, M21, M31, and M41.
        /// </summary>
        public Float4 Column1
        {
            get => new Float4(M11, M21, M31, M41);
            set
            {
                M11 = value.X;
                M21 = value.Y;
                M31 = value.Z;
                M41 = value.W;
            }
        }

        /// <summary>
        /// Gets or sets the second column in the matrix; that is M12, M22, M32, and M42.
        /// </summary>
        public Float4 Column2
        {
            get => new Float4(M12, M22, M32, M42);
            set
            {
                M12 = value.X;
                M22 = value.Y;
                M32 = value.Z;
                M42 = value.W;
            }
        }

        /// <summary>
        /// Gets or sets the third column in the matrix; that is M13, M23, M33, and M43.
        /// </summary>
        public Float4 Column3
        {
            get => new Float4(M13, M23, M33, M43);
            set
            {
                M13 = value.X;
                M23 = value.Y;
                M33 = value.Z;
                M43 = value.W;
            }
        }

        /// <summary>
        /// Gets or sets the fourth column in the matrix; that is M14, M24, M34, and M44.
        /// </summary>
        public Float4 Column4
        {
            get => new Float4(M14, M24, M34, M44);
            set
            {
                M14 = value.X;
                M24 = value.Y;
                M34 = value.Z;
                M44 = value.W;
            }
        }

        /// <summary>
        /// Gets or sets the translation of the matrix; that is M41, M42, and M43.
        /// </summary>
        public Float3 TranslationVector
        {
            get => new Float3(M41, M42, M43);
            set
            {
                M41 = value.X;
                M42 = value.Y;
                M43 = value.Z;
            }
        }

        /// <summary>
        /// Gets or sets the scale of the matrix; that is M11, M22, and M33.
        /// </summary>
        public Float3 ScaleVector
        {
            get => new Float3(M11, M22, M33);
            set
            {
                M11 = value.X;
                M22 = value.Y;
                M33 = value.Z;
            }
        }

        /// <summary>
        /// Gets a value indicating whether this instance is an identity matrix.
        /// </summary>
        public bool IsIdentity => Equals(Identity);

        /// <summary>
        /// Gets or sets the component at the specified index.
        /// </summary>
        /// <param name="index">The zero-based index of the component to access.</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, 15].</exception>
        public float this[int index]
        {
            get
            {
                switch (index)
                {
                case 0: return M11;
                case 1: return M12;
                case 2: return M13;
                case 3: return M14;
                case 4: return M21;
                case 5: return M22;
                case 6: return M23;
                case 7: return M24;
                case 8: return M31;
                case 9: return M32;
                case 10: return M33;
                case 11: return M34;
                case 12: return M41;
                case 13: return M42;
                case 14: return M43;
                case 15: return M44;
                }
                throw new ArgumentOutOfRangeException(nameof(index), "Indices for Matrix run from 0 to 15, inclusive.");
            }

            set
            {
                switch (index)
                {
                case 0:
                    M11 = value;
                    break;
                case 1:
                    M12 = value;
                    break;
                case 2:
                    M13 = value;
                    break;
                case 3:
                    M14 = value;
                    break;
                case 4:
                    M21 = value;
                    break;
                case 5:
                    M22 = value;
                    break;
                case 6:
                    M23 = value;
                    break;
                case 7:
                    M24 = value;
                    break;
                case 8:
                    M31 = value;
                    break;
                case 9:
                    M32 = value;
                    break;
                case 10:
                    M33 = value;
                    break;
                case 11:
                    M34 = value;
                    break;
                case 12:
                    M41 = value;
                    break;
                case 13:
                    M42 = value;
                    break;
                case 14:
                    M43 = value;
                    break;
                case 15:
                    M44 = value;
                    break;
                default: throw new ArgumentOutOfRangeException(nameof(index), "Indices for Matrix run from 0 to 15, inclusive.");
                }
            }
        }

        /// <summary>
        /// Gets or sets the component at the specified index.
        /// </summary>
        /// <value>The value of the matrix component, depending on the index.</value>
        /// <param name="row">The row of the matrix to access.</param>
        /// <param name="column">The column of the matrix to access.</param>
        /// <returns>The value of the component at the specified index.</returns>
        /// <exception cref="System.ArgumentOutOfRangeException">Thrown when the <paramref name="row" /> or <paramref name="column" />is out of the range [0, 3].</exception>
        public float this[int row, int column]
        {
            get
            {
                if (row < 0 || row > 3)
                    throw new ArgumentOutOfRangeException(nameof(row), "Rows and columns for matrices run from 0 to 3, inclusive.");
                if (column < 0 || column > 3)
                    throw new ArgumentOutOfRangeException(nameof(column), "Rows and columns for matrices run from 0 to 3, inclusive.");
                return this[row * 4 + column];
            }
            set
            {
                if (row < 0 || row > 3)
                    throw new ArgumentOutOfRangeException(nameof(row), "Rows and columns for matrices run from 0 to 3, inclusive.");
                if (column < 0 || column > 3)
                    throw new ArgumentOutOfRangeException(nameof(column), "Rows and columns for matrices run from 0 to 3, inclusive.");
                this[row * 4 + column] = value;
            }
        }

        /// <summary>
        /// Calculates the determinant of the matrix.
        /// </summary>
        /// <returns>The determinant of the matrix.</returns>
        public float Determinant()
        {
            float temp1 = M33 * M44 - M34 * M43;
            float temp2 = M32 * M44 - M34 * M42;
            float temp3 = M32 * M43 - M33 * M42;
            float temp4 = M31 * M44 - M34 * M41;
            float temp5 = M31 * M43 - M33 * M41;
            float temp6 = M31 * M42 - M32 * M41;
            return M11 * (M22 * temp1 - M23 * temp2 + M24 * temp3) - M12 * (M21 * temp1 - M23 * temp4 + M24 * temp5) + M13 * (M21 * temp2 - M22 * temp4 + M24 * temp6) - M14 * (M21 * temp3 - M22 * temp5 + M23 * temp6);
        }

        /// <summary>
        /// Inverts the matrix.
        /// </summary>
        public void Invert()
        {
            Invert(ref this, out this);
        }

        /// <summary>
        /// Transposes the matrix.
        /// </summary>
        public void Transpose()
        {
            Transpose(ref this, out this);
        }

        /// <summary>
        /// Orthogonalizes the specified matrix.
        /// </summary>
        /// <remarks>
        /// <para>
        ///   Orthogonalization is the process of making all rows orthogonal to each other. This
        ///   means that any given row in the matrix will be orthogonal to any other given row in the
        ///   matrix.
        /// </para>
        /// <para>
        ///   Because this method uses the modified Gram-Schmidt process, the resulting matrix
        ///   tends to be numerically unstable. The numeric stability decreases according to the rows
        ///   so that the first row is the most stable and the last row is the least stable.
        /// </para>
        /// <para>
        ///   This operation is performed on the rows of the matrix rather than the columns.
        ///   If you wish for this operation to be performed on the columns, first transpose the
        ///   input and than transpose the output.
        /// </para>
        /// </remarks>
        public void Orthogonalize()
        {
            Orthogonalize(ref this, out this);
        }

        /// <summary>
        /// Orthonormalizes the specified matrix.
        /// </summary>
        /// <remarks>
        /// <para>
        ///   Orthonormalization is the process of making all rows and columns orthogonal to each
        ///   other and making all rows and columns of unit length. This means that any given row will
        ///   be orthogonal to any other given row and any given column will be orthogonal to any other
        ///   given column. Any given row will not be orthogonal to any given column. Every row and every
        ///   column will be of unit length.
        /// </para>
        /// <para>
        ///   Because this method uses the modified Gram-Schmidt process, the resulting matrix
        ///   tends to be numerically unstable. The numeric stability decreases according to the rows
        ///   so that the first row is the most stable and the last row is the least stable.
        /// </para>
        /// <para>
        ///   This operation is performed on the rows of the matrix rather than the columns.
        ///   If you wish for this operation to be performed on the columns, first transpose the
        ///   input and than transpose the output.
        /// </para>
        /// </remarks>
        public void Orthonormalize()
        {
            Orthonormalize(ref this, out this);
        }

        /// <summary>
        /// Decomposes a matrix into an orthonormalized matrix Q and a right triangular matrix R.
        /// </summary>
        /// <param name="Q">When the method completes, contains the orthonormalized matrix of the decomposition.</param>
        /// <param name="R">When the method completes, contains the right triangular matrix of the decomposition.</param>
        public void DecomposeQR(out Matrix Q, out Matrix R)
        {
            Matrix temp = this;
            temp.Transpose();
            Orthonormalize(ref temp, out Q);
            Q.Transpose();

            R = new Matrix
            {
                M11 = Float4.Dot(Q.Column1, Column1),
                M12 = Float4.Dot(Q.Column1, Column2),
                M13 = Float4.Dot(Q.Column1, Column3),
                M14 = Float4.Dot(Q.Column1, Column4),

                M22 = Float4.Dot(Q.Column2, Column2),
                M23 = Float4.Dot(Q.Column2, Column3),
                M24 = Float4.Dot(Q.Column2, Column4),

                M33 = Float4.Dot(Q.Column3, Column3),
                M34 = Float4.Dot(Q.Column3, Column4),

                M44 = Float4.Dot(Q.Column4, Column4)
            };
        }

        /// <summary>
        /// Decomposes a matrix into a lower triangular matrix L and an orthonormalized matrix Q.
        /// </summary>
        /// <param name="L">When the method completes, contains the lower triangular matrix of the decomposition.</param>
        /// <param name="Q">When the method completes, contains the orthonormalized matrix of the decomposition.</param>
        public void DecomposeLQ(out Matrix L, out Matrix Q)
        {
            Orthonormalize(ref this, out Q);

            L = new Matrix
            {
                M11 = Float4.Dot(Q.Row1, Row1),

                M21 = Float4.Dot(Q.Row1, Row2),
                M22 = Float4.Dot(Q.Row2, Row2),

                M31 = Float4.Dot(Q.Row1, Row3),
                M32 = Float4.Dot(Q.Row2, Row3),
                M33 = Float4.Dot(Q.Row3, Row3),

                M41 = Float4.Dot(Q.Row1, Row4),
                M42 = Float4.Dot(Q.Row2, Row4),
                M43 = Float4.Dot(Q.Row3, Row4),
                M44 = Float4.Dot(Q.Row4, Row4)
            };
        }

        /// <summary>
        /// Decomposes a matrix into a scale, rotation, and translation.
        /// </summary>
        /// <param name="transform">When the method completes, contains the transformation of the decomposed matrix.</param>
        /// <remarks>This method is designed to decompose an SRT transformation matrix only.</remarks>
        public void Decompose(out Transform transform)
        {
            Decompose(out transform.Scale, out Matrix3x3 rotationMatrix, out Float3 translation);
            Quaternion.RotationMatrix(ref rotationMatrix, out transform.Orientation);
            transform.Translation = translation;
        }

        /// <summary>
        /// Decomposes a matrix into a scale, rotation, and translation.
        /// </summary>
        /// <param name="scale">When the method completes, contains the scaling component of the decomposed matrix.</param>
        /// <param name="rotation">When the method completes, contains the rotation component of the decomposed matrix.</param>
        /// <param name="translation">When the method completes, contains the translation component of the decomposed matrix.</param>
        /// <remarks>This method is designed to decompose an SRT transformation matrix only.</remarks>
        public void Decompose(out Float3 scale, out Matrix3x3 rotation, out Float3 translation)
        {
            // Get the translation
            translation.X = M41;
            translation.Y = M42;
            translation.Z = M43;

            // Scaling is the length of the rows
            scale.X = (float)Math.Sqrt(M11 * M11 + M12 * M12 + M13 * M13);
            scale.Y = (float)Math.Sqrt(M21 * M21 + M22 * M22 + M23 * M23);
            scale.Z = (float)Math.Sqrt(M31 * M31 + M32 * M32 + M33 * M33);

            // If any of the scaling factors are zero, than the rotation matrix can not exist
            if (Mathf.IsZero(scale.X) || Mathf.IsZero(scale.Y) || Mathf.IsZero(scale.Z))
            {
                rotation = Matrix3x3.Identity;
                return;
            }

            // The rotation is the left over matrix after dividing out the scaling
            rotation = new Matrix3x3
            {
                M11 = M11 / scale.X,
                M12 = M12 / scale.X,
                M13 = M13 / scale.X,
                M21 = M21 / scale.Y,
                M22 = M22 / scale.Y,
                M23 = M23 / scale.Y,
                M31 = M31 / scale.Z,
                M32 = M32 / scale.Z,
                M33 = M33 / scale.Z,
            };
        }

        /// <summary>
        /// Decomposes a matrix into a scale, rotation, and translation.
        /// [Deprecated on 20.02.2024, expires on 20.02.2026]
        /// </summary>
        /// <param name="scale">When the method completes, contains the scaling component of the decomposed matrix.</param>
        /// <param name="rotation">When the method completes, contains the rotation component of the decomposed matrix.</param>
        /// <param name="translation">When the method completes, contains the translation component of the decomposed matrix.</param>
        /// <remarks>This method is designed to decompose an SRT transformation matrix only.</remarks>
        [Obsolete("Deprecated in v1.8")]
        public void Decompose(out Float3 scale, out Matrix rotation, out Float3 translation)
        {
            Decompose(out scale, out Matrix3x3 r, out translation);
            rotation = new Matrix(r);
        }

        /// <summary>
        /// Decomposes a matrix into a scale, rotation, and translation.
        /// </summary>
        /// <param name="scale">When the method completes, contains the scaling component of the decomposed matrix.</param>
        /// <param name="rotation">When the method completes, contains the rotation component of the decomposed matrix.</param>
        /// <param name="translation">When the method completes, contains the translation component of the decomposed matrix.</param>
        /// <remarks>This method is designed to decompose an SRT transformation matrix only.</remarks>
        public void Decompose(out Float3 scale, out Quaternion rotation, out Float3 translation)
        {
            Decompose(out scale, out Matrix3x3 rotationMatrix, out translation);
            Quaternion.RotationMatrix(ref rotationMatrix, out rotation);
        }

        /// <summary>
        /// Decomposes a uniform scale matrix into a scale, rotation, and translation.
        /// A uniform scale matrix has the same scale in every axis.
        /// </summary>
        /// <param name="scale">When the method completes, contains the scaling component of the decomposed matrix.</param>
        /// <param name="rotation">When the method completes, contains the rotation component of the decomposed matrix.</param>
        /// <param name="translation">When the method completes, contains the translation component of the decomposed matrix.</param>
        /// <remarks>This method is designed to decompose an SRT transformation matrix only.</remarks>
        public void DecomposeUniformScale(out float scale, out Quaternion rotation, out Float3 translation)
        {
            // Get the translation
            translation.X = M41;
            translation.Y = M42;
            translation.Z = M43;

            // Scaling is the length of the rows. ( just take one row since this is a uniform matrix)
            scale = (float)Math.Sqrt(M11 * M11 + M12 * M12 + M13 * M13);

            // If any of the scaling factors are zero, then the rotation matrix can not exist
            if (Math.Abs(scale) < 1e-12f)
            {
                rotation = Quaternion.Identity;
                return;
            }

            // The rotation is the left over matrix after dividing out the scaling
            float invScale = 1f / scale;
            var rotationMatrix = new Matrix
            {
                M11 = M11 * invScale,
                M12 = M12 * invScale,
                M13 = M13 * invScale,
                M21 = M21 * invScale,
                M22 = M22 * invScale,
                M23 = M23 * invScale,
                M31 = M31 * invScale,
                M32 = M32 * invScale,
                M33 = M33 * invScale,
                M44 = 1f
            };
            Quaternion.RotationMatrix(ref rotationMatrix, out rotation);
        }

        /// <summary>
        /// Exchanges two rows in the matrix.
        /// </summary>
        /// <param name="firstRow">The first row to exchange. This is an index of the row starting at zero.</param>
        /// <param name="secondRow">The second row to exchange. This is an index of the row starting at zero.</param>
        public void ExchangeRows(int firstRow, int secondRow)
        {
            if (firstRow < 0)
                throw new ArgumentOutOfRangeException(nameof(firstRow), "The parameter firstRow must be greater than or equal to zero.");
            if (firstRow > 3)
                throw new ArgumentOutOfRangeException(nameof(firstRow), "The parameter firstRow must be less than or equal to three.");
            if (secondRow < 0)
                throw new ArgumentOutOfRangeException(nameof(secondRow), "The parameter secondRow must be greater than or equal to zero.");
            if (secondRow > 3)
                throw new ArgumentOutOfRangeException(nameof(secondRow), "The parameter secondRow must be less than or equal to three.");
            if (firstRow == secondRow)
                return;

            float temp0 = this[secondRow, 0];
            float temp1 = this[secondRow, 1];
            float temp2 = this[secondRow, 2];
            float temp3 = this[secondRow, 3];

            this[secondRow, 0] = this[firstRow, 0];
            this[secondRow, 1] = this[firstRow, 1];
            this[secondRow, 2] = this[firstRow, 2];
            this[secondRow, 3] = this[firstRow, 3];

            this[firstRow, 0] = temp0;
            this[firstRow, 1] = temp1;
            this[firstRow, 2] = temp2;
            this[firstRow, 3] = temp3;
        }

        /// <summary>
        /// Exchanges two columns in the matrix.
        /// </summary>
        /// <param name="firstColumn">The first column to exchange. This is an index of the column starting at zero.</param>
        /// <param name="secondColumn">The second column to exchange. This is an index of the column starting at zero.</param>
        public void ExchangeColumns(int firstColumn, int secondColumn)
        {
            if (firstColumn < 0)
                throw new ArgumentOutOfRangeException(nameof(firstColumn), "The parameter firstColumn must be greater than or equal to zero.");
            if (firstColumn > 3)
                throw new ArgumentOutOfRangeException(nameof(firstColumn), "The parameter firstColumn must be less than or equal to three.");
            if (secondColumn < 0)
                throw new ArgumentOutOfRangeException(nameof(secondColumn), "The parameter secondColumn must be greater than or equal to zero.");
            if (secondColumn > 3)
                throw new ArgumentOutOfRangeException(nameof(secondColumn), "The parameter secondColumn must be less than or equal to three.");
            if (firstColumn == secondColumn)
                return;

            float temp0 = this[0, secondColumn];
            float temp1 = this[1, secondColumn];
            float temp2 = this[2, secondColumn];
            float temp3 = this[3, secondColumn];

            this[0, secondColumn] = this[0, firstColumn];
            this[1, secondColumn] = this[1, firstColumn];
            this[2, secondColumn] = this[2, firstColumn];
            this[3, secondColumn] = this[3, firstColumn];

            this[0, firstColumn] = temp0;
            this[1, firstColumn] = temp1;
            this[2, firstColumn] = temp2;
            this[3, firstColumn] = temp3;
        }

        /// <summary>
        /// Creates an array containing the elements of the matrix.
        /// </summary>
        /// <returns>A sixteen-element array containing the components of the matrix.</returns>
        public float[] ToArray()
        {
            return new[]
            {
                M11,
                M12,
                M13,
                M14,
                M21,
                M22,
                M23,
                M24,
                M31,
                M32,
                M33,
                M34,
                M41,
                M42,
                M43,
                M44
            };
        }

        /// <summary>
        /// Determines the sum of two matrices.
        /// </summary>
        /// <param name="left">The first matrix to add.</param>
        /// <param name="right">The second matrix to add.</param>
        /// <param name="result">When the method completes, contains the sum of the two matrices.</param>
        public static void Add(ref Matrix left, ref Matrix right, out Matrix result)
        {
            result.M11 = left.M11 + right.M11;
            result.M12 = left.M12 + right.M12;
            result.M13 = left.M13 + right.M13;
            result.M14 = left.M14 + right.M14;
            result.M21 = left.M21 + right.M21;
            result.M22 = left.M22 + right.M22;
            result.M23 = left.M23 + right.M23;
            result.M24 = left.M24 + right.M24;
            result.M31 = left.M31 + right.M31;
            result.M32 = left.M32 + right.M32;
            result.M33 = left.M33 + right.M33;
            result.M34 = left.M34 + right.M34;
            result.M41 = left.M41 + right.M41;
            result.M42 = left.M42 + right.M42;
            result.M43 = left.M43 + right.M43;
            result.M44 = left.M44 + right.M44;
        }

        /// <summary>
        /// Determines the sum of two matrices.
        /// </summary>
        /// <param name="left">The first matrix to add.</param>
        /// <param name="right">The second matrix to add.</param>
        /// <returns>The sum of the two matrices.</returns>
        public static Matrix Add(Matrix left, Matrix right)
        {
            Add(ref left, ref right, out var result);
            return result;
        }

        /// <summary>
        /// Determines the difference between two matrices.
        /// </summary>
        /// <param name="left">The first matrix to subtract.</param>
        /// <param name="right">The second matrix to subtract.</param>
        /// <param name="result">When the method completes, contains the difference between the two matrices.</param>
        public static void Subtract(ref Matrix left, ref Matrix right, out Matrix result)
        {
            result.M11 = left.M11 - right.M11;
            result.M12 = left.M12 - right.M12;
            result.M13 = left.M13 - right.M13;
            result.M14 = left.M14 - right.M14;
            result.M21 = left.M21 - right.M21;
            result.M22 = left.M22 - right.M22;
            result.M23 = left.M23 - right.M23;
            result.M24 = left.M24 - right.M24;
            result.M31 = left.M31 - right.M31;
            result.M32 = left.M32 - right.M32;
            result.M33 = left.M33 - right.M33;
            result.M34 = left.M34 - right.M34;
            result.M41 = left.M41 - right.M41;
            result.M42 = left.M42 - right.M42;
            result.M43 = left.M43 - right.M43;
            result.M44 = left.M44 - right.M44;
        }

        /// <summary>
        /// Determines the difference between two matrices.
        /// </summary>
        /// <param name="left">The first matrix to subtract.</param>
        /// <param name="right">The second matrix to subtract.</param>
        /// <returns>The difference between the two matrices.</returns>
        public static Matrix Subtract(Matrix left, Matrix right)
        {
            Subtract(ref left, ref right, out var result);
            return result;
        }

        /// <summary>
        /// Scales a matrix by the given value.
        /// </summary>
        /// <param name="left">The matrix to scale.</param>
        /// <param name="right">The amount by which to scale.</param>
        /// <param name="result">When the method completes, contains the scaled matrix.</param>
        public static void Multiply(ref Matrix left, float right, out Matrix result)
        {
            result.M11 = left.M11 * right;
            result.M12 = left.M12 * right;
            result.M13 = left.M13 * right;
            result.M14 = left.M14 * right;
            result.M21 = left.M21 * right;
            result.M22 = left.M22 * right;
            result.M23 = left.M23 * right;
            result.M24 = left.M24 * right;
            result.M31 = left.M31 * right;
            result.M32 = left.M32 * right;
            result.M33 = left.M33 * right;
            result.M34 = left.M34 * right;
            result.M41 = left.M41 * right;
            result.M42 = left.M42 * right;
            result.M43 = left.M43 * right;
            result.M44 = left.M44 * right;
        }

        /// <summary>
        /// Scales a matrix by the given value.
        /// </summary>
        /// <param name="left">The matrix to scale.</param>
        /// <param name="right">The amount by which to scale.</param>
        /// <returns>The scaled matrix.</returns>
        public static Matrix Multiply(Matrix left, float right)
        {
            Multiply(ref left, right, out var result);
            return result;
        }

        /// <summary>
        /// Determines the product of two matrices.
        /// </summary>
        /// <param name="left">The first matrix to multiply.</param>
        /// <param name="right">The second matrix to multiply.</param>
        /// <param name="result">The product of the two matrices.</param>
        public static void Multiply(ref Matrix left, ref Matrix right, out Matrix result)
        {
            result = new Matrix
            {
                M11 = left.M11 * right.M11 + left.M12 * right.M21 + left.M13 * right.M31 + left.M14 * right.M41,
                M12 = left.M11 * right.M12 + left.M12 * right.M22 + left.M13 * right.M32 + left.M14 * right.M42,
                M13 = left.M11 * right.M13 + left.M12 * right.M23 + left.M13 * right.M33 + left.M14 * right.M43,
                M14 = left.M11 * right.M14 + left.M12 * right.M24 + left.M13 * right.M34 + left.M14 * right.M44,
                M21 = left.M21 * right.M11 + left.M22 * right.M21 + left.M23 * right.M31 + left.M24 * right.M41,
                M22 = left.M21 * right.M12 + left.M22 * right.M22 + left.M23 * right.M32 + left.M24 * right.M42,
                M23 = left.M21 * right.M13 + left.M22 * right.M23 + left.M23 * right.M33 + left.M24 * right.M43,
                M24 = left.M21 * right.M14 + left.M22 * right.M24 + left.M23 * right.M34 + left.M24 * right.M44,
                M31 = left.M31 * right.M11 + left.M32 * right.M21 + left.M33 * right.M31 + left.M34 * right.M41,
                M32 = left.M31 * right.M12 + left.M32 * right.M22 + left.M33 * right.M32 + left.M34 * right.M42,
                M33 = left.M31 * right.M13 + left.M32 * right.M23 + left.M33 * right.M33 + left.M34 * right.M43,
                M34 = left.M31 * right.M14 + left.M32 * right.M24 + left.M33 * right.M34 + left.M34 * right.M44,
                M41 = left.M41 * right.M11 + left.M42 * right.M21 + left.M43 * right.M31 + left.M44 * right.M41,
                M42 = left.M41 * right.M12 + left.M42 * right.M22 + left.M43 * right.M32 + left.M44 * right.M42,
                M43 = left.M41 * right.M13 + left.M42 * right.M23 + left.M43 * right.M33 + left.M44 * right.M43,
                M44 = left.M41 * right.M14 + left.M42 * right.M24 + left.M43 * right.M34 + left.M44 * right.M44
            };
        }

        /// <summary>
        /// Determines the product of two matrices.
        /// </summary>
        /// <param name="left">The first matrix to multiply.</param>
        /// <param name="right">The second matrix to multiply.</param>
        /// <returns>The product of the two matrices.</returns>
        public static Matrix Multiply(Matrix left, Matrix right)
        {
            Multiply(ref left, ref right, out var result);
            return result;
        }

        /// <summary>
        /// Scales a matrix by the given value.
        /// </summary>
        /// <param name="left">The matrix to scale.</param>
        /// <param name="right">The amount by which to scale.</param>
        /// <param name="result">When the method completes, contains the scaled matrix.</param>
        public static void Divide(ref Matrix left, float right, out Matrix result)
        {
            float inv = 1.0f / right;
            result.M11 = left.M11 * inv;
            result.M12 = left.M12 * inv;
            result.M13 = left.M13 * inv;
            result.M14 = left.M14 * inv;
            result.M21 = left.M21 * inv;
            result.M22 = left.M22 * inv;
            result.M23 = left.M23 * inv;
            result.M24 = left.M24 * inv;
            result.M31 = left.M31 * inv;
            result.M32 = left.M32 * inv;
            result.M33 = left.M33 * inv;
            result.M34 = left.M34 * inv;
            result.M41 = left.M41 * inv;
            result.M42 = left.M42 * inv;
            result.M43 = left.M43 * inv;
            result.M44 = left.M44 * inv;
        }

        /// <summary>
        /// Scales a matrix by the given value.
        /// </summary>
        /// <param name="left">The matrix to scale.</param>
        /// <param name="right">The amount by which to scale.</param>
        /// <returns>The scaled matrix.</returns>
        public static Matrix Divide(Matrix left, float right)
        {
            Divide(ref left, right, out var result);
            return result;
        }

        /// <summary>
        /// Determines the quotient of two matrices.
        /// </summary>
        /// <param name="left">The first matrix to divide.</param>
        /// <param name="right">The second matrix to divide.</param>
        /// <param name="result">When the method completes, contains the quotient of the two matrices.</param>
        public static void Divide(ref Matrix left, ref Matrix right, out Matrix result)
        {
            result.M11 = left.M11 / right.M11;
            result.M12 = left.M12 / right.M12;
            result.M13 = left.M13 / right.M13;
            result.M14 = left.M14 / right.M14;
            result.M21 = left.M21 / right.M21;
            result.M22 = left.M22 / right.M22;
            result.M23 = left.M23 / right.M23;
            result.M24 = left.M24 / right.M24;
            result.M31 = left.M31 / right.M31;
            result.M32 = left.M32 / right.M32;
            result.M33 = left.M33 / right.M33;
            result.M34 = left.M34 / right.M34;
            result.M41 = left.M41 / right.M41;
            result.M42 = left.M42 / right.M42;
            result.M43 = left.M43 / right.M43;
            result.M44 = left.M44 / right.M44;
        }

        /// <summary>
        /// Determines the quotient of two matrices.
        /// </summary>
        /// <param name="left">The first matrix to divide.</param>
        /// <param name="right">The second matrix to divide.</param>
        /// <returns>The quotient of the two matrices.</returns>
        public static Matrix Divide(Matrix left, Matrix right)
        {
            Divide(ref left, ref right, out var result);
            return result;
        }

        /// <summary>
        /// Performs the exponential operation on a matrix.
        /// </summary>
        /// <param name="value">The matrix to perform the operation on.</param>
        /// <param name="exponent">The exponent to raise the matrix to.</param>
        /// <param name="result">When the method completes, contains the exponential matrix.</param>
        /// <exception cref="System.ArgumentOutOfRangeException">Thrown when the <paramref name="exponent" /> is negative.</exception>
        public static void Exponent(ref Matrix value, int exponent, out Matrix result)
        {
            // Source: http://rosettacode.org
            // Reference: http://rosettacode.org/wiki/Matrix-exponentiation_operator

            if (exponent < 0)
                throw new ArgumentOutOfRangeException(nameof(exponent), "The exponent can not be negative.");
            if (exponent == 0)
            {
                result = Identity;
                return;
            }
            if (exponent == 1)
            {
                result = value;
                return;
            }

            Matrix identity = Identity;
            Matrix temp = value;

            while (true)
            {
                if ((exponent & 1) != 0)
                    identity *= temp;

                exponent /= 2;

                if (exponent > 0)
                    temp *= temp;
                else
                    break;
            }

            result = identity;
        }

        /// <summary>
        /// Performs the exponential operation on a matrix.
        /// </summary>
        /// <param name="value">The matrix to perform the operation on.</param>
        /// <param name="exponent">The exponent to raise the matrix to.</param>
        /// <returns>The exponential matrix.</returns>
        /// <exception cref="System.ArgumentOutOfRangeException">Thrown when the <paramref name="exponent" /> is negative.</exception>
        public static Matrix Exponent(Matrix value, int exponent)
        {
            Exponent(ref value, exponent, out var result);
            return result;
        }

        /// <summary>
        /// Negates a matrix.
        /// </summary>
        /// <param name="value">The matrix to be negated.</param>
        /// <param name="result">When the method completes, contains the negated matrix.</param>
        public static void Negate(ref Matrix value, out Matrix result)
        {
            result.M11 = -value.M11;
            result.M12 = -value.M12;
            result.M13 = -value.M13;
            result.M14 = -value.M14;
            result.M21 = -value.M21;
            result.M22 = -value.M22;
            result.M23 = -value.M23;
            result.M24 = -value.M24;
            result.M31 = -value.M31;
            result.M32 = -value.M32;
            result.M33 = -value.M33;
            result.M34 = -value.M34;
            result.M41 = -value.M41;
            result.M42 = -value.M42;
            result.M43 = -value.M43;
            result.M44 = -value.M44;
        }

        /// <summary>
        /// Negates a matrix.
        /// </summary>
        /// <param name="value">The matrix to be negated.</param>
        /// <returns>The negated matrix.</returns>
        public static Matrix Negate(Matrix value)
        {
            Negate(ref value, out var result);
            return result;
        }

        /// <summary>
        /// Performs a linear interpolation between two matrices.
        /// </summary>
        /// <param name="start">Start matrix.</param>
        /// <param name="end">End matrix.</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 matrices.</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 Matrix start, ref Matrix end, float amount, out Matrix result)
        {
            result.M11 = Mathf.Lerp(start.M11, end.M11, amount);
            result.M12 = Mathf.Lerp(start.M12, end.M12, amount);
            result.M13 = Mathf.Lerp(start.M13, end.M13, amount);
            result.M14 = Mathf.Lerp(start.M14, end.M14, amount);
            result.M21 = Mathf.Lerp(start.M21, end.M21, amount);
            result.M22 = Mathf.Lerp(start.M22, end.M22, amount);
            result.M23 = Mathf.Lerp(start.M23, end.M23, amount);
            result.M24 = Mathf.Lerp(start.M24, end.M24, amount);
            result.M31 = Mathf.Lerp(start.M31, end.M31, amount);
            result.M32 = Mathf.Lerp(start.M32, end.M32, amount);
            result.M33 = Mathf.Lerp(start.M33, end.M33, amount);
            result.M34 = Mathf.Lerp(start.M34, end.M34, amount);
            result.M41 = Mathf.Lerp(start.M41, end.M41, amount);
            result.M42 = Mathf.Lerp(start.M42, end.M42, amount);
            result.M43 = Mathf.Lerp(start.M43, end.M43, amount);
            result.M44 = Mathf.Lerp(start.M44, end.M44, amount);
        }

        /// <summary>
        /// Performs a linear interpolation between two matrices.
        /// </summary>
        /// <param name="start">Start matrix.</param>
        /// <param name="end">End matrix.</param>
        /// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end" />.</param>
        /// <returns>The linear interpolation of the two matrices.</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 Matrix Lerp(Matrix start, Matrix end, float amount)
        {
            Lerp(ref start, ref end, amount, out var result);
            return result;
        }

        /// <summary>
        /// Performs a cubic interpolation between two matrices.
        /// </summary>
        /// <param name="start">Start matrix.</param>
        /// <param name="end">End matrix.</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 matrices.</param>
        public static void SmoothStep(ref Matrix start, ref Matrix end, float amount, out Matrix result)
        {
            amount = Mathf.SmoothStep(amount);
            Lerp(ref start, ref end, amount, out result);
        }

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

        /// <summary>
        /// Calculates the transpose of the specified matrix.
        /// </summary>
        /// <param name="value">The matrix whose transpose is to be calculated.</param>
        /// <param name="result">When the method completes, contains the transpose of the specified matrix.</param>
        public static void Transpose(ref Matrix value, out Matrix result)
        {
            result = new Matrix
            {
                M11 = value.M11,
                M12 = value.M21,
                M13 = value.M31,
                M14 = value.M41,
                M21 = value.M12,
                M22 = value.M22,
                M23 = value.M32,
                M24 = value.M42,
                M31 = value.M13,
                M32 = value.M23,
                M33 = value.M33,
                M34 = value.M43,
                M41 = value.M14,
                M42 = value.M24,
                M43 = value.M34,
                M44 = value.M44
            };
        }

        /// <summary>
        /// Calculates the transpose of the specified matrix.
        /// </summary>
        /// <param name="value">The matrix whose transpose is to be calculated.</param>
        /// <param name="result">When the method completes, contains the transpose of the specified matrix.</param>
        public static void TransposeByRef(ref Matrix value, ref Matrix result)
        {
            result.M11 = value.M11;
            result.M12 = value.M21;
            result.M13 = value.M31;
            result.M14 = value.M41;
            result.M21 = value.M12;
            result.M22 = value.M22;
            result.M23 = value.M32;
            result.M24 = value.M42;
            result.M31 = value.M13;
            result.M32 = value.M23;
            result.M33 = value.M33;
            result.M34 = value.M43;
            result.M41 = value.M14;
            result.M42 = value.M24;
            result.M43 = value.M34;
            result.M44 = value.M44;
        }

        /// <summary>
        /// Calculates the transpose of the specified matrix.
        /// </summary>
        /// <param name="value">The matrix whose transpose is to be calculated.</param>
        /// <returns>The transpose of the specified matrix.</returns>
        public static Matrix Transpose(Matrix value)
        {
            Transpose(ref value, out var result);
            return result;
        }

        /// <summary>
        /// Calculates the inverse of the specified matrix.
        /// </summary>
        /// <param name="value">The matrix whose inverse is to be calculated.</param>
        /// <param name="result">When the method completes, contains the inverse of the specified matrix.</param>
        public static void Invert(ref Matrix value, out Matrix result)
        {
            float b0 = value.M31 * value.M42 - value.M32 * value.M41;
            float b1 = value.M31 * value.M43 - value.M33 * value.M41;
            float b2 = value.M34 * value.M41 - value.M31 * value.M44;
            float b3 = value.M32 * value.M43 - value.M33 * value.M42;
            float b4 = value.M34 * value.M42 - value.M32 * value.M44;
            float b5 = value.M33 * value.M44 - value.M34 * value.M43;

            float d11 = value.M22 * b5 + value.M23 * b4 + value.M24 * b3;
            float d12 = value.M21 * b5 + value.M23 * b2 + value.M24 * b1;
            float d13 = value.M21 * -b4 + value.M22 * b2 + value.M24 * b0;
            float d14 = value.M21 * b3 + value.M22 * -b1 + value.M23 * b0;

            float det = value.M11 * d11 - value.M12 * d12 + value.M13 * d13 - value.M14 * d14;
            if (Math.Abs(det) < 1e-12f)
            {
                result = Zero;
                return;
            }

            det = 1f / det;

            float a0 = value.M11 * value.M22 - value.M12 * value.M21;
            float a1 = value.M11 * value.M23 - value.M13 * value.M21;
            float a2 = value.M14 * value.M21 - value.M11 * value.M24;
            float a3 = value.M12 * value.M23 - value.M13 * value.M22;
            float a4 = value.M14 * value.M22 - value.M12 * value.M24;
            float a5 = value.M13 * value.M24 - value.M14 * value.M23;

            float d21 = value.M12 * b5 + value.M13 * b4 + value.M14 * b3;
            float d22 = value.M11 * b5 + value.M13 * b2 + value.M14 * b1;
            float d23 = value.M11 * -b4 + value.M12 * b2 + value.M14 * b0;
            float d24 = value.M11 * b3 + value.M12 * -b1 + value.M13 * b0;

            float d31 = value.M42 * a5 + value.M43 * a4 + value.M44 * a3;
            float d32 = value.M41 * a5 + value.M43 * a2 + value.M44 * a1;
            float d33 = value.M41 * -a4 + value.M42 * a2 + value.M44 * a0;
            float d34 = value.M41 * a3 + value.M42 * -a1 + value.M43 * a0;

            float d41 = value.M32 * a5 + value.M33 * a4 + value.M34 * a3;
            float d42 = value.M31 * a5 + value.M33 * a2 + value.M34 * a1;
            float d43 = value.M31 * -a4 + value.M32 * a2 + value.M34 * a0;
            float d44 = value.M31 * a3 + value.M32 * -a1 + value.M33 * a0;

            result.M11 = +d11 * det;
            result.M12 = -d21 * det;
            result.M13 = +d31 * det;
            result.M14 = -d41 * det;
            result.M21 = -d12 * det;
            result.M22 = +d22 * det;
            result.M23 = -d32 * det;
            result.M24 = +d42 * det;
            result.M31 = +d13 * det;
            result.M32 = -d23 * det;
            result.M33 = +d33 * det;
            result.M34 = -d43 * det;
            result.M41 = -d14 * det;
            result.M42 = +d24 * det;
            result.M43 = -d34 * det;
            result.M44 = +d44 * det;
        }

        /// <summary>
        /// Calculates the inverse of the specified matrix.
        /// </summary>
        /// <param name="value">The matrix whose inverse is to be calculated.</param>
        /// <returns>The inverse of the specified matrix.</returns>
        public static Matrix Invert(Matrix value)
        {
            value.Invert();
            return value;
        }

        /// <summary>
        /// Orthogonalizes the specified matrix.
        /// </summary>
        /// <param name="value">The matrix to orthogonalize.</param>
        /// <param name="result">When the method completes, contains the orthogonalized matrix.</param>
        /// <remarks>
        /// <para>
        ///   Orthogonalization is the process of making all rows orthogonal to each other. This
        ///   means that any given row in the matrix will be orthogonal to any other given row in the
        ///   matrix.
        /// </para>
        /// <para>
        ///   Because this method uses the modified Gram-Schmidt process, the resulting matrix
        ///   tends to be numerically unstable. The numeric stability decreases according to the rows
        ///   so that the first row is the most stable and the last row is the least stable.
        /// </para>
        /// <para>
        ///   This operation is performed on the rows of the matrix rather than the columns.
        ///   If you wish for this operation to be performed on the columns, first transpose the
        ///   input and than transpose the output.
        /// </para>
        /// </remarks>
        public static void Orthogonalize(ref Matrix value, out Matrix result)
        {
            //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

            //By separating the above algorithm into multiple lines, we actually increase accuracy.
            result = value;

            result.Row2 -= Float4.Dot(result.Row1, result.Row2) / Float4.Dot(result.Row1, result.Row1) * result.Row1;

            result.Row3 -= Float4.Dot(result.Row1, result.Row3) / Float4.Dot(result.Row1, result.Row1) * result.Row1;
            result.Row3 -= Float4.Dot(result.Row2, result.Row3) / Float4.Dot(result.Row2, result.Row2) * result.Row2;

            result.Row4 -= Float4.Dot(result.Row1, result.Row4) / Float4.Dot(result.Row1, result.Row1) * result.Row1;
            result.Row4 -= Float4.Dot(result.Row2, result.Row4) / Float4.Dot(result.Row2, result.Row2) * result.Row2;
            result.Row4 -= Float4.Dot(result.Row3, result.Row4) / Float4.Dot(result.Row3, result.Row3) * result.Row3;
        }

        /// <summary>
        /// Orthogonalizes the specified matrix.
        /// </summary>
        /// <param name="value">The matrix to orthogonalize.</param>
        /// <returns>The orthogonalized matrix.</returns>
        /// <remarks>
        /// <para>
        ///   Orthogonalization is the process of making all rows orthogonal to each other. This
        ///   means that any given row in the matrix will be orthogonal to any other given row in the
        ///   matrix.
        /// </para>
        /// <para>
        ///   Because this method uses the modified Gram-Schmidt process, the resulting matrix
        ///   tends to be numerically unstable. The numeric stability decreases according to the rows
        ///   so that the first row is the most stable and the last row is the least stable.
        /// </para>
        /// <para>
        ///   This operation is performed on the rows of the matrix rather than the columns.
        ///   If you wish for this operation to be performed on the columns, first transpose the
        ///   input and than transpose the output.
        /// </para>
        /// </remarks>
        public static Matrix Orthogonalize(Matrix value)
        {
            Orthogonalize(ref value, out var result);
            return result;
        }

        /// <summary>
        /// Orthonormalizes the specified matrix.
        /// </summary>
        /// <param name="value">The matrix to orthonormalize.</param>
        /// <param name="result">When the method completes, contains the orthonormalized matrix.</param>
        /// <remarks>
        /// <para>
        ///   Orthonormalization is the process of making all rows and columns orthogonal to each
        ///   other and making all rows and columns of unit length. This means that any given row will
        ///   be orthogonal to any other given row and any given column will be orthogonal to any other
        ///   given column. Any given row will not be orthogonal to any given column. Every row and every
        ///   column will be of unit length.
        /// </para>
        /// <para>
        ///   Because this method uses the modified Gram-Schmidt process, the resulting matrix
        ///   tends to be numerically unstable. The numeric stability decreases according to the rows
        ///   so that the first row is the most stable and the last row is the least stable.
        /// </para>
        /// <para>
        ///   This operation is performed on the rows of the matrix rather than the columns.
        ///   If you wish for this operation to be performed on the columns, first transpose the
        ///   input and than transpose the output.
        /// </para>
        /// </remarks>
        public static void Orthonormalize(ref Matrix value, out Matrix result)
        {
            //Uses the modified Gram-Schmidt process.
            //Because we are making unit vectors, we can optimize the math for orthonormalization
            //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|

            //By separating the above algorithm into multiple lines, we actually increase accuracy.
            result = value;

            result.Row1 = Float4.Normalize(result.Row1);

            result.Row2 -= Float4.Dot(result.Row1, result.Row2) * result.Row1;
            result.Row2 = Float4.Normalize(result.Row2);

            result.Row3 -= Float4.Dot(result.Row1, result.Row3) * result.Row1;
            result.Row3 -= Float4.Dot(result.Row2, result.Row3) * result.Row2;
            result.Row3 = Float4.Normalize(result.Row3);

            result.Row4 -= Float4.Dot(result.Row1, result.Row4) * result.Row1;
            result.Row4 -= Float4.Dot(result.Row2, result.Row4) * result.Row2;
            result.Row4 -= Float4.Dot(result.Row3, result.Row4) * result.Row3;
            result.Row4 = Float4.Normalize(result.Row4);
        }

        /// <summary>
        /// Orthonormalizes the specified matrix.
        /// </summary>
        /// <param name="value">The matrix to orthonormalize.</param>
        /// <returns>The orthonormalized matrix.</returns>
        /// <remarks>
        /// <para>
        ///   Orthonormalization is the process of making all rows and columns orthogonal to each
        ///   other and making all rows and columns of unit length. This means that any given row will
        ///   be orthogonal to any other given row and any given column will be orthogonal to any other
        ///   given column. Any given row will not be orthogonal to any given column. Every row and every
        ///   column will be of unit length.
        /// </para>
        /// <para>
        ///   Because this method uses the modified Gram-Schmidt process, the resulting matrix
        ///   tends to be numerically unstable. The numeric stability decreases according to the rows
        ///   so that the first row is the most stable and the last row is the least stable.
        /// </para>
        /// <para>
        ///   This operation is performed on the rows of the matrix rather than the columns.
        ///   If you wish for this operation to be performed on the columns, first transpose the
        ///   input and than transpose the output.
        /// </para>
        /// </remarks>
        public static Matrix Orthonormalize(Matrix value)
        {
            Orthonormalize(ref value, out var result);
            return result;
        }

        /// <summary>
        /// Brings the matrix into upper triangular form using elementary row operations.
        /// </summary>
        /// <param name="value">The matrix to put into upper triangular form.</param>
        /// <param name="result">When the method completes, contains the upper triangular matrix.</param>
        /// <remarks>
        /// If the matrix is not invertible (i.e. its determinant is zero) than the result of this
        /// method may produce Single.Nan and Single.Inf values. When the matrix represents a system
        /// of linear equations, than this often means that either no solution exists or an infinite
        /// number of solutions exist.
        /// </remarks>
        public static void UpperTriangularForm(ref Matrix value, out Matrix result)
        {
            // Adapted from the row echelon code
            result = value;
            var lead = 0;
            var rowCount = 4;
            var columnCount = 4;

            for (var r = 0; r < rowCount; ++r)
            {
                if (columnCount <= lead)
                    return;

                int i = r;

                while (Mathf.IsZero(result[i, lead]))
                {
                    i++;

                    if (i == rowCount)
                    {
                        i = r;
                        lead++;

                        if (lead == columnCount)
                            return;
                    }
                }

                if (i != r)
                    result.ExchangeRows(i, r);

                float multiplier = 1f / result[r, lead];

                for (; i < rowCount; ++i)
                    if (i != r)
                    {
                        result[i, 0] -= result[r, 0] * multiplier * result[i, lead];
                        result[i, 1] -= result[r, 1] * multiplier * result[i, lead];
                        result[i, 2] -= result[r, 2] * multiplier * result[i, lead];
                        result[i, 3] -= result[r, 3] * multiplier * result[i, lead];
                    }

                lead++;
            }
        }

        /// <summary>
        /// Brings the matrix into upper triangular form using elementary row operations.
        /// </summary>
        /// <param name="value">The matrix to put into upper triangular form.</param>
        /// <returns>The upper triangular matrix.</returns>
        /// <remarks>
        /// If the matrix is not invertible (i.e. its determinant is zero) than the result of this
        /// method may produce Single.Nan and Single.Inf values. When the matrix represents a system
        /// of linear equations, than this often means that either no solution exists or an infinite
        /// number of solutions exist.
        /// </remarks>
        public static Matrix UpperTriangularForm(Matrix value)
        {
            UpperTriangularForm(ref value, out var result);
            return result;
        }

        /// <summary>
        /// Brings the matrix into lower triangular form using elementary row operations.
        /// </summary>
        /// <param name="value">The matrix to put into lower triangular form.</param>
        /// <param name="result">When the method completes, contains the lower triangular matrix.</param>
        /// <remarks>
        /// If the matrix is not invertible (i.e. its determinant is zero) than the result of this
        /// method may produce Single.Nan and Single.Inf values. When the matrix represents a system
        /// of linear equations, than this often means that either no solution exists or an infinite
        /// number of solutions exist.
        /// </remarks>
        public static void LowerTriangularForm(ref Matrix value, out Matrix result)
        {
            // Adapted from the row echelon code
            Matrix temp = value;
            Transpose(ref temp, out result);

            var lead = 0;
            var rowCount = 4;
            var columnCount = 4;

            for (var r = 0; r < rowCount; ++r)
            {
                if (columnCount <= lead)
                    return;

                int i = r;

                while (Mathf.IsZero(result[i, lead]))
                {
                    i++;

                    if (i == rowCount)
                    {
                        i = r;
                        lead++;

                        if (lead == columnCount)
                            return;
                    }
                }

                if (i != r)
                    result.ExchangeRows(i, r);

                float multiplier = 1f / result[r, lead];

                for (; i < rowCount; ++i)
                    if (i != r)
                    {
                        result[i, 0] -= result[r, 0] * multiplier * result[i, lead];
                        result[i, 1] -= result[r, 1] * multiplier * result[i, lead];
                        result[i, 2] -= result[r, 2] * multiplier * result[i, lead];
                        result[i, 3] -= result[r, 3] * multiplier * result[i, lead];
                    }

                lead++;
            }

            Transpose(ref result, out result);
        }

        /// <summary>
        /// Brings the matrix into lower triangular form using elementary row operations.
        /// </summary>
        /// <param name="value">The matrix to put into lower triangular form.</param>
        /// <returns>The lower triangular matrix.</returns>
        /// <remarks>
        /// If the matrix is not invertible (i.e. its determinant is zero) than the result of this
        /// method may produce Single.Nan and Single.Inf values. When the matrix represents a system
        /// of linear equations, than this often means that either no solution exists or an infinite
        /// number of solutions exist.
        /// </remarks>
        public static Matrix LowerTriangularForm(Matrix value)
        {
            LowerTriangularForm(ref value, out var result);
            return result;
        }

        /// <summary>
        /// Brings the matrix into row echelon form using elementary row operations;
        /// </summary>
        /// <param name="value">The matrix to put into row echelon form.</param>
        /// <param name="result">When the method completes, contains the row echelon form of the matrix.</param>
        public static void RowEchelonForm(ref Matrix value, out Matrix result)
        {
            // Source: Wikipedia pseudo code
            // Reference: http://en.wikipedia.org/wiki/Row_echelon_form#Pseudocode

            result = value;
            var lead = 0;
            var rowCount = 4;
            var columnCount = 4;

            for (var r = 0; r < rowCount; ++r)
            {
                if (columnCount <= lead)
                    return;

                int i = r;

                while (Mathf.IsZero(result[i, lead]))
                {
                    i++;

                    if (i == rowCount)
                    {
                        i = r;
                        lead++;

                        if (lead == columnCount)
                            return;
                    }
                }

                if (i != r)
                    result.ExchangeRows(i, r);

                float multiplier = 1f / result[r, lead];
                result[r, 0] *= multiplier;
                result[r, 1] *= multiplier;
                result[r, 2] *= multiplier;
                result[r, 3] *= multiplier;

                for (; i < rowCount; ++i)
                    if (i != r)
                    {
                        result[i, 0] -= result[r, 0] * result[i, lead];
                        result[i, 1] -= result[r, 1] * result[i, lead];
                        result[i, 2] -= result[r, 2] * result[i, lead];
                        result[i, 3] -= result[r, 3] * result[i, lead];
                    }

                lead++;
            }
        }

        /// <summary>
        /// Brings the matrix into row echelon form using elementary row operations;
        /// </summary>
        /// <param name="value">The matrix to put into row echelon form.</param>
        /// <returns>When the method completes, contains the row echelon form of the matrix.</returns>
        public static Matrix RowEchelonForm(Matrix value)
        {
            RowEchelonForm(ref value, out var result);
            return result;
        }

        /// <summary>
        /// Brings the matrix into reduced row echelon form using elementary row operations.
        /// </summary>
        /// <param name="value">The matrix to put into reduced row echelon form.</param>
        /// <param name="augment">The fifth column of the matrix.</param>
        /// <param name="result">When the method completes, contains the resultant matrix after the operation.</param>
        /// <param name="augmentResult">When the method completes, contains the resultant fifth column of the matrix.</param>
        /// <remarks>
        /// <para>
        ///   The fifth column is often called the augmented part of the matrix. This is because the fifth
        ///   column is really just an extension of the matrix so that there is a place to put all of the
        ///   non-zero components after the operation is complete.
        /// </para>
        /// <para>
        ///   Often times the resultant matrix will the identity matrix or a matrix similar to the identity
        ///   matrix. Sometimes, however, that is not possible and numbers other than zero and one may appear.
        /// </para>
        /// <para>
        ///   This method can be used to solve systems of linear equations. Upon completion of this method,
        ///   the <paramref name="augmentResult" /> will contain the solution for the system. It is up to the user
        ///   to analyze both the input and the result to determine if a solution really exists.
        /// </para>
        /// </remarks>
        public static void ReducedRowEchelonForm(ref Matrix value, ref Float4 augment, out Matrix result, out Float4 augmentResult)
        {
            // Source: http://rosettacode.org
            // Reference: http://rosettacode.org/wiki/Reduced_row_echelon_form

            var matrix = new float[4, 5];

            matrix[0, 0] = value[0, 0];
            matrix[0, 1] = value[0, 1];
            matrix[0, 2] = value[0, 2];
            matrix[0, 3] = value[0, 3];
            matrix[0, 4] = augment[0];

            matrix[1, 0] = value[1, 0];
            matrix[1, 1] = value[1, 1];
            matrix[1, 2] = value[1, 2];
            matrix[1, 3] = value[1, 3];
            matrix[1, 4] = augment[1];

            matrix[2, 0] = value[2, 0];
            matrix[2, 1] = value[2, 1];
            matrix[2, 2] = value[2, 2];
            matrix[2, 3] = value[2, 3];
            matrix[2, 4] = augment[2];

            matrix[3, 0] = value[3, 0];
            matrix[3, 1] = value[3, 1];
            matrix[3, 2] = value[3, 2];
            matrix[3, 3] = value[3, 3];
            matrix[3, 4] = augment[3];

            var lead = 0;
            var rowCount = 4;
            var columnCount = 5;

            for (var r = 0; r < rowCount; r++)
            {
                if (columnCount <= lead)
                    break;

                int i = r;

                while (Mathf.IsZero(matrix[i, lead]))
                {
                    i++;

                    if (i == rowCount)
                    {
                        i = r;
                        lead++;

                        if (columnCount == lead)
                            break;
                    }
                }

                for (var j = 0; j < columnCount; j++)
                {
                    float temp = matrix[r, j];
                    matrix[r, j] = matrix[i, j];
                    matrix[i, j] = temp;
                }

                float div = matrix[r, lead];

                for (var j = 0; j < columnCount; j++)
                    matrix[r, j] /= div;

                for (var j = 0; j < rowCount; j++)
                    if (j != r)
                    {
                        float sub = matrix[j, lead];
                        for (var k = 0; k < columnCount; k++)
                            matrix[j, k] -= sub * matrix[r, k];
                    }

                lead++;
            }

            result.M11 = matrix[0, 0];
            result.M12 = matrix[0, 1];
            result.M13 = matrix[0, 2];
            result.M14 = matrix[0, 3];

            result.M21 = matrix[1, 0];
            result.M22 = matrix[1, 1];
            result.M23 = matrix[1, 2];
            result.M24 = matrix[1, 3];

            result.M31 = matrix[2, 0];
            result.M32 = matrix[2, 1];
            result.M33 = matrix[2, 2];
            result.M34 = matrix[2, 3];

            result.M41 = matrix[3, 0];
            result.M42 = matrix[3, 1];
            result.M43 = matrix[3, 2];
            result.M44 = matrix[3, 3];

            augmentResult.X = matrix[0, 4];
            augmentResult.Y = matrix[1, 4];
            augmentResult.Z = matrix[2, 4];
            augmentResult.W = matrix[3, 4];
        }

        /// <summary>
        /// Creates a left-handed spherical billboard that rotates around a specified object position.
        /// </summary>
        /// <param name="objectPosition">The position of the object around which the billboard will rotate.</param>
        /// <param name="cameraPosition">The position of the camera.</param>
        /// <param name="cameraUpFloat">The up vector of the camera.</param>
        /// <param name="cameraForwardFloat">The forward vector of the camera.</param>
        /// <param name="result">When the method completes, contains the created billboard matrix.</param>
        public static void Billboard(ref Float3 objectPosition, ref Float3 cameraPosition, ref Float3 cameraUpFloat, ref Float3 cameraForwardFloat, out Matrix result)
        {
            Float3 difference = cameraPosition - objectPosition;

            float lengthSq = difference.LengthSquared;
            if (Mathf.IsZero(lengthSq))
                difference = -cameraForwardFloat;
            else
                difference *= (float)(1.0 / Math.Sqrt(lengthSq));

            Float3.Cross(ref cameraUpFloat, ref difference, out var crossed);
            crossed.Normalize();
            Float3.Cross(ref difference, ref crossed, out var final);

            result.M11 = crossed.X;
            result.M12 = crossed.Y;
            result.M13 = crossed.Z;
            result.M14 = 0.0f;
            result.M21 = final.X;
            result.M22 = final.Y;
            result.M23 = final.Z;
            result.M24 = 0.0f;
            result.M31 = difference.X;
            result.M32 = difference.Y;
            result.M33 = difference.Z;
            result.M34 = 0.0f;
            result.M41 = objectPosition.X;
            result.M42 = objectPosition.Y;
            result.M43 = objectPosition.Z;
            result.M44 = 1.0f;
        }

        /// <summary>
        /// Creates a left-handed spherical billboard that rotates around a specified object position.
        /// </summary>
        /// <param name="objectPosition">The position of the object around which the billboard will rotate.</param>
        /// <param name="cameraPosition">The position of the camera.</param>
        /// <param name="cameraUpFloat">The up vector of the camera.</param>
        /// <param name="cameraForwardFloat">The forward vector of the camera.</param>
        /// <returns>The created billboard matrix.</returns>
        public static Matrix Billboard(Float3 objectPosition, Float3 cameraPosition, Float3 cameraUpFloat, Float3 cameraForwardFloat)
        {
            Billboard(ref objectPosition, ref cameraPosition, ref cameraUpFloat, ref cameraForwardFloat, out var result);
            return result;
        }

        /// <summary>
        /// Creates a left-handed, look-at matrix.
        /// </summary>
        /// <param name="eye">The position of the viewer's eye.</param>
        /// <param name="target">The camera look-at target.</param>
        /// <param name="up">The camera's up vector.</param>
        /// <param name="result">When the method completes, contains the created look-at matrix.</param>
        public static void LookAt(ref Float3 eye, ref Float3 target, ref Float3 up, out Matrix result)
        {
            Float3.Subtract(ref target, ref eye, out var zaxis);
            zaxis.Normalize();
            Float3.Cross(ref up, ref zaxis, out var xaxis);
            xaxis.Normalize();
            Float3.Cross(ref zaxis, ref xaxis, out var yaxis);

            result = Identity;
            result.M11 = xaxis.X;
            result.M21 = xaxis.Y;
            result.M31 = xaxis.Z;
            result.M12 = yaxis.X;
            result.M22 = yaxis.Y;
            result.M32 = yaxis.Z;
            result.M13 = zaxis.X;
            result.M23 = zaxis.Y;
            result.M33 = zaxis.Z;

            Float3.Dot(ref xaxis, ref eye, out result.M41);
            Float3.Dot(ref yaxis, ref eye, out result.M42);
            Float3.Dot(ref zaxis, ref eye, out result.M43);

            result.M41 = -result.M41;
            result.M42 = -result.M42;
            result.M43 = -result.M43;
        }

        /// <summary>
        /// Creates a left-handed, look-at matrix.
        /// </summary>
        /// <param name="eye">The position of the viewer's eye.</param>
        /// <param name="target">The camera look-at target.</param>
        /// <param name="up">The camera's up vector.</param>
        /// <returns>The created look-at matrix.</returns>
        public static Matrix LookAt(Float3 eye, Float3 target, Float3 up)
        {
            LookAt(ref eye, ref target, ref up, out var result);
            return result;
        }

        /// <summary>
        /// Creates a left-handed, orthographic projection matrix.
        /// </summary>
        /// <param name="width">Width of the viewing volume.</param>
        /// <param name="height">Height of the viewing volume.</param>
        /// <param name="znear">Minimum z-value of the viewing volume.</param>
        /// <param name="zfar">Maximum z-value of the viewing volume.</param>
        /// <param name="result">When the method completes, contains the created projection matrix.</param>
        public static void Ortho(float width, float height, float znear, float zfar, out Matrix result)
        {
            float halfWidth = width * 0.5f;
            float halfHeight = height * 0.5f;
            OrthoOffCenter(-halfWidth, halfWidth, -halfHeight, halfHeight, znear, zfar, out result);
        }

        /// <summary>
        /// Creates a left-handed, orthographic projection matrix.
        /// </summary>
        /// <param name="width">Width of the viewing volume.</param>
        /// <param name="height">Height of the viewing volume.</param>
        /// <param name="znear">Minimum z-value of the viewing volume.</param>
        /// <param name="zfar">Maximum z-value of the viewing volume.</param>
        /// <returns>The created projection matrix.</returns>
        public static Matrix Ortho(float width, float height, float znear, float zfar)
        {
            Ortho(width, height, znear, zfar, out var result);
            return result;
        }

        /// <summary>
        /// Creates a left-handed, customized orthographic projection matrix.
        /// </summary>
        /// <param name="left">Minimum x-value of the viewing volume.</param>
        /// <param name="right">Maximum x-value of the viewing volume.</param>
        /// <param name="bottom">Minimum y-value of the viewing volume.</param>
        /// <param name="top">Maximum y-value of the viewing volume.</param>
        /// <param name="znear">Minimum z-value of the viewing volume.</param>
        /// <param name="zfar">Maximum z-value of the viewing volume.</param>
        /// <param name="result">When the method completes, contains the created projection matrix.</param>
        public static void OrthoOffCenter(float left, float right, float bottom, float top, float znear, float zfar, out Matrix result)
        {
            float zRange = 1.0f / (zfar - znear);
            result = Identity;
            result.M11 = 2.0f / (right - left);
            result.M22 = 2.0f / (top - bottom);
            result.M33 = zRange;
            result.M41 = (left + right) / (left - right);
            result.M42 = (top + bottom) / (bottom - top);
            result.M43 = -znear * zRange;
        }

        /// <summary>
        /// Creates a left-handed, customized orthographic projection matrix.
        /// </summary>
        /// <param name="left">Minimum x-value of the viewing volume.</param>
        /// <param name="right">Maximum x-value of the viewing volume.</param>
        /// <param name="bottom">Minimum y-value of the viewing volume.</param>
        /// <param name="top">Maximum y-value of the viewing volume.</param>
        /// <param name="znear">Minimum z-value of the viewing volume.</param>
        /// <param name="zfar">Maximum z-value of the viewing volume.</param>
        /// <returns>The created projection matrix.</returns>
        public static Matrix OrthoOffCenter(float left, float right, float bottom, float top, float znear, float zfar)
        {
            OrthoOffCenter(left, right, bottom, top, znear, zfar, out var result);
            return result;
        }

        /// <summary>
        /// Creates a left-handed, perspective projection matrix.
        /// </summary>
        /// <param name="width">Width of the viewing volume.</param>
        /// <param name="height">Height of the viewing volume.</param>
        /// <param name="znear">Minimum z-value of the viewing volume.</param>
        /// <param name="zfar">Maximum z-value of the viewing volume.</param>
        /// <param name="result">When the method completes, contains the created projection matrix.</param>
        public static void Perspective(float width, float height, float znear, float zfar, out Matrix result)
        {
            float halfWidth = width * 0.5f;
            float halfHeight = height * 0.5f;
            PerspectiveOffCenter(-halfWidth, halfWidth, -halfHeight, halfHeight, znear, zfar, out result);
        }

        /// <summary>
        /// Creates a left-handed, perspective projection matrix.
        /// </summary>
        /// <param name="width">Width of the viewing volume.</param>
        /// <param name="height">Height of the viewing volume.</param>
        /// <param name="znear">Minimum z-value of the viewing volume.</param>
        /// <param name="zfar">Maximum z-value of the viewing volume.</param>
        /// <returns>The created projection matrix.</returns>
        public static Matrix Perspective(float width, float height, float znear, float zfar)
        {
            Perspective(width, height, znear, zfar, out var result);
            return result;
        }

        /// <summary>
        /// Creates a left-handed, perspective projection matrix based on a field of view.
        /// </summary>
        /// <param name="fov">Field of view in the y direction, in radians.</param>
        /// <param name="aspect">Aspect ratio, defined as view space width divided by height.</param>
        /// <param name="znear">Minimum z-value of the viewing volume.</param>
        /// <param name="zfar">Maximum z-value of the viewing volume.</param>
        /// <param name="result">When the method completes, contains the created projection matrix.</param>
        public static void PerspectiveFov(float fov, float aspect, float znear, float zfar, out Matrix result)
        {
            var yScale = (float)(1.0f / Math.Tan(fov * 0.5f));
            var q = zfar / (zfar - znear);
            result = new Matrix
            {
                M11 = yScale / aspect,
                M22 = yScale,
                M33 = q,
                M34 = 1.0f,
                M43 = -q * znear,
            };
        }

        /// <summary>
        /// Creates a left-handed, perspective projection matrix based on a field of view.
        /// </summary>
        /// <param name="fov">Field of view in the y direction, in radians.</param>
        /// <param name="aspect">Aspect ratio, defined as view space width divided by height.</param>
        /// <param name="znear">Minimum z-value of the viewing volume.</param>
        /// <param name="zfar">Maximum z-value of the viewing volume.</param>
        /// <returns>The created projection matrix.</returns>
        public static Matrix PerspectiveFov(float fov, float aspect, float znear, float zfar)
        {
            PerspectiveFov(fov, aspect, znear, zfar, out var result);
            return result;
        }

        /// <summary>
        /// Creates a left-handed, customized perspective projection matrix.
        /// </summary>
        /// <param name="left">Minimum x-value of the viewing volume.</param>
        /// <param name="right">Maximum x-value of the viewing volume.</param>
        /// <param name="bottom">Minimum y-value of the viewing volume.</param>
        /// <param name="top">Maximum y-value of the viewing volume.</param>
        /// <param name="znear">Minimum z-value of the viewing volume.</param>
        /// <param name="zfar">Maximum z-value of the viewing volume.</param>
        /// <param name="result">When the method completes, contains the created projection matrix.</param>
        public static void PerspectiveOffCenter(float left, float right, float bottom, float top, float znear, float zfar, out Matrix result)
        {
            float zRange = zfar / (zfar - znear);
            result = new Matrix
            {
                M11 = 2.0f * znear / (right - left),
                M22 = 2.0f * znear / (top - bottom),
                M31 = (left + right) / (left - right),
                M32 = (top + bottom) / (bottom - top),
                M33 = zRange,
                M34 = 1.0f,
                M43 = -znear * zRange,
            };
        }

        /// <summary>
        /// Creates a left-handed, customized perspective projection matrix.
        /// </summary>
        /// <param name="left">Minimum x-value of the viewing volume.</param>
        /// <param name="right">Maximum x-value of the viewing volume.</param>
        /// <param name="bottom">Minimum y-value of the viewing volume.</param>
        /// <param name="top">Maximum y-value of the viewing volume.</param>
        /// <param name="znear">Minimum z-value of the viewing volume.</param>
        /// <param name="zfar">Maximum z-value of the viewing volume.</param>
        /// <returns>The created projection matrix.</returns>
        public static Matrix PerspectiveOffCenter(float left, float right, float bottom, float top, float znear, float zfar)
        {
            PerspectiveOffCenter(left, right, bottom, top, znear, zfar, out var result);
            return result;
        }

        /// <summary>
        /// Creates a matrix that scales along the x-axis, y-axis, and y-axis.
        /// </summary>
        /// <param name="scale">Scaling factor for all three axes.</param>
        /// <param name="result">When the method completes, contains the created scaling matrix.</param>
        public static void Scaling(ref Float3 scale, out Matrix result)
        {
            Scaling(scale.X, scale.Y, scale.Z, out result);
        }

        /// <summary>
        /// Creates a matrix that scales along the x-axis, y-axis, and y-axis.
        /// </summary>
        /// <param name="scale">Scaling factor for all three axes.</param>
        /// <returns>The created scaling matrix.</returns>
        public static Matrix Scaling(Float3 scale)
        {
            Scaling(ref scale, out var result);
            return result;
        }

        /// <summary>
        /// Creates a matrix that scales along the x-axis, y-axis, and y-axis.
        /// </summary>
        /// <param name="x">Scaling factor that is applied along the x-axis.</param>
        /// <param name="y">Scaling factor that is applied along the y-axis.</param>
        /// <param name="z">Scaling factor that is applied along the z-axis.</param>
        /// <param name="result">When the method completes, contains the created scaling matrix.</param>
        public static void Scaling(float x, float y, float z, out Matrix result)
        {
            result = Identity;
            result.M11 = x;
            result.M22 = y;
            result.M33 = z;
        }

        /// <summary>
        /// Creates a matrix that scales along the x-axis, y-axis, and y-axis.
        /// </summary>
        /// <param name="x">Scaling factor that is applied along the x-axis.</param>
        /// <param name="y">Scaling factor that is applied along the y-axis.</param>
        /// <param name="z">Scaling factor that is applied along the z-axis.</param>
        /// <returns>The created scaling matrix.</returns>
        public static Matrix Scaling(float x, float y, float z)
        {
            Scaling(x, y, z, out var result);
            return result;
        }

        /// <summary>
        /// Creates a matrix that uniformly scales along all three axis.
        /// </summary>
        /// <param name="scale">The uniform scale that is applied along all axis.</param>
        /// <param name="result">When the method completes, contains the created scaling matrix.</param>
        public static void Scaling(float scale, out Matrix result)
        {
            result = Identity;
            result.M11 = result.M22 = result.M33 = scale;
        }

        /// <summary>
        /// Creates a matrix that uniformly scales along all three axis.
        /// </summary>
        /// <param name="scale">The uniform scale that is applied along all axis.</param>
        /// <returns>The created scaling matrix.</returns>
        public static Matrix Scaling(float scale)
        {
            Scaling(scale, out var result);
            return result;
        }

        /// <summary>
        /// Creates a matrix that rotates around the x-axis.
        /// </summary>
        /// <param name="angle">
        /// Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis
        /// toward the origin.
        /// </param>
        /// <param name="result">When the method completes, contains the created rotation matrix.</param>
        public static void RotationX(float angle, out Matrix result)
        {
            var cos = (float)Math.Cos(angle);
            var sin = (float)Math.Sin(angle);
            result = Identity;
            result.M22 = cos;
            result.M23 = sin;
            result.M32 = -sin;
            result.M33 = cos;
        }

        /// <summary>
        /// Creates a matrix that rotates around the x-axis.
        /// </summary>
        /// <param name="angle">
        /// Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis
        /// toward the origin.
        /// </param>
        /// <returns>The created rotation matrix.</returns>
        public static Matrix RotationX(float angle)
        {
            RotationX(angle, out var result);
            return result;
        }

        /// <summary>
        /// Creates a matrix that rotates around the y-axis.
        /// </summary>
        /// <param name="angle">
        /// Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis
        /// toward the origin.
        /// </param>
        /// <param name="result">When the method completes, contains the created rotation matrix.</param>
        public static void RotationY(float angle, out Matrix result)
        {
            var cos = (float)Math.Cos(angle);
            var sin = (float)Math.Sin(angle);
            result = Identity;
            result.M11 = cos;
            result.M13 = -sin;
            result.M31 = sin;
            result.M33 = cos;
        }

        /// <summary>
        /// Creates a matrix that rotates around the y-axis.
        /// </summary>
        /// <param name="angle">
        /// Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis
        /// toward the origin.
        /// </param>
        /// <returns>The created rotation matrix.</returns>
        public static Matrix RotationY(float angle)
        {
            RotationY(angle, out var result);
            return result;
        }

        /// <summary>
        /// Creates a matrix that rotates around the z-axis.
        /// </summary>
        /// <param name="angle">
        /// Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis
        /// toward the origin.
        /// </param>
        /// <param name="result">When the method completes, contains the created rotation matrix.</param>
        public static void RotationZ(float angle, out Matrix result)
        {
            var cos = (float)Math.Cos(angle);
            var sin = (float)Math.Sin(angle);
            result = Identity;
            result.M11 = cos;
            result.M12 = sin;
            result.M21 = -sin;
            result.M22 = cos;
        }

        /// <summary>
        /// Creates a matrix that rotates around the z-axis.
        /// </summary>
        /// <param name="angle">
        /// Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis
        /// toward the origin.
        /// </param>
        /// <returns>The created rotation matrix.</returns>
        public static Matrix RotationZ(float angle)
        {
            RotationZ(angle, out var result);
            return result;
        }

        /// <summary>
        /// Creates a matrix that rotates around an arbitrary axis.
        /// </summary>
        /// <param name="axis">The axis around which to rotate. This parameter is assumed to be normalized.</param>
        /// <param name="angle">Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.</param>
        /// <param name="result">When the method completes, contains the created rotation matrix.</param>
        public static void RotationAxis(ref Float3 axis, float angle, out Matrix result)
        {
            float x = axis.X;
            float y = axis.Y;
            float z = axis.Z;
            var cos = (float)Math.Cos(angle);
            var sin = (float)Math.Sin(angle);
            float xx = x * x;
            float yy = y * y;
            float zz = z * z;
            float xy = x * y;
            float xz = x * z;
            float yz = y * z;

            result = Identity;
            result.M11 = xx + cos * (1.0f - xx);
            result.M12 = xy - cos * xy + sin * z;
            result.M13 = xz - cos * xz - sin * y;
            result.M21 = xy - cos * xy - sin * z;
            result.M22 = yy + cos * (1.0f - yy);
            result.M23 = yz - cos * yz + sin * x;
            result.M31 = xz - cos * xz + sin * y;
            result.M32 = yz - cos * yz - sin * x;
            result.M33 = zz + cos * (1.0f - zz);
        }

        /// <summary>
        /// Creates a matrix that rotates around an arbitrary axis.
        /// </summary>
        /// <param name="axis">The axis around which to rotate. This parameter is assumed to be normalized.</param>
        /// <param name="angle">Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.</param>
        /// <returns>The created rotation matrix.</returns>
        public static Matrix RotationAxis(Float3 axis, float angle)
        {
            RotationAxis(ref axis, angle, out var result);
            return result;
        }

        /// <summary>
        /// Creates a rotation matrix from a quaternion.
        /// </summary>
        /// <param name="rotation">The quaternion to use to build the matrix.</param>
        /// <param name="result">The created rotation matrix.</param>
        public static void RotationQuaternion(ref Quaternion rotation, out Matrix result)
        {
            float xx = rotation.X * rotation.X;
            float yy = rotation.Y * rotation.Y;
            float zz = rotation.Z * rotation.Z;
            float xy = rotation.X * rotation.Y;
            float zw = rotation.Z * rotation.W;
            float zx = rotation.Z * rotation.X;
            float yw = rotation.Y * rotation.W;
            float yz = rotation.Y * rotation.Z;
            float xw = rotation.X * rotation.W;

            result = Identity;
            result.M11 = 1.0f - 2.0f * (yy + zz);
            result.M12 = 2.0f * (xy + zw);
            result.M13 = 2.0f * (zx - yw);
            result.M21 = 2.0f * (xy - zw);
            result.M22 = 1.0f - 2.0f * (zz + xx);
            result.M23 = 2.0f * (yz + xw);
            result.M31 = 2.0f * (zx + yw);
            result.M32 = 2.0f * (yz - xw);
            result.M33 = 1.0f - 2.0f * (yy + xx);
        }

        /// <summary>
        /// Creates a rotation matrix from a quaternion.
        /// </summary>
        /// <param name="rotation">The quaternion to use to build the matrix.</param>
        /// <returns>The created rotation matrix.</returns>
        public static Matrix RotationQuaternion(Quaternion rotation)
        {
            RotationQuaternion(ref rotation, out var result);
            return result;
        }

        /// <summary>
        /// Creates a rotation matrix with a specified yaw, pitch, and roll.
        /// </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">When the method completes, contains the created rotation matrix.</param>
        public static void RotationYawPitchRoll(float yaw, float pitch, float roll, out Matrix result)
        {
            Quaternion.RotationYawPitchRoll(yaw, pitch, roll, out var quaternion);
            RotationQuaternion(ref quaternion, out result);
        }

        /// <summary>
        /// Creates a rotation matrix with a specified yaw, pitch, and roll.
        /// </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>The created rotation matrix.</returns>
        public static Matrix RotationYawPitchRoll(float yaw, float pitch, float roll)
        {
            RotationYawPitchRoll(yaw, pitch, roll, out var result);
            return result;
        }

        /// <summary>
        /// Creates a translation matrix using the specified offsets.
        /// </summary>
        /// <param name="value">The offset for all three coordinate planes.</param>
        /// <param name="result">When the method completes, contains the created translation matrix.</param>
        public static void Translation(ref Float3 value, out Matrix result)
        {
            Translation(value.X, value.Y, value.Z, out result);
        }

        /// <summary>
        /// Creates a translation matrix using the specified offsets.
        /// </summary>
        /// <param name="value">The offset for all three coordinate planes.</param>
        /// <returns>The created translation matrix.</returns>
        public static Matrix Translation(Float3 value)
        {
            Translation(ref value, out var result);
            return result;
        }

        /// <summary>
        /// Creates a translation matrix using the specified offsets.
        /// </summary>
        /// <param name="x">X-coordinate offset.</param>
        /// <param name="y">Y-coordinate offset.</param>
        /// <param name="z">Z-coordinate offset.</param>
        /// <param name="result">When the method completes, contains the created translation matrix.</param>
        public static void Translation(float x, float y, float z, out Matrix result)
        {
            result = Identity;
            result.M41 = x;
            result.M42 = y;
            result.M43 = z;
        }

        /// <summary>
        /// Creates a translation matrix using the specified offsets.
        /// </summary>
        /// <param name="x">X-coordinate offset.</param>
        /// <param name="y">Y-coordinate offset.</param>
        /// <param name="z">Z-coordinate offset.</param>
        /// <returns>The created translation matrix.</returns>
        public static Matrix Translation(float x, float y, float z)
        {
            Translation(x, y, z, out var result);
            return result;
        }

        /// <summary>
        /// Creates a skew/shear matrix by means of a translation vector, a rotation vector, and a rotation angle.
        /// shearing is performed in the direction of translation vector, where translation vector and rotation vector define the
        /// shearing plane.
        /// The effect is such that the skewed rotation vector has the specified angle with rotation itself.
        /// </summary>
        /// <param name="angle">The rotation angle.</param>
        /// <param name="rotationVec">The rotation vector</param>
        /// <param name="transVec">The translation vector</param>
        /// <param name="matrix">Contains the created skew/shear matrix. </param>
        public static void Skew(float angle, ref Float3 rotationVec, ref Float3 transVec, out Matrix matrix)
        {
            // http://elckerlyc.ewi.utwente.nl/browser/Elckerlyc/Hmi/HmiMath/src/hmi/math/Mat3f.java
            var MINIMAL_SKEW_ANGLE = 0.000001f;
            Float3 e0 = rotationVec;
            Float3 e1 = Float3.Normalize(transVec);
            Float3.Dot(ref rotationVec, ref e1, out var rv1);
            e0 += rv1 * e1;
            Float3.Dot(ref rotationVec, ref e0, out var rv0);
            var cosA = (float)Math.Cos(angle);
            var sinA = (float)Math.Sin(angle);
            float rr0 = rv0 * cosA - rv1 * sinA;
            float rr1 = rv0 * sinA + rv1 * cosA;
            if (rr0 < MINIMAL_SKEW_ANGLE)
                throw new ArgumentException("Illegal skew angle");
            float d = rr1 / rr0 - rv1 / rv0;
            matrix = Identity;
            matrix.M11 = d * e1[0] * e0[0] + 1.0f;
            matrix.M12 = d * e1[0] * e0[1];
            matrix.M13 = d * e1[0] * e0[2];
            matrix.M21 = d * e1[1] * e0[0];
            matrix.M22 = d * e1[1] * e0[1] + 1.0f;
            matrix.M23 = d * e1[1] * e0[2];
            matrix.M31 = d * e1[2] * e0[0];
            matrix.M32 = d * e1[2] * e0[1];
            matrix.M33 = d * e1[2] * e0[2] + 1.0f;
        }

        /// <summary>
        /// Creates a 3D affine transformation matrix.
        /// </summary>
        /// <param name="scaling">Scaling factor.</param>
        /// <param name="rotation">The rotation of the transformation.</param>
        /// <param name="translation">The translation factor of the transformation.</param>
        /// <param name="result">When the method completes, contains the created affine transformation matrix.</param>
        public static void AffineTransformation(float scaling, ref Quaternion rotation, ref Float3 translation, out Matrix result)
        {
            result = Scaling(scaling) * RotationQuaternion(rotation) * Translation(translation);
        }

        /// <summary>
        /// Creates a 3D affine transformation matrix.
        /// </summary>
        /// <param name="scaling">Scaling factor.</param>
        /// <param name="rotation">The rotation of the transformation.</param>
        /// <param name="translation">The translation factor of the transformation.</param>
        /// <returns>The created affine transformation matrix.</returns>
        public static Matrix AffineTransformation(float scaling, Quaternion rotation, Float3 translation)
        {
            AffineTransformation(scaling, ref rotation, ref translation, out var result);
            return result;
        }

        /// <summary>
        /// Creates a 3D affine transformation matrix.
        /// </summary>
        /// <param name="scaling">Scaling factor.</param>
        /// <param name="rotationCenter">The center of the rotation.</param>
        /// <param name="rotation">The rotation of the transformation.</param>
        /// <param name="translation">The translation factor of the transformation.</param>
        /// <param name="result">When the method completes, contains the created affine transformation matrix.</param>
        public static void AffineTransformation(float scaling, ref Float3 rotationCenter, ref Quaternion rotation, ref Float3 translation, out Matrix result)
        {
            result = Scaling(scaling) * Translation(-rotationCenter) * RotationQuaternion(rotation) *
                     Translation(rotationCenter) * Translation(translation);
        }

        /// <summary>
        /// Creates a 3D affine transformation matrix.
        /// </summary>
        /// <param name="scaling">Scaling factor.</param>
        /// <param name="rotationCenter">The center of the rotation.</param>
        /// <param name="rotation">The rotation of the transformation.</param>
        /// <param name="translation">The translation factor of the transformation.</param>
        /// <returns>The created affine transformation matrix.</returns>
        public static Matrix AffineTransformation(float scaling, Float3 rotationCenter, Quaternion rotation, Float3 translation)
        {
            AffineTransformation(scaling, ref rotationCenter, ref rotation, ref translation, out var result);
            return result;
        }

        /// <summary>
        /// Creates a 2D affine transformation matrix.
        /// </summary>
        /// <param name="scaling">Scaling factor.</param>
        /// <param name="rotation">The rotation of the transformation.</param>
        /// <param name="translation">The translation factor of the transformation.</param>
        /// <param name="result">When the method completes, contains the created affine transformation matrix.</param>
        public static void AffineTransformation2D(float scaling, float rotation, ref Float2 translation, out Matrix result)
        {
            result = Scaling(scaling, scaling, 1.0f) * RotationZ(rotation) * Translation((Float3)translation);
        }

        /// <summary>
        /// Creates a 2D affine transformation matrix.
        /// </summary>
        /// <param name="scaling">Scaling factor.</param>
        /// <param name="rotation">The rotation of the transformation.</param>
        /// <param name="translation">The translation factor of the transformation.</param>
        /// <returns>The created affine transformation matrix.</returns>
        public static Matrix AffineTransformation2D(float scaling, float rotation, Float2 translation)
        {
            AffineTransformation2D(scaling, rotation, ref translation, out var result);
            return result;
        }

        /// <summary>
        /// Creates a 2D affine transformation matrix.
        /// </summary>
        /// <param name="scaling">Scaling factor.</param>
        /// <param name="rotationCenter">The center of the rotation.</param>
        /// <param name="rotation">The rotation of the transformation.</param>
        /// <param name="translation">The translation factor of the transformation.</param>
        /// <param name="result">When the method completes, contains the created affine transformation matrix.</param>
        public static void AffineTransformation2D(float scaling, ref Float2 rotationCenter, float rotation, ref Float2 translation, out Matrix result)
        {
            result = Scaling(scaling, scaling, 1.0f) * Translation((Float3)(-rotationCenter)) * RotationZ(rotation) * Translation((Float3)rotationCenter) * Translation((Float3)translation);
        }

        /// <summary>
        /// Creates a 2D affine transformation matrix.
        /// </summary>
        /// <param name="scaling">Scaling factor.</param>
        /// <param name="rotationCenter">The center of the rotation.</param>
        /// <param name="rotation">The rotation of the transformation.</param>
        /// <param name="translation">The translation factor of the transformation.</param>
        /// <returns>The created affine transformation matrix.</returns>
        public static Matrix AffineTransformation2D(float scaling, Float2 rotationCenter, float rotation, Float2 translation)
        {
            AffineTransformation2D(scaling, ref rotationCenter, rotation, ref translation, out var result);
            return result;
        }

        /// <summary>
        /// Creates a matrix that contains both the X, Y and Z rotation, as well as scaling and translation.
        /// </summary>
        /// <param name="translation">The translation.</param>
        /// <param name="rotation">Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.</param>
        /// <param name="scaling">The scaling.</param>
        /// <returns>The created transformation matrix.</returns>
        public static Matrix Transformation(Float3 scaling, Quaternion rotation, Float3 translation)
        {
            Transformation(ref scaling, ref rotation, ref translation, out var result);
            return result;
        }

        /// <summary>
        /// Creates a matrix that contains both the X, Y and Z rotation, as well as scaling and translation.
        /// </summary>
        /// <param name="translation">The translation.</param>
        /// <param name="rotation">Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.</param>
        /// <param name="scaling">The scaling.</param>
        /// <param name="result">When the method completes, contains the created transformation matrix.</param>
        public static void Transformation(ref Float3 scaling, ref Quaternion rotation, ref Float3 translation, out Matrix result)
        {
            // Equivalent to:
            //result =
            //    Matrix.Scaling(scaling)
            //    *Matrix.RotationX(rotation.X)
            //    *Matrix.RotationY(rotation.Y)
            //    *Matrix.RotationZ(rotation.Z)
            //    *Matrix.Position(translation);

            // Rotation
            float xx = rotation.X * rotation.X;
            float yy = rotation.Y * rotation.Y;
            float zz = rotation.Z * rotation.Z;
            float xy = rotation.X * rotation.Y;
            float zw = rotation.Z * rotation.W;
            float zx = rotation.Z * rotation.X;
            float yw = rotation.Y * rotation.W;
            float yz = rotation.Y * rotation.Z;
            float xw = rotation.X * rotation.W;
            result.M11 = 1.0f - 2.0f * (yy + zz);
            result.M12 = 2.0f * (xy + zw);
            result.M13 = 2.0f * (zx - yw);
            result.M21 = 2.0f * (xy - zw);
            result.M22 = 1.0f - 2.0f * (zz + xx);
            result.M23 = 2.0f * (yz + xw);
            result.M31 = 2.0f * (zx + yw);
            result.M32 = 2.0f * (yz - xw);
            result.M33 = 1.0f - 2.0f * (yy + xx);

            // Position
            result.M41 = translation.X;
            result.M42 = translation.Y;
            result.M43 = translation.Z;

            // Scale
            result.M11 *= scaling.X;
            result.M12 *= scaling.X;
            result.M13 *= scaling.X;
            result.M21 *= scaling.Y;
            result.M22 *= scaling.Y;
            result.M23 *= scaling.Y;
            result.M31 *= scaling.Z;
            result.M32 *= scaling.Z;
            result.M33 *= scaling.Z;

            result.M14 = 0.0f;
            result.M24 = 0.0f;
            result.M34 = 0.0f;
            result.M44 = 1.0f;
        }

        /// <summary>
        /// Creates a transformation matrix.
        /// </summary>
        /// <param name="scalingCenter">Center point of the scaling operation.</param>
        /// <param name="scalingRotation">Scaling rotation amount.</param>
        /// <param name="scaling">Scaling factor.</param>
        /// <param name="rotationCenter">The center of the rotation.</param>
        /// <param name="rotation">The rotation of the transformation.</param>
        /// <param name="translation">The translation factor of the transformation.</param>
        /// <param name="result">When the method completes, contains the created transformation matrix.</param>
        public static void Transformation(ref Float3 scalingCenter, ref Quaternion scalingRotation, ref Float3 scaling, ref Float3 rotationCenter, ref Quaternion rotation, ref Float3 translation, out Matrix result)
        {
            Matrix sr = RotationQuaternion(scalingRotation);
            result = Translation(-scalingCenter) * Transpose(sr) * Scaling(scaling) * sr * Translation(scalingCenter) * Translation(-rotationCenter) * RotationQuaternion(rotation) * Translation(rotationCenter) * Translation(translation);
        }

        /// <summary>
        /// Creates a transformation matrix.
        /// </summary>
        /// <param name="scalingCenter">Center point of the scaling operation.</param>
        /// <param name="scalingRotation">Scaling rotation amount.</param>
        /// <param name="scaling">Scaling factor.</param>
        /// <param name="rotationCenter">The center of the rotation.</param>
        /// <param name="rotation">The rotation of the transformation.</param>
        /// <param name="translation">The translation factor of the transformation.</param>
        /// <returns>The created transformation matrix.</returns>
        public static Matrix Transformation(Float3 scalingCenter, Quaternion scalingRotation, Float3 scaling, Float3 rotationCenter, Quaternion rotation, Float3 translation)
        {
            Transformation(ref scalingCenter, ref scalingRotation, ref scaling, ref rotationCenter, ref rotation, ref translation, out var result);
            return result;
        }

        /// <summary>
        /// Creates a 2D transformation matrix.
        /// </summary>
        /// <param name="scalingCenter">Center point of the scaling operation.</param>
        /// <param name="scalingRotation">Scaling rotation amount.</param>
        /// <param name="scaling">Scaling factor.</param>
        /// <param name="rotationCenter">The center of the rotation.</param>
        /// <param name="rotation">The rotation of the transformation.</param>
        /// <param name="translation">The translation factor of the transformation.</param>
        /// <param name="result">When the method completes, contains the created transformation matrix.</param>
        public static void Transformation2D(ref Float2 scalingCenter, float scalingRotation, ref Float2 scaling, ref Float2 rotationCenter, float rotation, ref Float2 translation, out Matrix result)
        {
            result = Translation((Float3)(-scalingCenter)) * RotationZ(-scalingRotation) * Scaling((Float3)scaling) * RotationZ(scalingRotation) * Translation((Float3)scalingCenter) * Translation((Float3)(-rotationCenter)) * RotationZ(rotation) * Translation((Float3)rotationCenter) * Translation((Float3)translation);
            result.M33 = 1f;
            result.M44 = 1f;
        }

        /// <summary>
        /// Creates a 2D transformation matrix.
        /// </summary>
        /// <param name="scalingCenter">Center point of the scaling operation.</param>
        /// <param name="scalingRotation">Scaling rotation amount.</param>
        /// <param name="scaling">Scaling factor.</param>
        /// <param name="rotationCenter">The center of the rotation.</param>
        /// <param name="rotation">The rotation of the transformation.</param>
        /// <param name="translation">The translation factor of the transformation.</param>
        /// <returns>The created transformation matrix.</returns>
        public static Matrix Transformation2D(Float2 scalingCenter, float scalingRotation, Float2 scaling, Float2 rotationCenter, float rotation, Float2 translation)
        {
            Transformation2D(ref scalingCenter, scalingRotation, ref scaling, ref rotationCenter, rotation, ref translation, out var result);
            return result;
        }

        /// <summary>
        /// Creates the world matrix from the specified parameters
        /// </summary>
        /// <param name="position">The position of the object. This value is used in translation operations.</param>
        /// <param name="forward">The forward direction of the object.</param>
        /// <param name="up">The upward direction of the object; usually [0, 1, 0].</param>
        /// <returns>The created world matrix of given transformation world</returns>
        public static Matrix CreateWorld(Float3 position, Float3 forward, Float3 up)
        {
            CreateWorld(ref position, ref forward, ref up, out var result);
            return result;
        }

        /// <summary>
        /// Creates the world matrix from the specified parameters
        /// </summary>
        /// <param name="position">The position of the object. This value is used in translation operations.</param>
        /// <param name="forward">The forward direction of the object.</param>
        /// <param name="up">The upward direction of the object; usually [0, 1, 0].</param>
        /// <param name="result">>When the method completes, contains the created world matrix of given transformation world.</param>
        public static void CreateWorld(ref Float3 position, ref Float3 forward, ref Float3 up, out Matrix result)
        {
            Float3.Normalize(ref forward, out var vector3);
            vector3 = vector3.Negative;
            Float3 vector31 = Float3.Cross(up, vector3);
            vector31.Normalize();
            Float3.Cross(ref vector3, ref vector31, out var vector32);
            result = new Matrix
            (
             vector31.X,
             vector31.Y,
             vector31.Z,
             0.0f,
             vector32.X,
             vector32.Y,
             vector32.Z,
             0.0f,
             vector3.X,
             vector3.Y,
             vector3.Z,
             0.0f,
             position.X,
             position.Y,
             position.Z,
             1.0f
            );
        }

        /// <summary>
        /// Creates a new matrix that rotates around an arbitrary vector.
        /// </summary>
        /// <param name="axis">The axis to rotate around.</param>
        /// <param name="angle">The angle to rotate around the vector.</param>
        /// <returns>The created rotation matrix.</returns>
        public static Matrix CreateFromAxisAngle(Float3 axis, float angle)
        {
            CreateFromAxisAngle(ref axis, angle, out var result);
            return result;
        }

        /// <summary>
        /// Creates a new matrix that rotates around an arbitrary vector.
        /// </summary>
        /// <param name="axis">The axis to rotate around.</param>
        /// <param name="angle">The angle to rotate around the vector.</param>
        /// <param name="result">When the method completes, contains the created rotation matrix.</param>
        public static void CreateFromAxisAngle(ref Float3 axis, float angle, out Matrix result)
        {
            float x = axis.X;
            float y = axis.Y;
            float z = axis.Z;
            float single = Mathf.Sin(angle);
            float single1 = Mathf.Cos(angle);
            float single2 = x * x;
            float single3 = y * y;
            float single4 = z * z;
            float single5 = x * y;
            float single6 = x * z;
            float single7 = y * z;
            result = new Matrix
            (
             single2 + single1 * (1.0f - single2),
             single5 - single1 * single5 + single * z,
             single6 - single1 * single6 - single * y,
             0.0f,
             single5 - single1 * single5 - single * z,
             single3 + single1 * (1.0f - single3),
             single7 - single1 * single7 + single * x,
             0.0f,
             single6 - single1 * single6 + single * y,
             single7 - single1 * single7 - single * x,
             single4 + single1 * (1.0f - single4),
             0.0f,
             0.0f,
             0.0f,
             0.0f,
             1.0f
            );
        }

        /// <summary>
        /// Adds two matrices.
        /// </summary>
        /// <param name="left">The first matrix to add.</param>
        /// <param name="right">The second matrix to add.</param>
        /// <returns>The sum of the two matrices.</returns>
        public static Matrix operator +(Matrix left, Matrix right)
        {
            Add(ref left, ref right, out var result);
            return result;
        }

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

        /// <summary>
        /// Subtracts two matrices.
        /// </summary>
        /// <param name="left">The first matrix to subtract.</param>
        /// <param name="right">The second matrix to subtract.</param>
        /// <returns>The difference between the two matrices.</returns>
        public static Matrix operator -(Matrix left, Matrix right)
        {
            Subtract(ref left, ref right, out var result);
            return result;
        }

        /// <summary>
        /// Negates a matrix.
        /// </summary>
        /// <param name="value">The matrix to negate.</param>
        /// <returns>The negated matrix.</returns>
        public static Matrix operator -(Matrix value)
        {
            Negate(ref value, out var result);
            return result;
        }

        /// <summary>
        /// Scales a matrix by a given value.
        /// </summary>
        /// <param name="right">The matrix to scale.</param>
        /// <param name="left">The amount by which to scale.</param>
        /// <returns>The scaled matrix.</returns>
        public static Matrix operator *(float left, Matrix right)
        {
            Multiply(ref right, left, out var result);
            return result;
        }

        /// <summary>
        /// Scales a matrix by a given value.
        /// </summary>
        /// <param name="left">The matrix to scale.</param>
        /// <param name="right">The amount by which to scale.</param>
        /// <returns>The scaled matrix.</returns>
        public static Matrix operator *(Matrix left, float right)
        {
            Multiply(ref left, right, out var result);
            return result;
        }

        /// <summary>
        /// Multiplies two matrices.
        /// </summary>
        /// <param name="left">The first matrix to multiply.</param>
        /// <param name="right">The second matrix to multiply.</param>
        /// <returns>The product of the two matrices.</returns>
        public static Matrix operator *(Matrix left, Matrix right)
        {
            Multiply(ref left, ref right, out var result);
            return result;
        }

        /// <summary>
        /// Scales a matrix by a given value.
        /// </summary>
        /// <param name="left">The matrix to scale.</param>
        /// <param name="right">The amount by which to scale.</param>
        /// <returns>The scaled matrix.</returns>
        public static Matrix operator /(Matrix left, float right)
        {
            Divide(ref left, right, out var result);
            return result;
        }

        /// <summary>
        /// Divides two matrices.
        /// </summary>
        /// <param name="left">The first matrix to divide.</param>
        /// <param name="right">The second matrix to divide.</param>
        /// <returns>The quotient of the two matrices.</returns>
        public static Matrix operator /(Matrix left, Matrix right)
        {
            Divide(ref left, ref right, out var result);
            return result;
        }

        /// <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 ==(Matrix left, Matrix 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 !=(Matrix left, Matrix right)
        {
            return !left.Equals(ref right);
        }

        /// <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, "[M11:{0} M12:{1} M13:{2} M14:{3}] [M21:{4} M22:{5} M23:{6} M24:{7}] [M31:{8} M32:{9} M33:{10} M34:{11}] [M41:{12} M42:{13} M43:{14} M44:{15}]",
                                 M11, M12, M13, M14, M21, M22, M23, M24, M31, M32, M33, M34, M41, M42, M43, M44);
        }

        /// <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(format, CultureInfo.CurrentCulture, "[M11:{0} M12:{1} M13:{2} M14:{3}] [M21:{4} M22:{5} M23:{6} M24:{7}] [M31:{8} M32:{9} M33:{10} M34:{11}] [M41:{12} M42:{13} M43:{14} M44:{15}]",
                                 M11.ToString(format, CultureInfo.CurrentCulture), M12.ToString(format, CultureInfo.CurrentCulture), M13.ToString(format, CultureInfo.CurrentCulture), M14.ToString(format, CultureInfo.CurrentCulture),
                                 M21.ToString(format, CultureInfo.CurrentCulture), M22.ToString(format, CultureInfo.CurrentCulture), M23.ToString(format, CultureInfo.CurrentCulture), M24.ToString(format, CultureInfo.CurrentCulture),
                                 M31.ToString(format, CultureInfo.CurrentCulture), M32.ToString(format, CultureInfo.CurrentCulture), M33.ToString(format, CultureInfo.CurrentCulture), M34.ToString(format, CultureInfo.CurrentCulture),
                                 M41.ToString(format, CultureInfo.CurrentCulture), M42.ToString(format, CultureInfo.CurrentCulture), M43.ToString(format, CultureInfo.CurrentCulture), M44.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, "[M11:{0} M12:{1} M13:{2} M14:{3}] [M21:{4} M22:{5} M23:{6} M24:{7}] [M31:{8} M32:{9} M33:{10} M34:{11}] [M41:{12} M42:{13} M43:{14} M44:{15}]",
                                 M11.ToString(formatProvider), M12.ToString(formatProvider), M13.ToString(formatProvider), M14.ToString(formatProvider),
                                 M21.ToString(formatProvider), M22.ToString(formatProvider), M23.ToString(formatProvider), M24.ToString(formatProvider),
                                 M31.ToString(formatProvider), M32.ToString(formatProvider), M33.ToString(formatProvider), M34.ToString(formatProvider),
                                 M41.ToString(formatProvider), M42.ToString(formatProvider), M43.ToString(formatProvider), M44.ToString(formatProvider));
        }

        /// <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(format, formatProvider, "[M11:{0} M12:{1} M13:{2} M14:{3}] [M21:{4} M22:{5} M23:{6} M24:{7}] [M31:{8} M32:{9} M33:{10} M34:{11}] [M41:{12} M42:{13} M43:{14} M44:{15}]",
                                 M11.ToString(format, formatProvider), M12.ToString(format, formatProvider), M13.ToString(format, formatProvider), M14.ToString(format, formatProvider),
                                 M21.ToString(format, formatProvider), M22.ToString(format, formatProvider), M23.ToString(format, formatProvider), M24.ToString(format, formatProvider),
                                 M31.ToString(format, formatProvider), M32.ToString(format, formatProvider), M33.ToString(format, formatProvider), M34.ToString(format, formatProvider),
                                 M41.ToString(format, formatProvider), M42.ToString(format, formatProvider), M43.ToString(format, formatProvider), M44.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
            {
                int hashCode = M11.GetHashCode();
                hashCode = (hashCode * 397) ^ M12.GetHashCode();
                hashCode = (hashCode * 397) ^ M13.GetHashCode();
                hashCode = (hashCode * 397) ^ M14.GetHashCode();
                hashCode = (hashCode * 397) ^ M21.GetHashCode();
                hashCode = (hashCode * 397) ^ M22.GetHashCode();
                hashCode = (hashCode * 397) ^ M23.GetHashCode();
                hashCode = (hashCode * 397) ^ M24.GetHashCode();
                hashCode = (hashCode * 397) ^ M31.GetHashCode();
                hashCode = (hashCode * 397) ^ M32.GetHashCode();
                hashCode = (hashCode * 397) ^ M33.GetHashCode();
                hashCode = (hashCode * 397) ^ M34.GetHashCode();
                hashCode = (hashCode * 397) ^ M41.GetHashCode();
                hashCode = (hashCode * 397) ^ M42.GetHashCode();
                hashCode = (hashCode * 397) ^ M43.GetHashCode();
                hashCode = (hashCode * 397) ^ M44.GetHashCode();
                return hashCode;
            }
        }

        /// <summary>
        /// Determines whether the specified <see cref="Matrix" /> is equal to this instance.
        /// </summary>
        /// <param name="other">The <see cref="Matrix" /> to compare with this instance.</param>
        /// <returns><c>true</c> if the specified <see cref="Matrix" /> is equal to this instance; otherwise, <c>false</c>.</returns>
        public bool Equals(ref Matrix other)
        {
            return Mathf.NearEqual(other.M11, M11) &&
                   Mathf.NearEqual(other.M12, M12) &&
                   Mathf.NearEqual(other.M13, M13) &&
                   Mathf.NearEqual(other.M14, M14) &&
                   Mathf.NearEqual(other.M21, M21) &&
                   Mathf.NearEqual(other.M22, M22) &&
                   Mathf.NearEqual(other.M23, M23) &&
                   Mathf.NearEqual(other.M24, M24) &&
                   Mathf.NearEqual(other.M31, M31) &&
                   Mathf.NearEqual(other.M32, M32) &&
                   Mathf.NearEqual(other.M33, M33) &&
                   Mathf.NearEqual(other.M34, M34) &&
                   Mathf.NearEqual(other.M41, M41) &&
                   Mathf.NearEqual(other.M42, M42) &&
                   Mathf.NearEqual(other.M43, M43) &&
                   Mathf.NearEqual(other.M44, M44);
        }

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