Matrix Struct

Namespace: Stride.Core.Mathematics
Assembly: Stride.Core.Mathematics.dll

Represents a 4x4 mathematical matrix.

[DataContract("float4x4")]
[DataStyle(DataStyle.Compact)]
public struct Matrix : IEquatable<Matrix>, IFormattable

Name		Description
Constructors
	Matrix(Single)	Initializes a new instance of the Matrix struct.
	Matrix(Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single)	Initializes a new instance of the Matrix struct.
	Matrix(Single[])	Initializes a new instance of the Matrix struct.
Fields
	Identity	The identity Matrix.
	M11	Value at row 1 column 1 of the matrix.
	M12	Value at row 1 column 2 of the matrix.
	M13	Value at row 1 column 3 of the matrix.
	M14	Value at row 1 column 4 of the matrix.
	M21	Value at row 2 column 1 of the matrix.
	M22	Value at row 2 column 2 of the matrix.
	M23	Value at row 2 column 3 of the matrix.
	M24	Value at row 2 column 4 of the matrix.
	M31	Value at row 3 column 1 of the matrix.
	M32	Value at row 3 column 2 of the matrix.
	M33	Value at row 3 column 3 of the matrix.
	M34	Value at row 3 column 4 of the matrix.
	M41	Value at row 4 column 1 of the matrix.
	M42	Value at row 4 column 2 of the matrix.
	M43	Value at row 4 column 3 of the matrix.
	M44	Value at row 4 column 4 of the matrix.
	SizeInBytes	The size of the Matrix type, in bytes.
	Zero	A Matrix with all of its components set to zero.
Properties
	Backward	Gets or sets the backward Vector3 of the matrix; that is M31, M32, and M33.
	Column1	Gets or sets the first column in the matrix; that is M11, M21, M31, and M41.
	Column2	Gets or sets the second column in the matrix; that is M12, M22, M32, and M42.
	Column3	Gets or sets the third column in the matrix; that is M13, M23, M33, and M43.
	Column4	Gets or sets the fourth column in the matrix; that is M14, M24, M34, and M44.
	Down	Gets or sets the down Vector3 of the matrix; that is -M21, -M22, and -M23.
	Forward	Gets or sets the forward Vector3 of the matrix; that is -M31, -M32, and -M33.
	IsIdentity	Gets a value indicating whether this instance is an identity matrix.
	Item[Int32]	Gets or sets the component at the specified index.
	Item[Int32, Int32]	Gets or sets the component at the specified index.
	Left	Gets or sets the left Vector3 of the matrix; that is -M11, -M12, and -M13.
	Right	Gets or sets the right Vector3 of the matrix; that is M11, M12, and M13.
	Row1	Gets or sets the first row in the matrix; that is M11, M12, M13, and M14.
	Row2	Gets or sets the second row in the matrix; that is M21, M22, M23, and M24.
	Row3	Gets or sets the third row in the matrix; that is M31, M32, M33, and M34.
	Row4	Gets or sets the fourth row in the matrix; that is M41, M42, M43, and M44.
	ScaleVector	Gets or sets the scale of the matrix; that is M11, M22, and M33.
	TranslationVector	Gets or sets the translation of the matrix; that is M41, M42, and M43.
	Up	Gets or sets the up Vector3 of the matrix; that is M21, M22, and M23.
Methods
	Add(Matrix, Matrix)	Determines the sum of two matrices.
	Add(ref Matrix, ref Matrix, out Matrix)	Determines the sum of two matrices.
	AffineTransformation(Single, Quaternion, Vector3)	Creates a 3D affine transformation matrix.
	AffineTransformation(Single, ref Quaternion, ref Vector3, out Matrix)	Creates a 3D affine transformation matrix.
	AffineTransformation(Single, Vector3, Quaternion, Vector3)	Creates a 3D affine transformation matrix.
	AffineTransformation(Single, ref Vector3, ref Quaternion, ref Vector3, out Matrix)	Creates a 3D affine transformation matrix.
	AffineTransformation2D(Single, Vector2, Single, Vector2)	Creates a 2D affine transformation matrix.
	AffineTransformation2D(Single, ref Vector2, Single, ref Vector2, out Matrix)	Creates a 2D affine transformation matrix.
	AffineTransformation2D(Single, Single, Vector2)	Creates a 2D affine transformation matrix.
	AffineTransformation2D(Single, Single, ref Vector2, out Matrix)	Creates a 2D affine transformation matrix.
	Billboard(Vector3, Vector3, Vector3, Vector3)	Creates a spherical billboard that rotates around a specified object position.
	Billboard(ref Vector3, ref Vector3, ref Vector3, ref Vector3, out Matrix)	Creates a spherical billboard that rotates around a specified object position.
	CopyMatrixFrom(Single*, Int32, Int32)	Copies a nxm matrix to this instance.
	Decompose(out Vector3, out Matrix, out Vector3)	Decomposes a matrix into a scale, rotation, and translation.
	Decompose(out Vector3, out Quaternion, out Vector3)	Decomposes a matrix into a scale, rotation, and translation.
	Decompose(out Vector3, out Vector3)	Decomposes a matrix into a scale, rotation, and translation.
	Decompose(out Single, out Single, out Single)	Decomposes a rotation matrix with the specified yaw, pitch, roll
	DecomposeLQ(out Matrix, out Matrix)	Decomposes a matrix into a lower triangular matrix L and an orthonormalized matrix Q.
	DecomposeQR(out Matrix, out Matrix)	Decomposes a matrix into an orthonormalized matrix Q and a right traingular matrix R.
	DecomposeXYZ(out Vector3)	Decomposes a rotation matrix with the specified X, Y and Z euler angles. Matrix.RotationX(rotation.X) * Matrix.RotationY(rotation.Y) * Matrix.RotationZ(rotation.Z) should represent the same rotation.
	Determinant()	Calculates the determinant of the matrix.
	Divide(Matrix, Matrix)	Determines the quotient of two matrices.
	Divide(Matrix, Single)	Scales a matrix by the given value.
	Divide(ref Matrix, ref Matrix, out Matrix)	Determines the quotient of two matrices.
	Divide(ref Matrix, Single, out Matrix)	Scales a matrix by the given value.
	Equals(Matrix)	Determines whether the specified Matrix is equal to this instance.
	Equals(Object)	Determines whether the specified System.Object is equal to this instance.
	ExchangeColumns(Int32, Int32)	Exchange columns.
	ExchangeRows(Int32, Int32)	Exchanges two rows in the matrix.
	Exponent(Matrix, Int32)	Performs the exponential operation on a matrix.
	Exponent(ref Matrix, Int32, out Matrix)	Performs the exponential operation on a matrix.
	GetHashCode()	Returns a hash code for this instance.
	Invert()	Inverts the matrix.
	Invert(Matrix)	Calculates the inverse of the specified matrix.
	Invert(ref Matrix, out Matrix)	Calculates the inverse of the specified matrix.
	Lerp(Matrix, Matrix, Single)	Performs a linear interpolation between two matrices.
	Lerp(ref Matrix, ref Matrix, Single, out Matrix)	Performs a linear interpolation between two matrices.
	LookAtLH(Vector3, Vector3, Vector3)	Creates a left-handed, look-at matrix.
	LookAtLH(ref Vector3, ref Vector3, ref Vector3, out Matrix)	Creates a left-handed, look-at matrix.
	LookAtRH(Vector3, Vector3, Vector3)	Creates a right-handed, look-at matrix.
	LookAtRH(ref Vector3, ref Vector3, ref Vector3, out Matrix)	Creates a right-handed, look-at matrix.
	LowerTriangularForm(Matrix)	Brings the matrix into lower triangular form using elementry row operations.
	LowerTriangularForm(ref Matrix, out Matrix)	Brings the matrix into lower triangular form using elementry row operations.
	Multiply(Matrix, Matrix)	Determines the product of two matrices.
	Multiply(Matrix, Single)	Scales a matrix by the given value.
	Multiply(ref Matrix, ref Matrix, out Matrix)	Determines the product of two matrices. Variables passed as `left` or `right` must not be used as the out parameter `result`, because `result` is calculated in-place.
	Multiply(ref Matrix, Single, out Matrix)	Scales a matrix by the given value.
	MultiplyRef(ref Matrix, ref Matrix, ref Matrix)	Determines the product of two matrices. Variables passed as `left` or `right` must not be used as the out parameter `result`, because `result` is calculated in-place.
	MultiplyTo(ref Matrix, ref Matrix, out Matrix)	Determines the product of two matrices. Variables passed as `left` or `right` must not be used as the out parameter `result`, because `result` is calculated in-place.
	Negate(Matrix)	Negates a matrix.
	Negate(ref Matrix, out Matrix)	Negates a matrix.
	Orthogonalize()	Orthogonalizes the specified matrix.
	Orthogonalize(Matrix)	Orthogonalizes the specified matrix.
	Orthogonalize(ref Matrix, out Matrix)	Orthogonalizes the specified matrix.
	OrthoLH(Single, Single, Single, Single)	Creates a left-handed, orthographic projection matrix.
	OrthoLH(Single, Single, Single, Single, out Matrix)	Creates a left-handed, orthographic projection matrix.
	Orthonormalize()	Orthonormalizes the specified matrix.
	Orthonormalize(Matrix)	Orthonormalizes the specified matrix.
	Orthonormalize(ref Matrix, out Matrix)	Orthonormalizes the specified matrix.
	OrthoOffCenterLH(Single, Single, Single, Single, Single, Single)	Creates a left-handed, customized orthographic projection matrix.
	OrthoOffCenterLH(Single, Single, Single, Single, Single, Single, out Matrix)	Creates a left-handed, customized orthographic projection matrix.
	OrthoOffCenterRH(Single, Single, Single, Single, Single, Single)	Creates a right-handed, customized orthographic projection matrix.
	OrthoOffCenterRH(Single, Single, Single, Single, Single, Single, out Matrix)	Creates a right-handed, customized orthographic projection matrix.
	OrthoRH(Single, Single, Single, Single)	Creates a right-handed, orthographic projection matrix.
	OrthoRH(Single, Single, Single, Single, out Matrix)	Creates a right-handed, orthographic projection matrix.
	PerspectiveFovLH(Single, Single, Single, Single)	Creates a left-handed, perspective projection matrix based on a field of view.
	PerspectiveFovLH(Single, Single, Single, Single, out Matrix)	Creates a left-handed, perspective projection matrix based on a field of view.
	PerspectiveFovRH(Single, Single, Single, Single)	Creates a right-handed, perspective projection matrix based on a field of view.
	PerspectiveFovRH(Single, Single, Single, Single, out Matrix)	Creates a right-handed, perspective projection matrix based on a field of view.
	PerspectiveLH(Single, Single, Single, Single)	Creates a left-handed, perspective projection matrix.
	PerspectiveLH(Single, Single, Single, Single, out Matrix)	Creates a left-handed, perspective projection matrix.
	PerspectiveOffCenterLH(Single, Single, Single, Single, Single, Single)	Creates a left-handed, customized perspective projection matrix.
	PerspectiveOffCenterLH(Single, Single, Single, Single, Single, Single, out Matrix)	Creates a left-handed, customized perspective projection matrix.
	PerspectiveOffCenterRH(Single, Single, Single, Single, Single, Single)	Creates a right-handed, customized perspective projection matrix.
	PerspectiveOffCenterRH(Single, Single, Single, Single, Single, Single, out Matrix)	Creates a right-handed, customized perspective projection matrix.
	PerspectiveRH(Single, Single, Single, Single)	Creates a right-handed, perspective projection matrix.
	PerspectiveRH(Single, Single, Single, Single, out Matrix)	Creates a right-handed, perspective projection matrix.
	ReducedRowEchelonForm(ref Matrix, ref Vector4, out Matrix, out Vector4)	Brings the matrix into reduced row echelon form using elementry row operations.
	Reflection(Plane)	Builds a matrix that can be used to reflect vectors about a plane.
	Reflection(ref Plane, out Matrix)	Builds a matrix that can be used to reflect vectors about a plane.
	RotationAxis(Vector3, Single)	Creates a matrix that rotates around an arbitary axis.
	RotationAxis(ref Vector3, Single, out Matrix)	Creates a matrix that rotates around an arbitary axis.
	RotationQuaternion(Quaternion)	Creates a rotation matrix from a quaternion.
	RotationQuaternion(ref Quaternion, out Matrix)	Creates a rotation matrix from a quaternion.
	RotationX(Single)	Creates a matrix that rotates around the x-axis.
	RotationX(Single, out Matrix)	Creates a matrix that rotates around the x-axis.
	RotationY(Single)	Creates a matrix that rotates around the y-axis.
	RotationY(Single, out Matrix)	Creates a matrix that rotates around the y-axis.
	RotationYawPitchRoll(Single, Single, Single)	Creates a rotation matrix with a specified yaw, pitch, and roll.
	RotationYawPitchRoll(Single, Single, Single, out Matrix)	Creates a rotation matrix with a specified yaw, pitch, and roll.
	RotationZ(Single)	Creates a matrix that rotates around the z-axis.
	RotationZ(Single, out Matrix)	Creates a matrix that rotates around the z-axis.
	RowEchelonForm(Matrix)	Brings the matrix into row echelon form using elementry row operations;
	RowEchelonForm(ref Matrix, out Matrix)	Brings the matrix into row echelon form using elementry row operations;
	Scaling(Vector3)	Creates a matrix that scales along the x-axis, y-axis, and y-axis.
	Scaling(ref Vector3, out Matrix)	Creates a matrix that scales along the x-axis, y-axis, and y-axis.
	Scaling(Single)	Creates a matrix that uniformally scales along all three axis.
	Scaling(Single, out Matrix)	Creates a matrix that uniformally scales along all three axis.
	Scaling(Single, Single, Single)	Creates a matrix that scales along the x-axis, y-axis, and y-axis.
	Scaling(Single, Single, Single, out Matrix)	Creates a matrix that scales along the x-axis, y-axis, and y-axis.
	Shadow(Vector4, Plane)	Creates a matrix that flattens geometry into a shadow.
	Shadow(ref Vector4, ref Plane, out Matrix)	Creates a matrix that flattens geometry into a shadow.
	SmoothStep(Matrix, Matrix, Single)	Performs a cubic interpolation between two matrices.
	SmoothStep(ref Matrix, ref Matrix, Single, out Matrix)	Performs a cubic interpolation between two matrices.
	Subtract(Matrix, Matrix)	Determines the difference between two matrices.
	Subtract(ref Matrix, ref Matrix, out Matrix)	Determines the difference between two matrices.
	ToArray()	Creates an array containing the elements of the matrix.
	ToString()	Returns a System.String that represents this instance.
	ToString(IFormatProvider)	Returns a System.String that represents this instance.
	ToString(String)	Returns a System.String that represents this instance.
	ToString(String, IFormatProvider)	Returns a System.String that represents this instance.
	Transformation(Vector3, Quaternion, Vector3, Vector3, Quaternion, Vector3)	Creates a transformation matrix.
	Transformation(ref Vector3, ref Quaternion, ref Vector3, out Matrix)	Creates a matrix that contains both the X, Y and Z rotation, as well as scaling and translation. Note: This function is NOT thead safe.
	Transformation(ref Vector3, ref Quaternion, ref Vector3, ref Vector3, ref Quaternion, ref Vector3, out Matrix)	Creates a transformation matrix.
	Transformation2D(Vector2, Single, Vector2, Vector2, Single, Vector2)	Creates a 2D transformation matrix.
	Transformation2D(ref Vector2, Single, ref Vector2, ref Vector2, Single, ref Vector2, out Matrix)	Creates a 2D transformation matrix.
	Translation(Vector3)	Creates a translation matrix using the specified offsets.
	Translation(ref Vector3, out Matrix)	Creates a translation matrix using the specified offsets.
	Translation(Single, Single, Single)	Creates a translation matrix using the specified offsets.
	Translation(Single, Single, Single, out Matrix)	Creates a translation matrix using the specified offsets.
	Transpose()	Transposes the matrix.
	Transpose(Matrix)	Calculates the transpose of the specified matrix.
	Transpose(ref Matrix, out Matrix)	Calculates the transpose of the specified matrix.
	TransposeMatrixFrom(Single*, Int32, Int32)	Transposes a nmx matrix to this instance.
	UpperTriangularForm(Matrix)	Brings the matrix into upper triangular form using elementry row operations.
	UpperTriangularForm(ref Matrix, out Matrix)	Brings the matrix into upper triangular form using elementry row operations.
Operators
	Addition(Matrix, Matrix)	Adds two matrices.
	Division(Matrix, Matrix)	Divides two matrices.
	Division(Matrix, Single)	Scales a matrix by a given value.
	Equality(Matrix, Matrix)	Tests for equality between two objects.
	Inequality(Matrix, Matrix)	Tests for inequality between two objects.
	Multiply(Matrix, Matrix)	Multiplies two matrices.
	Multiply(Matrix, Single)	Scales a matrix by a given value.
	Multiply(Single, Matrix)	Scales a matrix by a given value.
	Subtraction(Matrix, Matrix)	Subtracts two matrices.
	UnaryNegation(Matrix)	Negates a matrix.
	UnaryPlus(Matrix)	Assert a matrix (return it unchanged).

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Constructors

Matrix(Single)

Initializes a new instance of the Matrix struct.

public Matrix(float value)

Parameters

Type	Name	Description
System.Single	value	The value that will be assigned to all components.

Matrix(Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single)

Initializes a new instance of the Matrix struct.

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)

Parameters

Type	Name	Description
System.Single	M11	The value to assign at row 1 column 1 of the matrix.
System.Single	M12	The value to assign at row 1 column 2 of the matrix.
System.Single	M13	The value to assign at row 1 column 3 of the matrix.
System.Single	M14	The value to assign at row 1 column 4 of the matrix.
System.Single	M21	The value to assign at row 2 column 1 of the matrix.
System.Single	M22	The value to assign at row 2 column 2 of the matrix.
System.Single	M23	The value to assign at row 2 column 3 of the matrix.
System.Single	M24	The value to assign at row 2 column 4 of the matrix.
System.Single	M31	The value to assign at row 3 column 1 of the matrix.
System.Single	M32	The value to assign at row 3 column 2 of the matrix.
System.Single	M33	The value to assign at row 3 column 3 of the matrix.
System.Single	M34	The value to assign at row 3 column 4 of the matrix.
System.Single	M41	The value to assign at row 4 column 1 of the matrix.
System.Single	M42	The value to assign at row 4 column 2 of the matrix.
System.Single	M43	The value to assign at row 4 column 3 of the matrix.
System.Single	M44	The value to assign at row 4 column 4 of the matrix.

Matrix(Single[])

Initializes a new instance of the Matrix struct.

public Matrix(float[] values)

Parameters

Type	Name	Description
System.Single[]	values	The values to assign to the components of the matrix. This must be an array with sixteen elements.

Exceptions

Type	Condition
System.ArgumentNullException	Thrown when `values` is `null`.
System.ArgumentOutOfRangeException	Thrown when `values` contains more or less than sixteen elements.

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Fields

Identity

The identity Matrix.

public static readonly Matrix Identity

Field Value

Type	Description
Matrix

M11

Value at row 1 column 1 of the matrix.

public float M11

Field Value

Type	Description
System.Single

M12

Value at row 1 column 2 of the matrix.

public float M12

Field Value

Type	Description
System.Single

M13

Value at row 1 column 3 of the matrix.

public float M13

Field Value

Type	Description
System.Single

M14

Value at row 1 column 4 of the matrix.

public float M14

Field Value

Type	Description
System.Single

M21

Value at row 2 column 1 of the matrix.

public float M21

Field Value

Type	Description
System.Single

M22

Value at row 2 column 2 of the matrix.

public float M22

Field Value

Type	Description
System.Single

M23

Value at row 2 column 3 of the matrix.

public float M23

Field Value

Type	Description
System.Single

M24

Value at row 2 column 4 of the matrix.

public float M24

Field Value

Type	Description
System.Single

M31

Value at row 3 column 1 of the matrix.

public float M31

Field Value

Type	Description
System.Single

M32

Value at row 3 column 2 of the matrix.

public float M32

Field Value

Type	Description
System.Single

M33

Value at row 3 column 3 of the matrix.

public float M33

Field Value

Type	Description
System.Single

M34

Value at row 3 column 4 of the matrix.

public float M34

Field Value

Type	Description
System.Single

M41

Value at row 4 column 1 of the matrix.

public float M41

Field Value

Type	Description
System.Single

M42

Value at row 4 column 2 of the matrix.

public float M42

Field Value

Type	Description
System.Single

M43

Value at row 4 column 3 of the matrix.

public float M43

Field Value

Type	Description
System.Single

M44

Value at row 4 column 4 of the matrix.

public float M44

Field Value

Type	Description
System.Single

SizeInBytes

The size of the Matrix type, in bytes.

public static readonly int SizeInBytes

Field Value

Type	Description
System.Int32

Zero

A Matrix with all of its components set to zero.

public static readonly Matrix Zero

Field Value

Type	Description
Matrix

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Properties

Backward

Gets or sets the backward Vector3 of the matrix; that is M31, M32, and M33.

public Vector3 Backward { get; set; }

Property Value

Type	Description
Vector3

Column1

Gets or sets the first column in the matrix; that is M11, M21, M31, and M41.

public Vector4 Column1 { get; set; }

Property Value

Type	Description
Vector4

Column2

Gets or sets the second column in the matrix; that is M12, M22, M32, and M42.

public Vector4 Column2 { get; set; }

Property Value

Type	Description
Vector4

Column3

Gets or sets the third column in the matrix; that is M13, M23, M33, and M43.

public Vector4 Column3 { get; set; }

Property Value

Type	Description
Vector4

Column4

Gets or sets the fourth column in the matrix; that is M14, M24, M34, and M44.

public Vector4 Column4 { get; set; }

Property Value

Type	Description
Vector4

Down

Gets or sets the down Vector3 of the matrix; that is -M21, -M22, and -M23.

public Vector3 Down { get; set; }

Property Value

Type	Description
Vector3

Forward

Gets or sets the forward Vector3 of the matrix; that is -M31, -M32, and -M33.

public Vector3 Forward { get; set; }

Property Value

Type	Description
Vector3

IsIdentity

Gets a value indicating whether this instance is an identity matrix.

public readonly bool IsIdentity { get; }

Property Value

Type	Description
System.Boolean	`true` if this instance is an identity matrix; otherwise, `false`.

Item[Int32]

Gets or sets the component at the specified index.

public float this[int index] { get; set; }

Parameters

Type	Name	Description
System.Int32	index	The zero-based index of the component to access.

Property Value

Type	Description
System.Single	The value of the matrix component, depending on the index.

Exceptions

Type	Condition
System.ArgumentOutOfRangeException	Thrown when the `index` is out of the range [0, 15].

Item[Int32, Int32]

Gets or sets the component at the specified index.

public float this[int row, int column] { get; set; }

Parameters

Type	Name	Description
System.Int32	row	The row of the matrix to access.
System.Int32	column	The column of the matrix to access.

Property Value

Type	Description
System.Single	The value of the matrix component, depending on the index.

Exceptions

Type	Condition
System.ArgumentOutOfRangeException	Thrown when the `row` or `column`is out of the range [0, 3].

Left

Gets or sets the left Vector3 of the matrix; that is -M11, -M12, and -M13.

public Vector3 Left { get; set; }

Property Value

Type	Description
Vector3

Right

Gets or sets the right Vector3 of the matrix; that is M11, M12, and M13.

public Vector3 Right { get; set; }

Property Value

Type	Description
Vector3

Row1

Gets or sets the first row in the matrix; that is M11, M12, M13, and M14.

public Vector4 Row1 { get; set; }

Property Value

Type	Description
Vector4

Row2

Gets or sets the second row in the matrix; that is M21, M22, M23, and M24.

public Vector4 Row2 { get; set; }

Property Value

Type	Description
Vector4

Row3

Gets or sets the third row in the matrix; that is M31, M32, M33, and M34.

public Vector4 Row3 { get; set; }

Property Value

Type	Description
Vector4

Row4

Gets or sets the fourth row in the matrix; that is M41, M42, M43, and M44.

public Vector4 Row4 { get; set; }

Property Value

Type	Description
Vector4

ScaleVector

Gets or sets the scale of the matrix; that is M11, M22, and M33.

public Vector3 ScaleVector { get; set; }

Property Value

Type	Description
Vector3

Remarks

This property does not do any computation and will return a correct scale vector only if the matrix is a scale matrix.

TranslationVector

Gets or sets the translation of the matrix; that is M41, M42, and M43.

public Vector3 TranslationVector { get; set; }

Property Value

Type	Description
Vector3

Up

Gets or sets the up Vector3 of the matrix; that is M21, M22, and M23.

public Vector3 Up { get; set; }

Property Value

Type	Description
Vector3

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Methods

Add(Matrix, Matrix)

Determines the sum of two matrices.

public static Matrix Add(Matrix left, Matrix right)

Parameters

Type	Name	Description
Matrix	left	The first matrix to add.
Matrix	right	The second matrix to add.

Returns

Type	Description
Matrix	The sum of the two matrices.

Add(ref Matrix, ref Matrix, out Matrix)

Determines the sum of two matrices.

public static void Add(ref Matrix left, ref Matrix right, out Matrix result)

Parameters

Type	Name	Description
Matrix	left	The first matrix to add.
Matrix	right	The second matrix to add.
Matrix	result	When the method completes, contains the sum of the two matrices.

AffineTransformation(Single, Quaternion, Vector3)

Creates a 3D affine transformation matrix.

public static Matrix AffineTransformation(float scaling, Quaternion rotation, Vector3 translation)

Parameters

Type	Name	Description
System.Single	scaling	Scaling factor.
Quaternion	rotation	The rotation of the transformation.
Vector3	translation	The translation factor of the transformation.

Returns

Type	Description
Matrix	The created affine transformation matrix.

AffineTransformation(Single, ref Quaternion, ref Vector3, out Matrix)

Creates a 3D affine transformation matrix.

public static void AffineTransformation(float scaling, ref Quaternion rotation, ref Vector3 translation, out Matrix result)

Parameters

Type	Name	Description
System.Single	scaling	Scaling factor.
Quaternion	rotation	The rotation of the transformation.
Vector3	translation	The translation factor of the transformation.
Matrix	result	When the method completes, contains the created affine transformation matrix.

AffineTransformation(Single, Vector3, Quaternion, Vector3)

Creates a 3D affine transformation matrix.

public static Matrix AffineTransformation(float scaling, Vector3 rotationCenter, Quaternion rotation, Vector3 translation)

Parameters

Type	Name	Description
System.Single	scaling	Scaling factor.
Vector3	rotationCenter	The center of the rotation.
Quaternion	rotation	The rotation of the transformation.
Vector3	translation	The translation factor of the transformation.

Returns

Type	Description
Matrix	The created affine transformation matrix.

AffineTransformation(Single, ref Vector3, ref Quaternion, ref Vector3, out Matrix)

Creates a 3D affine transformation matrix.

public static void AffineTransformation(float scaling, ref Vector3 rotationCenter, ref Quaternion rotation, ref Vector3 translation, out Matrix result)

Parameters

Type	Name	Description
System.Single	scaling	Scaling factor.
Vector3	rotationCenter	The center of the rotation.
Quaternion	rotation	The rotation of the transformation.
Vector3	translation	The translation factor of the transformation.
Matrix	result	When the method completes, contains the created affine transformation matrix.

AffineTransformation2D(Single, Vector2, Single, Vector2)

Creates a 2D affine transformation matrix.

public static Matrix AffineTransformation2D(float scaling, Vector2 rotationCenter, float rotation, Vector2 translation)

Parameters

Type	Name	Description
System.Single	scaling	Scaling factor.
Vector2	rotationCenter	The center of the rotation.
System.Single	rotation	The rotation of the transformation.
Vector2	translation	The translation factor of the transformation.

Returns

Type	Description
Matrix	The created affine transformation matrix.

AffineTransformation2D(Single, ref Vector2, Single, ref Vector2, out Matrix)

Creates a 2D affine transformation matrix.

public static void AffineTransformation2D(float scaling, ref Vector2 rotationCenter, float rotation, ref Vector2 translation, out Matrix result)

Parameters

Type	Name	Description
System.Single	scaling	Scaling factor.
Vector2	rotationCenter	The center of the rotation.
System.Single	rotation	The rotation of the transformation.
Vector2	translation	The translation factor of the transformation.
Matrix	result	When the method completes, contains the created affine transformation matrix.

AffineTransformation2D(Single, Single, Vector2)

Creates a 2D affine transformation matrix.

public static Matrix AffineTransformation2D(float scaling, float rotation, Vector2 translation)

Parameters

Type	Name	Description
System.Single	scaling	Scaling factor.
System.Single	rotation	The rotation of the transformation.
Vector2	translation	The translation factor of the transformation.

Returns

Type	Description
Matrix	The created affine transformation matrix.

AffineTransformation2D(Single, Single, ref Vector2, out Matrix)

Creates a 2D affine transformation matrix.

public static void AffineTransformation2D(float scaling, float rotation, ref Vector2 translation, out Matrix result)

Parameters

Type	Name	Description
System.Single	scaling	Scaling factor.
System.Single	rotation	The rotation of the transformation.
Vector2	translation	The translation factor of the transformation.
Matrix	result	When the method completes, contains the created affine transformation matrix.

Billboard(Vector3, Vector3, Vector3, Vector3)

Creates a spherical billboard that rotates around a specified object position.

public static Matrix Billboard(Vector3 objectPosition, Vector3 cameraPosition, Vector3 cameraUpVector, Vector3 cameraForwardVector)

Parameters

Type	Name	Description
Vector3	objectPosition	The position of the object around which the billboard will rotate.
Vector3	cameraPosition	The position of the camera.
Vector3	cameraUpVector	The up vector of the camera.
Vector3	cameraForwardVector	The forward vector of the camera.

Returns

Type	Description
Matrix	The created billboard matrix.

Billboard(ref Vector3, ref Vector3, ref Vector3, ref Vector3, out Matrix)

Creates a spherical billboard that rotates around a specified object position.

public static void Billboard(ref Vector3 objectPosition, ref Vector3 cameraPosition, ref Vector3 cameraUpVector, ref Vector3 cameraForwardVector, out Matrix result)

Parameters

Type	Name	Description
Vector3	objectPosition	The position of the object around which the billboard will rotate.
Vector3	cameraPosition	The position of the camera.
Vector3	cameraUpVector	The up vector of the camera.
Vector3	cameraForwardVector	The forward vector of the camera.
Matrix	result	When the method completes, contains the created billboard matrix.

CopyMatrixFrom(Single*, Int32, Int32)

Copies a nxm matrix to this instance.

public void CopyMatrixFrom(float *src, int columns, int rows)

Parameters

Type	Name	Description
System.Single*	src	The source matrix.
System.Int32	columns	The number of columns.
System.Int32	rows	The number of rows.

Decompose(out Vector3, out Matrix, out Vector3)

Decomposes a matrix into a scale, rotation, and translation.

public bool Decompose(out Vector3 scale, out Matrix rotation, out Vector3 translation)

Parameters

Type	Name	Description
Vector3	scale	When the method completes, contains the scaling component of the decomposed matrix.
Matrix	rotation	When the method completes, contains the rotation component of the decomposed matrix.
Vector3	translation	When the method completes, contains the translation component of the decomposed matrix.

Returns

Type	Description
System.Boolean

Remarks

This method is designed to decompose an SRT transformation matrix only.

Decompose(out Vector3, out Quaternion, out Vector3)

Decomposes a matrix into a scale, rotation, and translation.

public bool Decompose(out Vector3 scale, out Quaternion rotation, out Vector3 translation)

Parameters

Type	Name	Description
Vector3	scale	When the method completes, contains the scaling component of the decomposed matrix.
Quaternion	rotation	When the method completes, contains the rotation component of the decomposed matrix.
Vector3	translation	When the method completes, contains the translation component of the decomposed matrix.

Returns

Type	Description
System.Boolean

Remarks

This method is designed to decompose an SRT transformation matrix only.

Decompose(out Vector3, out Vector3)

Decomposes a matrix into a scale, rotation, and translation.

public bool Decompose(out Vector3 scale, out Vector3 translation)

Parameters

Type	Name	Description
Vector3	scale	When the method completes, contains the scaling component of the decomposed matrix.
Vector3	translation	When the method completes, contains the translation component of the decomposed matrix.

Returns

Type	Description
System.Boolean	`true` if a rotation exist for this matrix, `false` otherwise.

Remarks

This method is designed to decompose an SRT transformation matrix only.

Decompose(out Single, out Single, out Single)

Decomposes a rotation matrix with the specified yaw, pitch, roll

public void Decompose(out float yaw, out float pitch, out float roll)

Parameters

Type	Name	Description
System.Single	yaw	The yaw.
System.Single	pitch	The pitch.
System.Single	roll	The roll.

DecomposeLQ(out Matrix, out Matrix)

Decomposes a matrix into a lower triangular matrix L and an orthonormalized matrix Q.

public void DecomposeLQ(out Matrix L, out Matrix Q)

Parameters

Type	Name	Description
Matrix	L	When the method completes, contains the lower triangular matrix of the decomposition.
Matrix	Q	When the method completes, contains the orthonormalized matrix of the decomposition.

DecomposeQR(out Matrix, out Matrix)

Decomposes a matrix into an orthonormalized matrix Q and a right traingular matrix R.

public void DecomposeQR(out Matrix Q, out Matrix R)

Parameters

Type	Name	Description
Matrix	Q	When the method completes, contains the orthonormalized matrix of the decomposition.
Matrix	R	When the method completes, contains the right triangular matrix of the decomposition.

DecomposeXYZ(out Vector3)

Decomposes a rotation matrix with the specified X, Y and Z euler angles. Matrix.RotationX(rotation.X) * Matrix.RotationY(rotation.Y) * Matrix.RotationZ(rotation.Z) should represent the same rotation.

public void DecomposeXYZ(out Vector3 rotation)

Parameters

Type	Name	Description
Vector3	rotation	The vector containing the 3 rotations angles to be applied in order.

Determinant()

Calculates the determinant of the matrix.

public float Determinant()

Returns

Type	Description
System.Single	The determinant of the matrix.

Divide(Matrix, Matrix)

Determines the quotient of two matrices.

public static Matrix Divide(Matrix left, Matrix right)

Parameters

Type	Name	Description
Matrix	left	The first matrix to divide.
Matrix	right	The second matrix to divide.

Returns

Type	Description
Matrix	The quotient of the two matrices.

Divide(Matrix, Single)

Scales a matrix by the given value.

public static Matrix Divide(Matrix left, float right)

Parameters

Type	Name	Description
Matrix	left	The matrix to scale.
System.Single	right	The amount by which to scale.

Returns

Type	Description
Matrix	The scaled matrix.

Divide(ref Matrix, ref Matrix, out Matrix)

Determines the quotient of two matrices.

public static void Divide(ref Matrix left, ref Matrix right, out Matrix result)

Parameters

Type	Name	Description
Matrix	left	The first matrix to divide.
Matrix	right	The second matrix to divide.
Matrix	result	When the method completes, contains the quotient of the two matrices.

Divide(ref Matrix, Single, out Matrix)

Scales a matrix by the given value.

public static void Divide(ref Matrix left, float right, out Matrix result)

Parameters

Type	Name	Description
Matrix	left	The matrix to scale.
System.Single	right	The amount by which to scale.
Matrix	result	When the method completes, contains the scaled matrix.

Equals(Matrix)

Determines whether the specified Matrix is equal to this instance.

public bool Equals(Matrix other)

Parameters

Type	Name	Description
Matrix	other	The Matrix to compare with this instance.

Returns

Type	Description
System.Boolean	`true` if the specified Matrix is equal to this instance; otherwise, `false`.

Equals(Object)

Determines whether the specified System.Object is equal to this instance.

public override bool Equals(object value)

Parameters

Type	Name	Description
System.Object	value	The System.Object to compare with this instance.

Returns

Type	Description
System.Boolean	`true` if the specified System.Object is equal to this instance; otherwise, `false`.

Overrides

System.ValueType.Equals(System.Object)

ExchangeColumns(Int32, Int32)

Exchange columns.

public void ExchangeColumns(int firstColumn, int secondColumn)

Parameters

Type	Name	Description
System.Int32	firstColumn	The first column to exchange.
System.Int32	secondColumn	The second column to exchange.

ExchangeRows(Int32, Int32)

Exchanges two rows in the matrix.

public void ExchangeRows(int firstRow, int secondRow)

Parameters

Type	Name	Description
System.Int32	firstRow	The first row to exchange. This is an index of the row starting at zero.
System.Int32	secondRow	The second row to exchange. This is an index of the row starting at zero.

Exponent(Matrix, Int32)

Performs the exponential operation on a matrix.

public static Matrix Exponent(Matrix value, int exponent)

Parameters

Type	Name	Description
Matrix	value	The matrix to perform the operation on.
System.Int32	exponent	The exponent to raise the matrix to.

Returns

Type	Description
Matrix	The exponential matrix.

Exceptions

Type	Condition
System.ArgumentOutOfRangeException	Thrown when the `exponent` is negative.

Exponent(ref Matrix, Int32, out Matrix)

Performs the exponential operation on a matrix.

public static void Exponent(ref Matrix value, int exponent, out Matrix result)

Parameters

Type	Name	Description
Matrix	value	The matrix to perform the operation on.
System.Int32	exponent	The exponent to raise the matrix to.
Matrix	result	When the method completes, contains the exponential matrix.

Exceptions

Type	Condition
System.ArgumentOutOfRangeException	Thrown when the `exponent` is negative.

GetHashCode()

Returns a hash code for this instance.

public override int GetHashCode()

Returns

Type	Description
System.Int32	A hash code for this instance, suitable for use in hashing algorithms and data structures like a hash table.

Overrides

System.ValueType.GetHashCode()

Invert()

Inverts the matrix.

public void Invert()

Invert(Matrix)

Calculates the inverse of the specified matrix.

public static Matrix Invert(Matrix value)

Parameters

Type	Name	Description
Matrix	value	The matrix whose inverse is to be calculated.

Returns

Type	Description
Matrix	The inverse of the specified matrix.

Invert(ref Matrix, out Matrix)

Calculates the inverse of the specified matrix.

public static void Invert(ref Matrix value, out Matrix result)

Parameters

Type	Name	Description
Matrix	value	The matrix whose inverse is to be calculated.
Matrix	result	When the method completes, contains the inverse of the specified matrix.

Lerp(Matrix, Matrix, Single)

Performs a linear interpolation between two matrices.

public static Matrix Lerp(Matrix start, Matrix end, float amount)

Parameters

Type	Name	Description
Matrix	start	Start matrix.
Matrix	end	End matrix.
System.Single	amount	Value between 0 and 1 indicating the weight of `end`.

Returns

Type	Description
Matrix	The linear interpolation of the two matrices.

Remarks

This method performs the linear interpolation based on the following formula.

start + (end - start) * amount

Passing amount a value of 0 will cause start to be returned; a value of 1 will cause end to be returned.

Lerp(ref Matrix, ref Matrix, Single, out Matrix)

Performs a linear interpolation between two matrices.

public static void Lerp(ref Matrix start, ref Matrix end, float amount, out Matrix result)

Parameters

Type	Name	Description
Matrix	start	Start matrix.
Matrix	end	End matrix.
System.Single	amount	Value between 0 and 1 indicating the weight of `end`.
Matrix	result	When the method completes, contains the linear interpolation of the two matrices.

Remarks

This method performs the linear interpolation based on the following formula.

start + (end - start) * amount

Passing amount a value of 0 will cause start to be returned; a value of 1 will cause end to be returned.

LookAtLH(Vector3, Vector3, Vector3)

Creates a left-handed, look-at matrix.

public static Matrix LookAtLH(Vector3 eye, Vector3 target, Vector3 up)

Parameters

Type	Name	Description
Vector3	eye	The position of the viewer's eye.
Vector3	target	The camera look-at target.
Vector3	up	The camera's up vector.

Returns

Type	Description
Matrix	The created look-at matrix.

LookAtLH(ref Vector3, ref Vector3, ref Vector3, out Matrix)

Creates a left-handed, look-at matrix.

public static void LookAtLH(ref Vector3 eye, ref Vector3 target, ref Vector3 up, out Matrix result)

Parameters

Type	Name	Description
Vector3	eye	The position of the viewer's eye.
Vector3	target	The camera look-at target.
Vector3	up	The camera's up vector.
Matrix	result	When the method completes, contains the created look-at matrix.

LookAtRH(Vector3, Vector3, Vector3)

Creates a right-handed, look-at matrix.

public static Matrix LookAtRH(Vector3 eye, Vector3 target, Vector3 up)

Parameters

Type	Name	Description
Vector3	eye	The position of the viewer's eye.
Vector3	target	The camera look-at target.
Vector3	up	The camera's up vector.

Returns

Type	Description
Matrix	The created look-at matrix.

LookAtRH(ref Vector3, ref Vector3, ref Vector3, out Matrix)

Creates a right-handed, look-at matrix.

public static void LookAtRH(ref Vector3 eye, ref Vector3 target, ref Vector3 up, out Matrix result)

Parameters

Type	Name	Description
Vector3	eye	The position of the viewer's eye.
Vector3	target	The camera look-at target.
Vector3	up	The camera's up vector.
Matrix	result	When the method completes, contains the created look-at matrix.

LowerTriangularForm(Matrix)

Brings the matrix into lower triangular form using elementry row operations.

public static Matrix LowerTriangularForm(Matrix value)

Parameters

Type	Name	Description
Matrix	value	The matrix to put into lower triangular form.

Returns

Type	Description
Matrix	The lower triangular matrix.

Remarks

If the matrix is not invertable (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.

LowerTriangularForm(ref Matrix, out Matrix)

Brings the matrix into lower triangular form using elementry row operations.

public static void LowerTriangularForm(ref Matrix value, out Matrix result)

Parameters

Type	Name	Description
Matrix	value	The matrix to put into lower triangular form.
Matrix	result	When the method completes, contains the lower triangular matrix.

Remarks

Multiply(Matrix, Matrix)

Determines the product of two matrices.

public static Matrix Multiply(Matrix left, Matrix right)

Parameters

Type	Name	Description
Matrix	left	The first matrix to multiply.
Matrix	right	The second matrix to multiply.

Returns

Type	Description
Matrix	The product of the two matrices.

Multiply(Matrix, Single)

Scales a matrix by the given value.

public static Matrix Multiply(Matrix left, float right)

Parameters

Type	Name	Description
Matrix	left	The matrix to scale.
System.Single	right	The amount by which to scale.

Returns

Type	Description
Matrix	The scaled matrix.

Multiply(ref Matrix, ref Matrix, out Matrix)

Determines the product of two matrices. Variables passed as left or right must not be used as the out parameter result, because result is calculated in-place.

public static void Multiply(ref Matrix left, ref Matrix right, out Matrix result)

Parameters

Type	Name	Description
Matrix	left	The first matrix to multiply.
Matrix	right	The second matrix to multiply.
Matrix	result	The product of the two matrices.

Multiply(ref Matrix, Single, out Matrix)

Scales a matrix by the given value.

public static void Multiply(ref Matrix left, float right, out Matrix result)

Parameters

Type	Name	Description
Matrix	left	The matrix to scale.
System.Single	right	The amount by which to scale.
Matrix	result	When the method completes, contains the scaled matrix.

MultiplyRef(ref Matrix, ref Matrix, ref Matrix)

Determines the product of two matrices. Variables passed as left or right must not be used as the out parameter result, because result is calculated in-place.

public static void MultiplyRef(ref Matrix left, ref Matrix right, ref Matrix result)

Parameters

Type	Name	Description
Matrix	left	The first matrix to multiply.
Matrix	right	The second matrix to multiply.
Matrix	result	The product of the two matrices.

MultiplyTo(ref Matrix, ref Matrix, out Matrix)

Determines the product of two matrices. Variables passed as left or right must not be used as the out parameter result, because result is calculated in-place.

public static void MultiplyTo(ref Matrix left, ref Matrix right, out Matrix result)

Parameters

Type	Name	Description
Matrix	left	The first matrix to multiply.
Matrix	right	The second matrix to multiply.
Matrix	result	The product of the two matrices.

Negate(Matrix)

Negates a matrix.

public static Matrix Negate(Matrix value)

Parameters

Type	Name	Description
Matrix	value	The matrix to be negated.

Returns

Type	Description
Matrix	The negated matrix.

Negate(ref Matrix, out Matrix)

Negates a matrix.

public static void Negate(ref Matrix value, out Matrix result)

Parameters

Type	Name	Description
Matrix	value	The matrix to be negated.
Matrix	result	When the method completes, contains the negated matrix.

Orthogonalize()

Orthogonalizes the specified matrix.

public void Orthogonalize()

Remarks

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.

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.

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.

Orthogonalize(Matrix)

Orthogonalizes the specified matrix.

public static Matrix Orthogonalize(Matrix value)

Parameters

Type	Name	Description
Matrix	value	The matrix to orthogonalize.

Returns

Type	Description
Matrix	The orthogonalized matrix.

Remarks

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.

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.

Orthogonalize(ref Matrix, out Matrix)

Orthogonalizes the specified matrix.

public static void Orthogonalize(ref Matrix value, out Matrix result)

Parameters

Type	Name	Description
Matrix	value	The matrix to orthogonalize.
Matrix	result	When the method completes, contains the orthogonalized matrix.

Remarks

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.

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.

OrthoLH(Single, Single, Single, Single)

Creates a left-handed, orthographic projection matrix.

public static Matrix OrthoLH(float width, float height, float znear, float zfar)

Parameters

Type	Name	Description
System.Single	width	Width of the viewing volume.
System.Single	height	Height of the viewing volume.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.

Returns

Type	Description
Matrix	The created projection matrix.

OrthoLH(Single, Single, Single, Single, out Matrix)

Creates a left-handed, orthographic projection matrix.

public static void OrthoLH(float width, float height, float znear, float zfar, out Matrix result)

Parameters

Type	Name	Description
System.Single	width	Width of the viewing volume.
System.Single	height	Height of the viewing volume.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.
Matrix	result	When the method completes, contains the created projection matrix.

Orthonormalize()

Orthonormalizes the specified matrix.

public void Orthonormalize()

Remarks

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.

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.

Orthonormalize(Matrix)

Orthonormalizes the specified matrix.

public static Matrix Orthonormalize(Matrix value)

Parameters

Type	Name	Description
Matrix	value	The matrix to orthonormalize.

Returns

Type	Description
Matrix	The orthonormalized matrix.

Remarks

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.

Orthonormalize(ref Matrix, out Matrix)

Orthonormalizes the specified matrix.

public static void Orthonormalize(ref Matrix value, out Matrix result)

Parameters

Type	Name	Description
Matrix	value	The matrix to orthonormalize.
Matrix	result	When the method completes, contains the orthonormalized matrix.

Remarks

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.

OrthoOffCenterLH(Single, Single, Single, Single, Single, Single)

Creates a left-handed, customized orthographic projection matrix.

public static Matrix OrthoOffCenterLH(float left, float right, float bottom, float top, float znear, float zfar)

Parameters

Type	Name	Description
System.Single	left	Minimum x-value of the viewing volume.
System.Single	right	Maximum x-value of the viewing volume.
System.Single	bottom	Minimum y-value of the viewing volume.
System.Single	top	Maximum y-value of the viewing volume.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.

Returns

Type	Description
Matrix	The created projection matrix.

OrthoOffCenterLH(Single, Single, Single, Single, Single, Single, out Matrix)

Creates a left-handed, customized orthographic projection matrix.

public static void OrthoOffCenterLH(float left, float right, float bottom, float top, float znear, float zfar, out Matrix result)

Parameters

Type	Name	Description
System.Single	left	Minimum x-value of the viewing volume.
System.Single	right	Maximum x-value of the viewing volume.
System.Single	bottom	Minimum y-value of the viewing volume.
System.Single	top	Maximum y-value of the viewing volume.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.
Matrix	result	When the method completes, contains the created projection matrix.

OrthoOffCenterRH(Single, Single, Single, Single, Single, Single)

Creates a right-handed, customized orthographic projection matrix.

public static Matrix OrthoOffCenterRH(float left, float right, float bottom, float top, float znear, float zfar)

Parameters

Type	Name	Description
System.Single	left	Minimum x-value of the viewing volume.
System.Single	right	Maximum x-value of the viewing volume.
System.Single	bottom	Minimum y-value of the viewing volume.
System.Single	top	Maximum y-value of the viewing volume.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.

Returns

Type	Description
Matrix	The created projection matrix.

OrthoOffCenterRH(Single, Single, Single, Single, Single, Single, out Matrix)

Creates a right-handed, customized orthographic projection matrix.

public static void OrthoOffCenterRH(float left, float right, float bottom, float top, float znear, float zfar, out Matrix result)

Parameters

Type	Name	Description
System.Single	left	Minimum x-value of the viewing volume.
System.Single	right	Maximum x-value of the viewing volume.
System.Single	bottom	Minimum y-value of the viewing volume.
System.Single	top	Maximum y-value of the viewing volume.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.
Matrix	result	When the method completes, contains the created projection matrix.

OrthoRH(Single, Single, Single, Single)

Creates a right-handed, orthographic projection matrix.

public static Matrix OrthoRH(float width, float height, float znear, float zfar)

Parameters

Type	Name	Description
System.Single	width	Width of the viewing volume.
System.Single	height	Height of the viewing volume.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.

Returns

Type	Description
Matrix	The created projection matrix.

OrthoRH(Single, Single, Single, Single, out Matrix)

Creates a right-handed, orthographic projection matrix.

public static void OrthoRH(float width, float height, float znear, float zfar, out Matrix result)

Parameters

Type	Name	Description
System.Single	width	Width of the viewing volume.
System.Single	height	Height of the viewing volume.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.
Matrix	result	When the method completes, contains the created projection matrix.

PerspectiveFovLH(Single, Single, Single, Single)

Creates a left-handed, perspective projection matrix based on a field of view.

public static Matrix PerspectiveFovLH(float fov, float aspect, float znear, float zfar)

Parameters

Type	Name	Description
System.Single	fov	Field of view in the y direction, in radians.
System.Single	aspect	Aspect ratio, defined as view space width divided by height.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.

Returns

Type	Description
Matrix	The created projection matrix.

PerspectiveFovLH(Single, Single, Single, Single, out Matrix)

Creates a left-handed, perspective projection matrix based on a field of view.

public static void PerspectiveFovLH(float fov, float aspect, float znear, float zfar, out Matrix result)

Parameters

Type	Name	Description
System.Single	fov	Field of view in the y direction, in radians.
System.Single	aspect	Aspect ratio, defined as view space width divided by height.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.
Matrix	result	When the method completes, contains the created projection matrix.

PerspectiveFovRH(Single, Single, Single, Single)

Creates a right-handed, perspective projection matrix based on a field of view.

public static Matrix PerspectiveFovRH(float fov, float aspect, float znear, float zfar)

Parameters

Type	Name	Description
System.Single	fov	Field of view in the y direction, in radians.
System.Single	aspect	Aspect ratio, defined as view space width divided by height.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.

Returns

Type	Description
Matrix	The created projection matrix.

PerspectiveFovRH(Single, Single, Single, Single, out Matrix)

Creates a right-handed, perspective projection matrix based on a field of view.

public static void PerspectiveFovRH(float fov, float aspect, float znear, float zfar, out Matrix result)

Parameters

Type	Name	Description
System.Single	fov	Field of view in the y direction, in radians.
System.Single	aspect	Aspect ratio, defined as view space width divided by height.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.
Matrix	result	When the method completes, contains the created projection matrix.

PerspectiveLH(Single, Single, Single, Single)

Creates a left-handed, perspective projection matrix.

public static Matrix PerspectiveLH(float width, float height, float znear, float zfar)

Parameters

Type	Name	Description
System.Single	width	Width of the viewing volume.
System.Single	height	Height of the viewing volume.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.

Returns

Type	Description
Matrix	The created projection matrix.

PerspectiveLH(Single, Single, Single, Single, out Matrix)

Creates a left-handed, perspective projection matrix.

public static void PerspectiveLH(float width, float height, float znear, float zfar, out Matrix result)

Parameters

Type	Name	Description
System.Single	width	Width of the viewing volume.
System.Single	height	Height of the viewing volume.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.
Matrix	result	When the method completes, contains the created projection matrix.

PerspectiveOffCenterLH(Single, Single, Single, Single, Single, Single)

Creates a left-handed, customized perspective projection matrix.

public static Matrix PerspectiveOffCenterLH(float left, float right, float bottom, float top, float znear, float zfar)

Parameters

Type	Name	Description
System.Single	left	Minimum x-value of the viewing volume.
System.Single	right	Maximum x-value of the viewing volume.
System.Single	bottom	Minimum y-value of the viewing volume.
System.Single	top	Maximum y-value of the viewing volume.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.

Returns

Type	Description
Matrix	The created projection matrix.

PerspectiveOffCenterLH(Single, Single, Single, Single, Single, Single, out Matrix)

Creates a left-handed, customized perspective projection matrix.

public static void PerspectiveOffCenterLH(float left, float right, float bottom, float top, float znear, float zfar, out Matrix result)

Parameters

Type	Name	Description
System.Single	left	Minimum x-value of the viewing volume.
System.Single	right	Maximum x-value of the viewing volume.
System.Single	bottom	Minimum y-value of the viewing volume.
System.Single	top	Maximum y-value of the viewing volume.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.
Matrix	result	When the method completes, contains the created projection matrix.

PerspectiveOffCenterRH(Single, Single, Single, Single, Single, Single)

Creates a right-handed, customized perspective projection matrix.

public static Matrix PerspectiveOffCenterRH(float left, float right, float bottom, float top, float znear, float zfar)

Parameters

Type	Name	Description
System.Single	left	Minimum x-value of the viewing volume.
System.Single	right	Maximum x-value of the viewing volume.
System.Single	bottom	Minimum y-value of the viewing volume.
System.Single	top	Maximum y-value of the viewing volume.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.

Returns

Type	Description
Matrix	The created projection matrix.

PerspectiveOffCenterRH(Single, Single, Single, Single, Single, Single, out Matrix)

Creates a right-handed, customized perspective projection matrix.

public static void PerspectiveOffCenterRH(float left, float right, float bottom, float top, float znear, float zfar, out Matrix result)

Parameters

Type	Name	Description
System.Single	left	Minimum x-value of the viewing volume.
System.Single	right	Maximum x-value of the viewing volume.
System.Single	bottom	Minimum y-value of the viewing volume.
System.Single	top	Maximum y-value of the viewing volume.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.
Matrix	result	When the method completes, contains the created projection matrix.

PerspectiveRH(Single, Single, Single, Single)

Creates a right-handed, perspective projection matrix.

public static Matrix PerspectiveRH(float width, float height, float znear, float zfar)

Parameters

Type	Name	Description
System.Single	width	Width of the viewing volume.
System.Single	height	Height of the viewing volume.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.

Returns

Type	Description
Matrix	The created projection matrix.

PerspectiveRH(Single, Single, Single, Single, out Matrix)

Creates a right-handed, perspective projection matrix.

public static void PerspectiveRH(float width, float height, float znear, float zfar, out Matrix result)

Parameters

Type	Name	Description
System.Single	width	Width of the viewing volume.
System.Single	height	Height of the viewing volume.
System.Single	znear	Minimum z-value of the viewing volume.
System.Single	zfar	Maximum z-value of the viewing volume.
Matrix	result	When the method completes, contains the created projection matrix.

ReducedRowEchelonForm(ref Matrix, ref Vector4, out Matrix, out Vector4)

Brings the matrix into reduced row echelon form using elementry row operations.

public static void ReducedRowEchelonForm(ref Matrix value, ref Vector4 augment, out Matrix result, out Vector4 augmentResult)

Parameters

Type	Name	Description
Matrix	value	The matrix to put into reduced row echelon form.
Vector4	augment	The fifth column of the matrix.
Matrix	result	When the method completes, contains the resultant matrix after the operation.
Vector4	augmentResult	When the method completes, contains the resultant fifth column of the matrix.

Remarks

The fifth column is often called the agumented 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.

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.

This method can be used to solve systems of linear equations. Upon completion of this method, the 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.

Reflection(Plane)

Builds a matrix that can be used to reflect vectors about a plane.

public static Matrix Reflection(Plane plane)

Parameters

Type	Name	Description
Plane	plane	The plane for which the reflection occurs. This parameter is assumed to be normalized.

Returns

Type	Description
Matrix	The reflection matrix.

Reflection(ref Plane, out Matrix)

Builds a matrix that can be used to reflect vectors about a plane.

public static void Reflection(ref Plane plane, out Matrix result)

Parameters

Type	Name	Description
Plane	plane	The plane for which the reflection occurs. This parameter is assumed to be normalized.
Matrix	result	When the method completes, contains the reflection matrix.

RotationAxis(Vector3, Single)

Creates a matrix that rotates around an arbitary axis.

public static Matrix RotationAxis(Vector3 axis, float angle)

Parameters

Type	Name	Description
Vector3	axis	The axis around which to rotate. This parameter is assumed to be normalized.
System.Single	angle	Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.

Returns

Type	Description
Matrix	The created rotation matrix.

RotationAxis(ref Vector3, Single, out Matrix)

Creates a matrix that rotates around an arbitary axis.

public static void RotationAxis(ref Vector3 axis, float angle, out Matrix result)

Parameters

Type	Name	Description
Vector3	axis	The axis around which to rotate. This parameter is assumed to be normalized.
System.Single	angle	Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.
Matrix	result	When the method completes, contains the created rotation matrix.

RotationQuaternion(Quaternion)

Creates a rotation matrix from a quaternion.

public static Matrix RotationQuaternion(Quaternion rotation)

Parameters

Type	Name	Description
Quaternion	rotation	The quaternion to use to build the matrix.

Returns

Type	Description
Matrix	The created rotation matrix.

RotationQuaternion(ref Quaternion, out Matrix)

Creates a rotation matrix from a quaternion.

public static void RotationQuaternion(ref Quaternion rotation, out Matrix result)

Parameters

Type	Name	Description
Quaternion	rotation	The quaternion to use to build the matrix.
Matrix	result	The created rotation matrix.

RotationX(Single)

Creates a matrix that rotates around the x-axis.

public static Matrix RotationX(float angle)

Parameters

Type	Name	Description
System.Single	angle	Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.

Returns

Type	Description
Matrix	The created rotation matrix.

RotationX(Single, out Matrix)

Creates a matrix that rotates around the x-axis.

public static void RotationX(float angle, out Matrix result)

Parameters

Type	Name	Description
System.Single	angle	Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.
Matrix	result	When the method completes, contains the created rotation matrix.

RotationY(Single)

Creates a matrix that rotates around the y-axis.

public static Matrix RotationY(float angle)

Parameters

Type	Name	Description
System.Single	angle	Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.

Returns

Type	Description
Matrix	The created rotation matrix.

RotationY(Single, out Matrix)

Creates a matrix that rotates around the y-axis.

public static void RotationY(float angle, out Matrix result)

Parameters

Type	Name	Description
System.Single	angle	Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.
Matrix	result	When the method completes, contains the created rotation matrix.

RotationYawPitchRoll(Single, Single, Single)

Creates a rotation matrix with a specified yaw, pitch, and roll.

public static Matrix RotationYawPitchRoll(float yaw, float pitch, float roll)

Parameters

Type	Name	Description
System.Single	yaw	Yaw around the y-axis, in radians.
System.Single	pitch	Pitch around the x-axis, in radians.
System.Single	roll	Roll around the z-axis, in radians.

Returns

Type	Description
Matrix	The created rotation matrix.

RotationYawPitchRoll(Single, Single, Single, out Matrix)

Creates a rotation matrix with a specified yaw, pitch, and roll.

public static void RotationYawPitchRoll(float yaw, float pitch, float roll, out Matrix result)

Parameters

Type	Name	Description
System.Single	yaw	Yaw around the y-axis, in radians.
System.Single	pitch	Pitch around the x-axis, in radians.
System.Single	roll	Roll around the z-axis, in radians.
Matrix	result	When the method completes, contains the created rotation matrix.

RotationZ(Single)

Creates a matrix that rotates around the z-axis.

public static Matrix RotationZ(float angle)

Parameters

Type	Name	Description
System.Single	angle	Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.

Returns

Type	Description
Matrix	The created rotation matrix.

RotationZ(Single, out Matrix)

Creates a matrix that rotates around the z-axis.

public static void RotationZ(float angle, out Matrix result)

Parameters

Type	Name	Description
System.Single	angle	Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.
Matrix	result	When the method completes, contains the created rotation matrix.

RowEchelonForm(Matrix)

Brings the matrix into row echelon form using elementry row operations;

public static Matrix RowEchelonForm(Matrix value)

Parameters

Type	Name	Description
Matrix	value	The matrix to put into row echelon form.

Returns

Type	Description
Matrix	When the method completes, contains the row echelon form of the matrix.

RowEchelonForm(ref Matrix, out Matrix)

Brings the matrix into row echelon form using elementry row operations;

public static void RowEchelonForm(ref Matrix value, out Matrix result)

Parameters

Type	Name	Description
Matrix	value	The matrix to put into row echelon form.
Matrix	result	When the method completes, contains the row echelon form of the matrix.

Scaling(Vector3)

Creates a matrix that scales along the x-axis, y-axis, and y-axis.

public static Matrix Scaling(Vector3 scale)

Parameters

Type	Name	Description
Vector3	scale	Scaling factor for all three axes.

Returns

Type	Description
Matrix	The created scaling matrix.

Scaling(ref Vector3, out Matrix)

Creates a matrix that scales along the x-axis, y-axis, and y-axis.

public static void Scaling(ref Vector3 scale, out Matrix result)

Parameters

Type	Name	Description
Vector3	scale	Scaling factor for all three axes.
Matrix	result	When the method completes, contains the created scaling matrix.

Scaling(Single)

Creates a matrix that uniformally scales along all three axis.

public static Matrix Scaling(float scale)

Parameters

Type	Name	Description
System.Single	scale	The uniform scale that is applied along all axis.

Returns

Type	Description
Matrix	The created scaling matrix.

Scaling(Single, out Matrix)

Creates a matrix that uniformally scales along all three axis.

public static void Scaling(float scale, out Matrix result)

Parameters

Type	Name	Description
System.Single	scale	The uniform scale that is applied along all axis.
Matrix	result	When the method completes, contains the created scaling matrix.

Scaling(Single, Single, Single)

Creates a matrix that scales along the x-axis, y-axis, and y-axis.

public static Matrix Scaling(float x, float y, float z)

Parameters

Type	Name	Description
System.Single	x	Scaling factor that is applied along the x-axis.
System.Single	y	Scaling factor that is applied along the y-axis.
System.Single	z	Scaling factor that is applied along the z-axis.

Returns

Type	Description
Matrix	The created scaling matrix.

Scaling(Single, Single, Single, out Matrix)

Creates a matrix that scales along the x-axis, y-axis, and y-axis.

public static void Scaling(float x, float y, float z, out Matrix result)

Parameters

Type	Name	Description
System.Single	x	Scaling factor that is applied along the x-axis.
System.Single	y	Scaling factor that is applied along the y-axis.
System.Single	z	Scaling factor that is applied along the z-axis.
Matrix	result	When the method completes, contains the created scaling matrix.

Shadow(Vector4, Plane)

Creates a matrix that flattens geometry into a shadow.

public static Matrix Shadow(Vector4 light, Plane plane)

Parameters

Type	Name	Description
Vector4	light	The light direction. If the W component is 0, the light is directional light; if the W component is 1, the light is a point light.
Plane	plane	The plane onto which to project the geometry as a shadow. This parameter is assumed to be normalized.

Returns

Type	Description
Matrix	The shadow matrix.

Shadow(ref Vector4, ref Plane, out Matrix)

Creates a matrix that flattens geometry into a shadow.

public static void Shadow(ref Vector4 light, ref Plane plane, out Matrix result)

Parameters

Type	Name	Description
Vector4	light	The light direction. If the W component is 0, the light is directional light; if the W component is 1, the light is a point light.
Plane	plane	The plane onto which to project the geometry as a shadow. This parameter is assumed to be normalized.
Matrix	result	When the method completes, contains the shadow matrix.

SmoothStep(Matrix, Matrix, Single)

Performs a cubic interpolation between two matrices.

public static Matrix SmoothStep(Matrix start, Matrix end, float amount)

Parameters

Type	Name	Description
Matrix	start	Start matrix.
Matrix	end	End matrix.
System.Single	amount	Value between 0 and 1 indicating the weight of `end`.

Returns

Type	Description
Matrix	The cubic interpolation of the two matrices.

SmoothStep(ref Matrix, ref Matrix, Single, out Matrix)

Performs a cubic interpolation between two matrices.

public static void SmoothStep(ref Matrix start, ref Matrix end, float amount, out Matrix result)

Parameters

Type	Name	Description
Matrix	start	Start matrix.
Matrix	end	End matrix.
System.Single	amount	Value between 0 and 1 indicating the weight of `end`.
Matrix	result	When the method completes, contains the cubic interpolation of the two matrices.

Subtract(Matrix, Matrix)

Determines the difference between two matrices.

public static Matrix Subtract(Matrix left, Matrix right)

Parameters

Type	Name	Description
Matrix	left	The first matrix to subtract.
Matrix	right	The second matrix to subtract.

Returns

Type	Description
Matrix	The difference between the two matrices.

Subtract(ref Matrix, ref Matrix, out Matrix)

Determines the difference between two matrices.

public static void Subtract(ref Matrix left, ref Matrix right, out Matrix result)

Parameters

Type	Name	Description
Matrix	left	The first matrix to subtract.
Matrix	right	The second matrix to subtract.
Matrix	result	When the method completes, contains the difference between the two matrices.

ToArray()

Creates an array containing the elements of the matrix.

public float[] ToArray()

Returns

Type	Description
System.Single[]	A sixteen-element array containing the components of the matrix.

ToString()

Returns a System.String that represents this instance.

public override string ToString()

Returns

Type	Description
System.String	A System.String that represents this instance.

Overrides

System.ValueType.ToString()

ToString(IFormatProvider)

Returns a System.String that represents this instance.

public string ToString(IFormatProvider formatProvider)

Parameters

Type	Name	Description
System.IFormatProvider	formatProvider	The format provider.

Returns

Type	Description
System.String	A System.String that represents this instance.

ToString(String)

Returns a System.String that represents this instance.

public string ToString(string format)

Parameters

Type	Name	Description
System.String	format	The format.

Returns

Type	Description
System.String	A System.String that represents this instance.

ToString(String, IFormatProvider)

Returns a System.String that represents this instance.

public string ToString(string format, IFormatProvider formatProvider)

Parameters

Type	Name	Description
System.String	format	The format.
System.IFormatProvider	formatProvider	The format provider.

Returns

Type	Description
System.String	A System.String that represents this instance.

Transformation(Vector3, Quaternion, Vector3, Vector3, Quaternion, Vector3)

Creates a transformation matrix.

public static Matrix Transformation(Vector3 scalingCenter, Quaternion scalingRotation, Vector3 scaling, Vector3 rotationCenter, Quaternion rotation, Vector3 translation)

Parameters

Type	Name	Description
Vector3	scalingCenter	Center point of the scaling operation.
Quaternion	scalingRotation	Scaling rotation amount.
Vector3	scaling	Scaling factor.
Vector3	rotationCenter	The center of the rotation.
Quaternion	rotation	The rotation of the transformation.
Vector3	translation	The translation factor of the transformation.

Returns

Type	Description
Matrix	The created transformation matrix.

Transformation(ref Vector3, ref Quaternion, ref Vector3, out Matrix)

Creates a matrix that contains both the X, Y and Z rotation, as well as scaling and translation. Note: This function is NOT thead safe.

public static void Transformation(ref Vector3 scaling, ref Quaternion rotation, ref Vector3 translation, out Matrix result)

Parameters

Type	Name	Description
Vector3	scaling	The scaling.
Quaternion	rotation	Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.
Vector3	translation	The translation.
Matrix	result	When the method completes, contains the created rotation matrix.

Transformation(ref Vector3, ref Quaternion, ref Vector3, ref Vector3, ref Quaternion, ref Vector3, out Matrix)

Creates a transformation matrix.

public static void Transformation(ref Vector3 scalingCenter, ref Quaternion scalingRotation, ref Vector3 scaling, ref Vector3 rotationCenter, ref Quaternion rotation, ref Vector3 translation, out Matrix result)

Parameters

Type	Name	Description
Vector3	scalingCenter	Center point of the scaling operation.
Quaternion	scalingRotation	Scaling rotation amount.
Vector3	scaling	Scaling factor.
Vector3	rotationCenter	The center of the rotation.
Quaternion	rotation	The rotation of the transformation.
Vector3	translation	The translation factor of the transformation.
Matrix	result	When the method completes, contains the created transformation matrix.

Transformation2D(Vector2, Single, Vector2, Vector2, Single, Vector2)

Creates a 2D transformation matrix.

public static Matrix Transformation2D(Vector2 scalingCenter, float scalingRotation, Vector2 scaling, Vector2 rotationCenter, float rotation, Vector2 translation)

Parameters

Type	Name	Description
Vector2	scalingCenter	Center point of the scaling operation.
System.Single	scalingRotation	Scaling rotation amount.
Vector2	scaling	Scaling factor.
Vector2	rotationCenter	The center of the rotation.
System.Single	rotation	The rotation of the transformation.
Vector2	translation	The translation factor of the transformation.

Returns

Type	Description
Matrix	The created transformation matrix.

Transformation2D(ref Vector2, Single, ref Vector2, ref Vector2, Single, ref Vector2, out Matrix)

Creates a 2D transformation matrix.

public static void Transformation2D(ref Vector2 scalingCenter, float scalingRotation, ref Vector2 scaling, ref Vector2 rotationCenter, float rotation, ref Vector2 translation, out Matrix result)

Parameters

Type	Name	Description
Vector2	scalingCenter	Center point of the scaling operation.
System.Single	scalingRotation	Scaling rotation amount.
Vector2	scaling	Scaling factor.
Vector2	rotationCenter	The center of the rotation.
System.Single	rotation	The rotation of the transformation.
Vector2	translation	The translation factor of the transformation.
Matrix	result	When the method completes, contains the created transformation matrix.

Translation(Vector3)

Creates a translation matrix using the specified offsets.

public static Matrix Translation(Vector3 value)

Parameters

Type	Name	Description
Vector3	value	The offset for all three coordinate planes.

Returns

Type	Description
Matrix	The created translation matrix.

Translation(ref Vector3, out Matrix)

Creates a translation matrix using the specified offsets.

public static void Translation(ref Vector3 value, out Matrix result)

Parameters

Type	Name	Description
Vector3	value	The offset for all three coordinate planes.
Matrix	result	When the method completes, contains the created translation matrix.

Translation(Single, Single, Single)

Creates a translation matrix using the specified offsets.

public static Matrix Translation(float x, float y, float z)

Parameters

Type	Name	Description
System.Single	x	X-coordinate offset.
System.Single	y	Y-coordinate offset.
System.Single	z	Z-coordinate offset.

Returns

Type	Description
Matrix	The created translation matrix.

Translation(Single, Single, Single, out Matrix)

Creates a translation matrix using the specified offsets.

public static void Translation(float x, float y, float z, out Matrix result)

Parameters

Type	Name	Description
System.Single	x	X-coordinate offset.
System.Single	y	Y-coordinate offset.
System.Single	z	Z-coordinate offset.
Matrix	result	When the method completes, contains the created translation matrix.

Transpose()

Transposes the matrix.

public void Transpose()

Transpose(Matrix)

Calculates the transpose of the specified matrix.

public static Matrix Transpose(Matrix value)

Parameters

Type	Name	Description
Matrix	value	The matrix whose transpose is to be calculated.

Returns

Type	Description
Matrix	The transpose of the specified matrix.

Transpose(ref Matrix, out Matrix)

Calculates the transpose of the specified matrix.

public static void Transpose(ref Matrix value, out Matrix result)

Parameters

Type	Name	Description
Matrix	value	The matrix whose transpose is to be calculated.
Matrix	result	When the method completes, contains the transpose of the specified matrix.

TransposeMatrixFrom(Single*, Int32, Int32)

Transposes a nmx matrix to this instance.

public void TransposeMatrixFrom(float *src, int columns, int rows)

Parameters

Type	Name	Description
System.Single*	src	The SRC.
System.Int32	columns	The columns.
System.Int32	rows	The rows.

UpperTriangularForm(Matrix)

Brings the matrix into upper triangular form using elementry row operations.

public static Matrix UpperTriangularForm(Matrix value)

Parameters

Type	Name	Description
Matrix	value	The matrix to put into upper triangular form.

Returns

Type	Description
Matrix	The upper triangular matrix.

Remarks

UpperTriangularForm(ref Matrix, out Matrix)

Brings the matrix into upper triangular form using elementry row operations.

public static void UpperTriangularForm(ref Matrix value, out Matrix result)

Parameters

Type	Name	Description
Matrix	value	The matrix to put into upper triangular form.
Matrix	result	When the method completes, contains the upper triangular matrix.

Remarks

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Operators

Addition(Matrix, Matrix)

Adds two matrices.

public static Matrix operator +(Matrix left, Matrix right)

Parameters

Type	Name	Description
Matrix	left	The first matrix to add.
Matrix	right	The second matrix to add.

Returns

Type	Description
Matrix	The sum of the two matrices.

Division(Matrix, Matrix)

Divides two matrices.

public static Matrix operator /(Matrix left, Matrix right)

Parameters

Type	Name	Description
Matrix	left	The first matrix to divide.
Matrix	right	The second matrix to divide.

Returns

Type	Description
Matrix	The quotient of the two matrices.

Division(Matrix, Single)

Scales a matrix by a given value.

public static Matrix operator /(Matrix left, float right)

Parameters

Type	Name	Description
Matrix	left	The matrix to scale.
System.Single	right	The amount by which to scale.

Returns

Type	Description
Matrix	The scaled matrix.

Equality(Matrix, Matrix)

Tests for equality between two objects.

public static bool operator ==(Matrix left, Matrix right)

Parameters

Type	Name	Description
Matrix	left	The first value to compare.
Matrix	right	The second value to compare.

Returns

Type	Description
System.Boolean	`true` if `left` has the same value as `right`; otherwise, `false`.

Inequality(Matrix, Matrix)

Tests for inequality between two objects.

public static bool operator !=(Matrix left, Matrix right)

Parameters

Type	Name	Description
Matrix	left	The first value to compare.
Matrix	right	The second value to compare.

Returns

Type	Description
System.Boolean	`true` if `left` has a different value than `right`; otherwise, `false`.

Multiply(Matrix, Matrix)

Multiplies two matrices.

public static Matrix operator *(Matrix left, Matrix right)

Parameters

Type	Name	Description
Matrix	left	The first matrix to multiply.
Matrix	right	The second matrix to multiply.

Returns

Type	Description
Matrix	The product of the two matrices.

Multiply(Matrix, Single)

Scales a matrix by a given value.

public static Matrix operator *(Matrix left, float right)

Parameters

Type	Name	Description
Matrix	left	The matrix to scale.
System.Single	right	The amount by which to scale.

Returns

Type	Description
Matrix	The scaled matrix.

Multiply(Single, Matrix)

Scales a matrix by a given value.

public static Matrix operator *(float left, Matrix right)

Parameters

Type	Name	Description
System.Single	left	The amount by which to scale.
Matrix	right	The matrix to scale.

Returns

Type	Description
Matrix	The scaled matrix.

Subtraction(Matrix, Matrix)

Subtracts two matrices.

public static Matrix operator -(Matrix left, Matrix right)

Parameters

Type	Name	Description
Matrix	left	The first matrix to subtract.
Matrix	right	The second matrix to subtract.

Returns

Type	Description
Matrix	The difference between the two matrices.

UnaryNegation(Matrix)

Negates a matrix.

public static Matrix operator -(Matrix value)

Parameters

Type	Name	Description
Matrix	value	The matrix to negate.

Returns

Type	Description
Matrix	The negated matrix.

UnaryPlus(Matrix)

Assert a matrix (return it unchanged).

public static Matrix operator +(Matrix value)

Parameters

Type	Name	Description
Matrix	value	The matrix to assert (unchange).

Returns

Type	Description
Matrix	The asserted (unchanged) matrix.

Extension Methods

ComponentBaseExtensions.DisposeBy<T>(T, ICollectorHolder)

ComponentBaseExtensions.RemoveDisposeBy<T>(T, ICollectorHolder)