Struct Matrix4

Represents a 4x4 matrix containing 3D rotation, scale, transform, and projection.

Implements

IEquatable<Matrix4>

IFormattable

IMultiplyOperators<Matrix4, Matrix4, Matrix4>

IMultiplyOperators<Matrix4, float, Matrix4>

IMultiplyOperators<Matrix4, Vector4, Vector4>

IMultiplyOperators<Matrix4, Matrix4x2, Matrix4x2>

IMultiplyOperators<Matrix4, Matrix4x3, Matrix4x3>

IAdditionOperators<Matrix4, Matrix4, Matrix4>

ISubtractionOperators<Matrix4, Matrix4, Matrix4>

IEqualityOperators<Matrix4, Matrix4, bool>

IAdditiveIdentity<Matrix4, Matrix4>

IMultiplicativeIdentity<Matrix4, Matrix4>

Inherited Members

object.Equals(object, object)

object.GetType()

object.ReferenceEquals(object, object)

Namespace: OpenTK.Mathematics

Assembly: OpenTK.Mathematics.dll

Syntax

[Serializable]
public struct Matrix4 : IEquatable<Matrix4>, IFormattable, IMultiplyOperators<Matrix4, Matrix4, Matrix4>, IMultiplyOperators<Matrix4, float, Matrix4>, IMultiplyOperators<Matrix4, Vector4, Vector4>, IMultiplyOperators<Matrix4, Matrix4x2, Matrix4x2>, IMultiplyOperators<Matrix4, Matrix4x3, Matrix4x3>, IAdditionOperators<Matrix4, Matrix4, Matrix4>, ISubtractionOperators<Matrix4, Matrix4, Matrix4>, IEqualityOperators<Matrix4, Matrix4, bool>, IAdditiveIdentity<Matrix4, Matrix4>, IMultiplicativeIdentity<Matrix4, Matrix4>

Constructors

Matrix4(Matrix3)

Initializes a new instance of the Matrix4 struct.

Declaration

public Matrix4(Matrix3 topLeft)

Parameters

Type	Name	Description
Matrix3	topLeft	The top left 3x3 of the matrix.

Matrix4(Vector4, Vector4, Vector4, Vector4)

Initializes a new instance of the Matrix4 struct.

Declaration

public Matrix4(Vector4 row0, Vector4 row1, Vector4 row2, Vector4 row3)

Parameters

Type	Name	Description
Vector4	row0	Top row of the matrix.
Vector4	row1	Second row of the matrix.
Vector4	row2	Third row of the matrix.
Vector4	row3	Bottom row of the matrix.

Matrix4(float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float)

Initializes a new instance of the Matrix4 struct.

Declaration

public Matrix4(float m00, float m01, float m02, float m03, float m10, float m11, float m12, float m13, float m20, float m21, float m22, float m23, float m30, float m31, float m32, float m33)

Parameters

Type	Name	Description
float	m00	First item of the first row of the matrix.
float	m01	Second item of the first row of the matrix.
float	m02	Third item of the first row of the matrix.
float	m03	Fourth item of the first row of the matrix.
float	m10	First item of the second row of the matrix.
float	m11	Second item of the second row of the matrix.
float	m12	Third item of the second row of the matrix.
float	m13	Fourth item of the second row of the matrix.
float	m20	First item of the third row of the matrix.
float	m21	Second item of the third row of the matrix.
float	m22	Third item of the third row of the matrix.
float	m23	Fourth item of the third row of the matrix.
float	m30	First item of the fourth row of the matrix.
float	m31	Second item of the fourth row of the matrix.
float	m32	Third item of the fourth row of the matrix.
float	m33	Fourth item of the fourth row of the matrix.

Fields

Identity

The identity matrix.

Declaration

public static readonly Matrix4 Identity

Field Value

Type	Description
Matrix4

Row0

Top row of the matrix.

Declaration

public Vector4 Row0

Field Value

Type	Description
Vector4

Row1

2nd row of the matrix.

Declaration

public Vector4 Row1

Field Value

Type	Description
Vector4

Row2

3rd row of the matrix.

Declaration

public Vector4 Row2

Field Value

Type	Description
Vector4

Row3

Bottom row of the matrix.

Declaration

public Vector4 Row3

Field Value

Type	Description
Vector4

Zero

The zero matrix.

Declaration

public static readonly Matrix4 Zero

Field Value

Type	Description
Matrix4

Properties

AdditiveIdentity

Gets the additive identity of the matrix, which is the zero matrix.

Declaration

public static Matrix4 AdditiveIdentity { get; }

Property Value

Type	Description
Matrix4

Column0

Gets or sets the first column of this matrix.

Declaration

public Vector4 Column0 { readonly get; set; }

Property Value

Type	Description
Vector4

Column1

Gets or sets the second column of this matrix.

Declaration

public Vector4 Column1 { readonly get; set; }

Property Value

Type	Description
Vector4

Column2

Gets or sets the third column of this matrix.

Declaration

public Vector4 Column2 { readonly get; set; }

Property Value

Type	Description
Vector4

Column3

Gets or sets the fourth column of this matrix.

Declaration

public Vector4 Column3 { readonly get; set; }

Property Value

Type	Description
Vector4

Determinant

Gets the determinant of this matrix.

Declaration

public readonly float Determinant { get; }

Property Value

Type	Description
float

Diagonal

Gets or sets the values along the main diagonal of the matrix.

Declaration

public Vector4 Diagonal { readonly get; set; }

Property Value

Type	Description
Vector4

this[int, int]

Gets or sets the value at a specified row and column.

Declaration

public float this[int rowIndex, int columnIndex] { readonly get; set; }

Parameters

Type	Name	Description
int	rowIndex	The index of the row.
int	columnIndex	The index of the column.

Property Value

Type	Description
float	The element at the given row and column index.

M11

Gets or sets the value at row 1, column 1 of this instance.

Declaration

public float M11 { readonly get; set; }

Property Value

Type	Description
float

M12

Gets or sets the value at row 1, column 2 of this instance.

Declaration

public float M12 { readonly get; set; }

Property Value

Type	Description
float

M13

Gets or sets the value at row 1, column 3 of this instance.

Declaration

public float M13 { readonly get; set; }

Property Value

Type	Description
float

M14

Gets or sets the value at row 1, column 4 of this instance.

Declaration

public float M14 { readonly get; set; }

Property Value

Type	Description
float

M21

Gets or sets the value at row 2, column 1 of this instance.

Declaration

public float M21 { readonly get; set; }

Property Value

Type	Description
float

M22

Gets or sets the value at row 2, column 2 of this instance.

Declaration

public float M22 { readonly get; set; }

Property Value

Type	Description
float

M23

Gets or sets the value at row 2, column 3 of this instance.

Declaration

public float M23 { readonly get; set; }

Property Value

Type	Description
float

M24

Gets or sets the value at row 2, column 4 of this instance.

Declaration

public float M24 { readonly get; set; }

Property Value

Type	Description
float

M31

Gets or sets the value at row 3, column 1 of this instance.

Declaration

public float M31 { readonly get; set; }

Property Value

Type	Description
float

M32

Gets or sets the value at row 3, column 2 of this instance.

Declaration

public float M32 { readonly get; set; }

Property Value

Type	Description
float

M33

Gets or sets the value at row 3, column 3 of this instance.

Declaration

public float M33 { readonly get; set; }

Property Value

Type	Description
float

M34

Gets or sets the value at row 3, column 4 of this instance.

Declaration

public float M34 { readonly get; set; }

Property Value

Type	Description
float

M41

Gets or sets the value at row 4, column 1 of this instance.

Declaration

public float M41 { readonly get; set; }

Property Value

Type	Description
float

M42

Gets or sets the value at row 4, column 2 of this instance.

Declaration

public float M42 { readonly get; set; }

Property Value

Type	Description
float

M43

Gets or sets the value at row 4, column 3 of this instance.

Declaration

public float M43 { readonly get; set; }

Property Value

Type	Description
float

M44

Gets or sets the value at row 4, column 4 of this instance.

Declaration

public float M44 { readonly get; set; }

Property Value

Type	Description
float

MultiplicativeIdentity

Gets the multiplicative identity of the matrix, which is the identity matrix.

Declaration

public static Matrix4 MultiplicativeIdentity { get; }

Property Value

Type	Description
Matrix4

Trace

Gets the trace of the matrix, the sum of the values along the diagonal.

Declaration

public readonly float Trace { get; }

Property Value

Type	Description
float

Methods

Add(Matrix4, Matrix4)

Adds two instances.

Declaration

[Pure]
public static Matrix4 Add(Matrix4 left, Matrix4 right)

Parameters

Type	Name	Description
Matrix4	left	The left operand of the addition.
Matrix4	right	The right operand of the addition.

Returns

Type	Description
Matrix4	A new instance that is the result of the addition.

Add(in Matrix4, in Matrix4, out Matrix4)

Adds two instances.

Declaration

public static void Add(in Matrix4 left, in Matrix4 right, out Matrix4 result)

Parameters

Type	Name	Description
Matrix4	left	The left operand of the addition.
Matrix4	right	The right operand of the addition.
Matrix4	result	A new instance that is the result of the addition.

ClearProjection()

Returns a copy of this Matrix4 without projection. (equivalent to setting Column3 = (0, 0, 0, 0)).

Declaration

[Obsolete("This function doesn't actually clear the projection of the matrix. This is equivalent of setting Column3 = (0, 0, 0, 0).")]
public readonly Matrix4 ClearProjection()

Returns

Type	Description
Matrix4	The matrix without projection.

ClearRotation()

Returns a copy of this Matrix4 without rotation.

Declaration

public readonly Matrix4 ClearRotation()

Returns

Type	Description
Matrix4	The matrix without rotation.

ClearScale()

Returns a copy of this Matrix4 without scale.

Declaration

public readonly Matrix4 ClearScale()

Returns

Type	Description
Matrix4	The matrix without scaling.

ClearTranslation()

Returns a copy of this Matrix4 without translation.

Declaration

public readonly Matrix4 ClearTranslation()

Returns

Type	Description
Matrix4	The matrix without translation.

CreateFromAxisAngle(Vector3, float)

Build a rotation matrix from the specified axis/angle rotation.

Declaration

[Pure]
public static Matrix4 CreateFromAxisAngle(Vector3 axis, float angle)

Parameters

Type	Name	Description
Vector3	axis	The axis to rotate about.
float	angle	Angle in radians to rotate counter-clockwise (looking in the direction of the given axis).

Returns

Type	Description
Matrix4	A matrix instance.

CreateFromAxisAngle(Vector3, float, out Matrix4)

Build a rotation matrix from the specified axis/angle rotation.

Declaration

public static void CreateFromAxisAngle(Vector3 axis, float angle, out Matrix4 result)

Parameters

Type	Name	Description
Vector3	axis	The axis to rotate about.
float	angle	Angle in radians to rotate counter-clockwise (looking in the direction of the given axis).
Matrix4	result	A matrix instance.

CreateFromQuaternion(Quaternion)

Builds a rotation matrix from a quaternion.

Declaration

[Pure]
public static Matrix4 CreateFromQuaternion(Quaternion q)

Parameters

Type	Name	Description
Quaternion	q	The quaternion to rotate by.

Returns

Type	Description
Matrix4	A matrix instance.

CreateFromQuaternion(in Quaternion, out Matrix4)

Builds a rotation matrix from a quaternion.

Declaration

public static void CreateFromQuaternion(in Quaternion q, out Matrix4 result)

Parameters

Type	Name	Description
Quaternion	q	The quaternion to rotate by.
Matrix4	result	A matrix instance.

CreateOrthographic(float, float, float, float)

Creates an orthographic projection matrix.

Declaration

[Pure]
public static Matrix4 CreateOrthographic(float width, float height, float depthNear, float depthFar)

Parameters

Type	Name	Description
float	width	The width of the projection volume.
float	height	The height of the projection volume.
float	depthNear	The near edge of the projection volume.
float	depthFar	The far edge of the projection volume.

Returns

Type	Description
Matrix4	The resulting Matrix4 instance.

CreateOrthographic(float, float, float, float, out Matrix4)

Creates an orthographic projection matrix.

Declaration

public static void CreateOrthographic(float width, float height, float depthNear, float depthFar, out Matrix4 result)

Parameters

Type	Name	Description
float	width	The width of the projection volume.
float	height	The height of the projection volume.
float	depthNear	The near edge of the projection volume.
float	depthFar	The far edge of the projection volume.
Matrix4	result	The resulting Matrix4 instance.

CreateOrthographicOffCenter(float, float, float, float, float, float)

Creates an orthographic projection matrix.

Declaration

[Pure]
public static Matrix4 CreateOrthographicOffCenter(float left, float right, float bottom, float top, float depthNear, float depthFar)

Parameters

Type	Name	Description
float	left	The left edge of the projection volume.
float	right	The right edge of the projection volume.
float	bottom	The bottom edge of the projection volume.
float	top	The top edge of the projection volume.
float	depthNear	The near edge of the projection volume.
float	depthFar	The far edge of the projection volume.

Returns

Type	Description
Matrix4	The resulting Matrix4 instance.

CreateOrthographicOffCenter(float, float, float, float, float, float, out Matrix4)

Creates an orthographic projection matrix.

Declaration

public static void CreateOrthographicOffCenter(float left, float right, float bottom, float top, float depthNear, float depthFar, out Matrix4 result)

Parameters

Type	Name	Description
float	left	The left edge of the projection volume.
float	right	The right edge of the projection volume.
float	bottom	The bottom edge of the projection volume.
float	top	The top edge of the projection volume.
float	depthNear	The near edge of the projection volume.
float	depthFar	The far edge of the projection volume.
Matrix4	result	The resulting Matrix4 instance.

CreatePerspectiveFieldOfView(float, float, float, float)

Creates a perspective projection matrix.

Declaration

[Pure]
public static Matrix4 CreatePerspectiveFieldOfView(float fovy, float aspect, float depthNear, float depthFar)

Parameters

Type	Name	Description
float	fovy	Angle of the field of view in the y direction (in radians).
float	aspect	Aspect ratio of the view (width / height).
float	depthNear	Distance to the near clip plane.
float	depthFar	Distance to the far clip plane.

Returns

Type	Description
Matrix4	A projection matrix that transforms camera space to raster space.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown under the following conditions: fovy is zero, less than zero or larger than Math.PI aspect is negative or zero depthNear is negative or zero depthFar is negative or zero depthNear is larger than depthFar

CreatePerspectiveFieldOfView(float, float, float, float, out Matrix4)

Creates a perspective projection matrix.

Declaration

public static void CreatePerspectiveFieldOfView(float fovy, float aspect, float depthNear, float depthFar, out Matrix4 result)

Parameters

Type	Name	Description
float	fovy	Angle of the field of view in the y direction (in radians).
float	aspect	Aspect ratio of the view (width / height).
float	depthNear	Distance to the near clip plane.
float	depthFar	Distance to the far clip plane.
Matrix4	result	A projection matrix that transforms camera space to raster space.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown under the following conditions: fovy is zero, less than zero or larger than Math.PI aspect is negative or zero depthNear is negative or zero depthFar is negative or zero depthNear is larger than depthFar

CreatePerspectiveOffCenter(float, float, float, float, float, float)

Creates an perspective projection matrix.

Declaration

[Pure]
public static Matrix4 CreatePerspectiveOffCenter(float left, float right, float bottom, float top, float depthNear, float depthFar)

Parameters

Type	Name	Description
float	left	Left edge of the view frustum.
float	right	Right edge of the view frustum.
float	bottom	Bottom edge of the view frustum.
float	top	Top edge of the view frustum.
float	depthNear	Distance to the near clip plane.
float	depthFar	Distance to the far clip plane.

Returns

Type	Description
Matrix4	A projection matrix that transforms camera space to raster space.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown under the following conditions: depthNear is negative or zero depthFar is negative or zero depthNear is larger than depthFar

CreatePerspectiveOffCenter(float, float, float, float, float, float, out Matrix4)

Creates an perspective projection matrix.

Declaration

public static void CreatePerspectiveOffCenter(float left, float right, float bottom, float top, float depthNear, float depthFar, out Matrix4 result)

Parameters

Type	Name	Description
float	left	Left edge of the view frustum.
float	right	Right edge of the view frustum.
float	bottom	Bottom edge of the view frustum.
float	top	Top edge of the view frustum.
float	depthNear	Distance to the near clip plane.
float	depthFar	Distance to the far clip plane.
Matrix4	result	A projection matrix that transforms camera space to raster space.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown under the following conditions: depthNear is negative or zero depthFar is negative or zero depthNear is larger than depthFar

CreateRotationX(float)

Builds a rotation matrix for a rotation around the x-axis.

Declaration

[Pure]
public static Matrix4 CreateRotationX(float angle)

Parameters

Type	Name	Description
float	angle	The counter-clockwise angle in radians.

Returns

Type	Description
Matrix4	The resulting Matrix4 instance.

CreateRotationX(float, out Matrix4)

Builds a rotation matrix for a rotation around the x-axis.

Declaration

public static void CreateRotationX(float angle, out Matrix4 result)

Parameters

Type	Name	Description
float	angle	The counter-clockwise angle in radians.
Matrix4	result	The resulting Matrix4 instance.

CreateRotationY(float)

Builds a rotation matrix for a rotation around the y-axis.

Declaration

[Pure]
public static Matrix4 CreateRotationY(float angle)

Parameters

Type	Name	Description
float	angle	The counter-clockwise angle in radians.

Returns

Type	Description
Matrix4	The resulting Matrix4 instance.

CreateRotationY(float, out Matrix4)

Builds a rotation matrix for a rotation around the y-axis.

Declaration

public static void CreateRotationY(float angle, out Matrix4 result)

Parameters

Type	Name	Description
float	angle	The counter-clockwise angle in radians.
Matrix4	result	The resulting Matrix4 instance.

CreateRotationZ(float)

Builds a rotation matrix for a rotation around the z-axis.

Declaration

[Pure]
public static Matrix4 CreateRotationZ(float angle)

Parameters

Type	Name	Description
float	angle	The counter-clockwise angle in radians.

Returns

Type	Description
Matrix4	The resulting Matrix4 instance.

CreateRotationZ(float, out Matrix4)

Builds a rotation matrix for a rotation around the z-axis.

Declaration

public static void CreateRotationZ(float angle, out Matrix4 result)

Parameters

Type	Name	Description
float	angle	The counter-clockwise angle in radians.
Matrix4	result	The resulting Matrix4 instance.

CreateScale(Vector3)

Creates a scale matrix.

Declaration

[Pure]
public static Matrix4 CreateScale(Vector3 scale)

Parameters

Type	Name	Description
Vector3	scale	Scale factors for the x, y, and z axes.

Returns

Type	Description
Matrix4	A scale matrix.

CreateScale(in Vector3, out Matrix4)

Creates a scale matrix.

Declaration

public static void CreateScale(in Vector3 scale, out Matrix4 result)

Parameters

Type	Name	Description
Vector3	scale	Scale factors for the x, y, and z axes.
Matrix4	result	A scale matrix.

CreateScale(float)

Creates a scale matrix.

Declaration

[Pure]
public static Matrix4 CreateScale(float scale)

Parameters

Type	Name	Description
float	scale	Single scale factor for the x, y, and z axes.

Returns

Type	Description
Matrix4	A scale matrix.

CreateScale(float, out Matrix4)

Creates a scale matrix.

Declaration

public static void CreateScale(float scale, out Matrix4 result)

Parameters

Type	Name	Description
float	scale	Single scale factor for the x, y, and z axes.
Matrix4	result	A scale matrix.

CreateScale(float, float, float)

Creates a scale matrix.

Declaration

[Pure]
public static Matrix4 CreateScale(float x, float y, float z)

Parameters

Type	Name	Description
float	x	Scale factor for the x axis.
float	y	Scale factor for the y axis.
float	z	Scale factor for the z axis.

Returns

Type	Description
Matrix4	A scale matrix.

CreateScale(float, float, float, out Matrix4)

Creates a scale matrix.

Declaration

public static void CreateScale(float x, float y, float z, out Matrix4 result)

Parameters

Type	Name	Description
float	x	Scale factor for the x axis.
float	y	Scale factor for the y axis.
float	z	Scale factor for the z axis.
Matrix4	result	A scale matrix.

CreateSwizzle(int, int, int, int)

Create a swizzle matrix that can be used to change the row order of matrices.

Declaration

public static Matrix4 CreateSwizzle(int rowForRow0, int rowForRow1, int rowForRow2, int rowForRow3)

Parameters

Type	Name	Description
int	rowForRow0	Which row to place in Row0.
int	rowForRow1	Which row to place in Row1.
int	rowForRow2	Which row to place in Row2.
int	rowForRow3	Which row to place in Row3.

Returns

Type	Description
Matrix4	The resulting swizzle matrix.

Remarks

If you are looking to swizzle vectors there are properties like Zyx that can do this more effectively.

CreateSwizzle(int, int, int, int, out Matrix4)

Create a swizzle matrix that can be used to change the row order of matrices.

Declaration

public static void CreateSwizzle(int rowForRow0, int rowForRow1, int rowForRow2, int rowForRow3, out Matrix4 result)

Parameters

Type	Name	Description
int	rowForRow0	Which row to place in Row0.
int	rowForRow1	Which row to place in Row1.
int	rowForRow2	Which row to place in Row2.
int	rowForRow3	Which row to place in Row3.
Matrix4	result	The resulting swizzle matrix.

Remarks

If you are looking to swizzle vectors there are properties like Zyx that can do this more effectively.

CreateTranslation(Vector3)

Creates a translation matrix.

Declaration

[Pure]
public static Matrix4 CreateTranslation(Vector3 vector)

Parameters

Type	Name	Description
Vector3	vector	The translation vector.

Returns

Type	Description
Matrix4	The resulting Matrix4 instance.

CreateTranslation(in Vector3, out Matrix4)

Creates a translation matrix.

Declaration

public static void CreateTranslation(in Vector3 vector, out Matrix4 result)

Parameters

Type	Name	Description
Vector3	vector	The translation vector.
Matrix4	result	The resulting Matrix4 instance.

CreateTranslation(float, float, float)

Creates a translation matrix.

Declaration

[Pure]
public static Matrix4 CreateTranslation(float x, float y, float z)

Parameters

Type	Name	Description
float	x	X translation.
float	y	Y translation.
float	z	Z translation.

Returns

Type	Description
Matrix4	The resulting Matrix4 instance.

CreateTranslation(float, float, float, out Matrix4)

Creates a translation matrix.

Declaration

public static void CreateTranslation(float x, float y, float z, out Matrix4 result)

Parameters

Type	Name	Description
float	x	X translation.
float	y	Y translation.
float	z	Z translation.
Matrix4	result	The resulting Matrix4 instance.

Equals(Matrix4)

Indicates whether the current matrix is equal to another matrix.

Declaration

[Pure]
public readonly bool Equals(Matrix4 other)

Parameters

Type	Name	Description
Matrix4	other	An matrix to compare with this matrix.

Returns

Type	Description
bool	true if the current matrix is equal to the matrix parameter; otherwise, false.

Equals(object)

Indicates whether this instance and a specified object are equal.

Declaration

[Pure]
public override readonly bool Equals(object obj)

Parameters

Type	Name	Description
object	obj	The object to compare tresult.

Returns

Type	Description
bool	True if the instances are equal; false otherwise.

Overrides

ValueType.Equals(object)

ExtractOrthographic(out float, out float, out float, out float)

Returns the orthographic projection parameters of this instance. This only works if the matrix was created using CreateOrthographic(float, float, float, float).

Declaration

public readonly void ExtractOrthographic(out float width, out float height, out float depthNear, out float depthFar)

Parameters

Type	Name	Description
float	width	The width of the projection volume.
float	height	The height of the projection volume.
float	depthNear	The distance to the near clip plane.
float	depthFar	The distance to the far clip plane.

ExtractOrthographicOffCenter(out float, out float, out float, out float, out float, out float)

Returns the off-center orthographic projection parameters of this instance. This only works if the matrix was created using CreateOrthographicOffCenter(float, float, float, float, float, float).

Declaration

public readonly void ExtractOrthographicOffCenter(out float left, out float right, out float bottom, out float top, out float depthNear, out float depthFar)

Parameters

Type	Name	Description
float	left	The left edge of the projection volume.
float	right	The right edge of the projection volume.
float	bottom	The bottom edge of the projection volume.
float	top	The top edge of the projection volume.
float	depthNear	The distance to the near clip plane.
float	depthFar	The distance to the far clip plane.

ExtractPerspectiveFieldOfView(out float, out float, out float, out float)

Returns the field of view projection parameters of this instance. This only works if the matrix was created using CreatePerspectiveFieldOfView(float, float, float, float).

Declaration

public readonly void ExtractPerspectiveFieldOfView(out float fovy, out float aspect, out float depthNear, out float depthFar)

Parameters

Type	Name	Description
float	fovy	Angle of the field of view in the y direction (in radians).
float	aspect	Aspect ratio of the view (width / height).
float	depthNear	The distance to the near clip plane.
float	depthFar	The distance to the far clip plane.

ExtractPerspectiveOffCenter(out float, out float, out float, out float, out float, out float)

Returns the off-center projection parameters of this instance. This only works if the matrix was created using CreatePerspectiveOffCenter(float, float, float, float, float, float).

Declaration

public readonly void ExtractPerspectiveOffCenter(out float left, out float right, out float bottom, out float top, out float depthNear, out float depthFar)

Parameters

Type	Name	Description
float	left	The left edge of the view frustum.
float	right	The right edge of the view frustum.
float	bottom	The bottom edge of the view frustum.
float	top	The top edge of the view frustum.
float	depthNear	The distance to the near clip plane.
float	depthFar	The distance to the far clip plane.

ExtractProjection()

Returns the projection component of this instance (equivalent to Column3).

Declaration

[Obsolete("Use Column3 if the old behaviour is needed, or use ExtractPerspective*() or ExtractOrthographic* instead.")]
public readonly Vector4 ExtractProjection()

Returns

Type	Description
Vector4	The projection (Column3).

ExtractRotation(bool)

Returns the rotation component of this instance. Quite slow.

Declaration

[Pure]
public readonly Quaternion ExtractRotation(bool rowNormalize = true)

Parameters

Type	Name	Description
bool	rowNormalize	Whether the method should row-normalize (i.e. remove scale from) the Matrix. Pass false if you know it's already normalized.

Returns

Type	Description
Quaternion	The rotation.

ExtractScale()

Returns the scale component of this instance.

Declaration

public readonly Vector3 ExtractScale()

Returns

Type	Description
Vector3	The scale.

ExtractTranslation()

Returns the translation component of this instance.

Declaration

public readonly Vector3 ExtractTranslation()

Returns

Type	Description
Vector3	The translation.

GetHashCode()

Returns the hashcode for this instance.

Declaration

public override readonly int GetHashCode()

Returns

Type	Description
int	A System.Int32 containing the unique hashcode for this instance.

Overrides

ValueType.GetHashCode()

Invert()

Converts this instance into its inverse.

Declaration

public void Invert()

Invert(Matrix4)

Calculate the inverse of the given matrix.

Declaration

[Pure]
public static Matrix4 Invert(Matrix4 mat)

Parameters

Type	Name	Description
Matrix4	mat	The matrix to invert.

Returns

Type	Description
Matrix4	The inverse of the given matrix.

Exceptions

Type	Condition
InvalidOperationException	Thrown if the Matrix4 is singular.

Invert(in Matrix4, out Matrix4)

Calculate the inverse of the given matrix.

Declaration

public static void Invert(in Matrix4 mat, out Matrix4 result)

Parameters

Type	Name	Description
Matrix4	mat	The matrix to invert.
Matrix4	result	The inverse of the given matrix if it has one, or the input if it is singular.

Exceptions

Type	Condition
InvalidOperationException	Thrown if the Matrix4 is singular.

Inverted()

Returns an inverted copy of this instance.

Declaration

public readonly Matrix4 Inverted()

Returns

Type	Description
Matrix4	The inverted copy.

Remarks

If the matrix is singular this function does not throw an exception, instead it returns the original un-inverted matrix.

LookAt(Vector3, Vector3, Vector3)

Build a world space to camera space matrix.

Declaration

[Pure]
public static Matrix4 LookAt(Vector3 eye, Vector3 target, Vector3 up)

Parameters

Type	Name	Description
Vector3	eye	Eye (camera) position in world space.
Vector3	target	Target position in world space.
Vector3	up	Up vector in world space (should not be parallel to the camera direction, that is target - eye).

Returns

Type	Description
Matrix4	A Matrix4 that transforms world space to camera space.

LookAt(float, float, float, float, float, float, float, float, float)

Build a world space to camera space matrix.

Declaration

[Pure]
public static Matrix4 LookAt(float eyeX, float eyeY, float eyeZ, float targetX, float targetY, float targetZ, float upX, float upY, float upZ)

Parameters

Type	Name	Description
float	eyeX	Eye (camera) X-position in world space.
float	eyeY	Eye (camera) Y-position in world space.
float	eyeZ	Eye (camera) Z-position in world space.
float	targetX	Target X-position in world space.
float	targetY	Target Y-position in world space.
float	targetZ	Target Z-position in world space.
float	upX	X of the up vector in world space (should not be parallel to the camera direction, that is target - eye).
float	upY	Y of the up vector in world space (should not be parallel to the camera direction, that is target - eye).
float	upZ	Z of the up vector in world space (should not be parallel to the camera direction, that is target - eye).

Returns

Type	Description
Matrix4	A Matrix4 that transforms world space to camera space.

Mult(Matrix4, Matrix4)

Multiplies two instances.

Declaration

[Pure]
public static Matrix4 Mult(Matrix4 left, Matrix4 right)

Parameters

Type	Name	Description
Matrix4	left	The left operand of the multiplication.
Matrix4	right	The right operand of the multiplication.

Returns

Type	Description
Matrix4	A new instance that is the result of the multiplication.

Mult(Matrix4, Matrix4x2)

Multiplies two instances.

Declaration

[Pure]
public static Matrix4x2 Mult(Matrix4 left, Matrix4x2 right)

Parameters

Type	Name	Description
Matrix4	left	The left operand of the multiplication.
Matrix4x2	right	The right operand of the multiplication.

Returns

Type	Description
Matrix4x2	A new instance that is the result of the multiplication.

Mult(Matrix4, Matrix4x3)

Multiplies two instances.

Declaration

[Pure]
public static Matrix4x3 Mult(Matrix4 left, Matrix4x3 right)

Parameters

Type	Name	Description
Matrix4	left	The left operand of the multiplication.
Matrix4x3	right	The right operand of the multiplication.

Returns

Type	Description
Matrix4x3	A new instance that is the result of the multiplication.

Mult(Matrix4, float)

Multiplies an instance by a scalar.

Declaration

[Pure]
public static Matrix4 Mult(Matrix4 left, float right)

Parameters

Type	Name	Description
Matrix4	left	The left operand of the multiplication.
float	right	The right operand of the multiplication.

Returns

Type	Description
Matrix4	A new instance that is the result of the multiplication.

Mult(in Matrix4, in Matrix4, out Matrix4)

Multiplies two instances.

Declaration

public static void Mult(in Matrix4 left, in Matrix4 right, out Matrix4 result)

Parameters

Type	Name	Description
Matrix4	left	The left operand of the multiplication.
Matrix4	right	The right operand of the multiplication.
Matrix4	result	A new instance that is the result of the multiplication.

Mult(in Matrix4, in Matrix4x2, out Matrix4x2)

Multiplies two instances.

Declaration

public static void Mult(in Matrix4 left, in Matrix4x2 right, out Matrix4x2 result)

Parameters

Type	Name	Description
Matrix4	left	The left operand of the multiplication.
Matrix4x2	right	The right operand of the multiplication.
Matrix4x2	result	A new instance that is the result of the multiplication.

Mult(in Matrix4, in Matrix4x3, out Matrix4x3)

Multiplies two instances.

Declaration

public static void Mult(in Matrix4 left, in Matrix4x3 right, out Matrix4x3 result)

Parameters

Type	Name	Description
Matrix4	left	The left operand of the multiplication.
Matrix4x3	right	The right operand of the multiplication.
Matrix4x3	result	A new instance that is the result of the multiplication.

Mult(in Matrix4, float, out Matrix4)

Multiplies an instance by a scalar.

Declaration

public static void Mult(in Matrix4 left, float right, out Matrix4 result)

Parameters

Type	Name	Description
Matrix4	left	The left operand of the multiplication.
float	right	The right operand of the multiplication.
Matrix4	result	A new instance that is the result of the multiplication.

Normalize()

Divides each element in the Matrix by the Determinant.

Declaration

public void Normalize()

Normalized()

Returns a normalized copy of this instance.

Declaration

public readonly Matrix4 Normalized()

Returns

Type	Description
Matrix4	The normalized copy.

Subtract(Matrix4, Matrix4)

Subtracts one instance from another.

Declaration

[Pure]
public static Matrix4 Subtract(Matrix4 left, Matrix4 right)

Parameters

Type	Name	Description
Matrix4	left	The left operand of the subraction.
Matrix4	right	The right operand of the subraction.

Returns

Type	Description
Matrix4	A new instance that is the result of the subraction.

Subtract(in Matrix4, in Matrix4, out Matrix4)

Subtracts one instance from another.

Declaration

public static void Subtract(in Matrix4 left, in Matrix4 right, out Matrix4 result)

Parameters

Type	Name	Description
Matrix4	left	The left operand of the subraction.
Matrix4	right	The right operand of the subraction.
Matrix4	result	A new instance that is the result of the subraction.

Swizzle(Matrix4, int, int, int, int)

Swizzles a matrix, i.e. switches rows of the matrix.

Declaration

public static Matrix4 Swizzle(Matrix4 mat, int rowForRow0, int rowForRow1, int rowForRow2, int rowForRow3)

Parameters

Type	Name	Description
Matrix4	mat	The matrix to swizzle.
int	rowForRow0	Which row to place in Row0.
int	rowForRow1	Which row to place in Row1.
int	rowForRow2	Which row to place in Row2.
int	rowForRow3	Which row to place in Row3.

Returns

Type	Description
Matrix4	The swizzled matrix.

Exceptions

Type	Condition
IndexOutOfRangeException	If any of the rows are outside of the range [0, 3].

Swizzle(in Matrix4, int, int, int, int, out Matrix4)

Swizzles a matrix, i.e. switches rows of the matrix.

Declaration

public static void Swizzle(in Matrix4 mat, int rowForRow0, int rowForRow1, int rowForRow2, int rowForRow3, out Matrix4 result)

Parameters

Type	Name	Description
Matrix4	mat	The matrix to swizzle.
int	rowForRow0	Which row to place in Row0.
int	rowForRow1	Which row to place in Row1.
int	rowForRow2	Which row to place in Row2.
int	rowForRow3	Which row to place in Row3.
Matrix4	result	The swizzled matrix.

Exceptions

Type	Condition
IndexOutOfRangeException	If any of the rows are outside of the range [0, 3].

Swizzle(int, int, int, int)

Swizzles this instance. Switches places of the rows of the matrix.

Declaration

public void Swizzle(int rowForRow0, int rowForRow1, int rowForRow2, int rowForRow3)

Parameters

Type	Name	Description
int	rowForRow0	Which row to place in Row0.
int	rowForRow1	Which row to place in Row1.
int	rowForRow2	Which row to place in Row2.
int	rowForRow3	Which row to place in Row3.

Swizzled(int, int, int, int)

Returns a swizzled copy of this instance.

Declaration

public readonly Matrix4 Swizzled(int rowForRow0, int rowForRow1, int rowForRow2, int rowForRow3)

Parameters

Type	Name	Description
int	rowForRow0	Which row to place in Row0.
int	rowForRow1	Which row to place in Row1.
int	rowForRow2	Which row to place in Row2.
int	rowForRow3	Which row to place in Row3.

Returns

Type	Description
Matrix4	The swizzled copy.

ToString()

Returns a System.String that represents the current Matrix4.

Declaration

public override readonly string ToString()

Returns

Type	Description
string	The string representation of the matrix.

Overrides

ValueType.ToString()

ToString(IFormatProvider)

Formats the value of the current instance using the specified format.

Declaration

public readonly string ToString(IFormatProvider formatProvider)

Parameters

Type	Name	Description
IFormatProvider	formatProvider	The provider to use to format the value. -or- A null reference (Nothing in Visual Basic) to obtain the numeric format information from the current locale setting of the operating system.

Returns

Type	Description
string	The value of the current instance in the specified format.

ToString(string)

Formats the value of the current instance using the specified format.

Declaration

public readonly string ToString(string format)

Parameters

Type	Name	Description
string	format	The format to use. -or- A null reference (Nothing in Visual Basic) to use the default format defined for the type of the IFormattable implementation.

Returns

Type	Description
string	The value of the current instance in the specified format.

ToString(string, IFormatProvider)

Formats the value of the current instance using the specified format.

Declaration

public readonly string ToString(string format, IFormatProvider formatProvider)

Parameters

Type	Name	Description
string	format	The format to use. -or- A null reference (Nothing in Visual Basic) to use the default format defined for the type of the IFormattable implementation.
IFormatProvider	formatProvider	The provider to use to format the value. -or- A null reference (Nothing in Visual Basic) to obtain the numeric format information from the current locale setting of the operating system.

Returns

Type	Description
string	The value of the current instance in the specified format.

Transpose()

Converts this instance into its transpose.

Declaration

public void Transpose()

Transpose(Matrix4)

Calculate the transpose of the given matrix.

Declaration

[Pure]
public static Matrix4 Transpose(Matrix4 mat)

Parameters

Type	Name	Description
Matrix4	mat	The matrix to transpose.

Returns

Type	Description
Matrix4	The transpose of the given matrix.

Transpose(in Matrix4, out Matrix4)

Calculate the transpose of the given matrix.

Declaration

public static void Transpose(in Matrix4 mat, out Matrix4 result)

Parameters

Type	Name	Description
Matrix4	mat	The matrix to transpose.
Matrix4	result	The result of the calculation.

Transposed()

Returns a transposed copy of this instance.

Declaration

public readonly Matrix4 Transposed()

Returns

Type	Description
Matrix4	The transposed copy.

Operators

operator +(Matrix4, Matrix4)

Matrix addition.

Declaration

[Pure]
public static Matrix4 operator +(Matrix4 left, Matrix4 right)

Parameters

Type	Name	Description
Matrix4	left	left-hand operand.
Matrix4	right	right-hand operand.

Returns

Type	Description
Matrix4	A new Matrix4 which holds the result of the addition.

operator ==(Matrix4, Matrix4)

Compares two instances for equality.

Declaration

[Pure]
public static bool operator ==(Matrix4 left, Matrix4 right)

Parameters

Type	Name	Description
Matrix4	left	The first instance.
Matrix4	right	The second instance.

Returns

Type	Description
bool	True, if left equals right; false otherwise.

explicit operator Matrix4x4(Matrix4)

Converts Matrix4 to Matrix4x4.

Declaration

[Pure]
public static explicit operator Matrix4x4(Matrix4 mat)

Parameters

Type	Name	Description
Matrix4	mat	The Matrix4 to cast.

Returns

Type	Description
Matrix4x4

explicit operator Matrix4(Matrix4x4)

Converts Matrix4x4 to Matrix4.

Declaration

[Pure]
public static explicit operator Matrix4(Matrix4x4 mat)

Parameters

Type	Name	Description
Matrix4x4	mat	The Matrix4 to cast.

Returns

Type	Description
Matrix4

operator !=(Matrix4, Matrix4)

Compares two instances for inequality.

Declaration

[Pure]
public static bool operator !=(Matrix4 left, Matrix4 right)

Parameters

Type	Name	Description
Matrix4	left	The first instance.
Matrix4	right	The second instance.

Returns

Type	Description
bool	True, if left does not equal right; false otherwise.

operator *(Matrix4, Matrix4)

Matrix multiplication.

Declaration

[Pure]
public static Matrix4 operator *(Matrix4 left, Matrix4 right)

Parameters

Type	Name	Description
Matrix4	left	left-hand operand.
Matrix4	right	right-hand operand.

Returns

Type	Description
Matrix4	A new Matrix4 which holds the result of the multiplication.

operator *(Matrix4, Matrix4x2)

Matrix multiplication.

Declaration

[Pure]
public static Matrix4x2 operator *(Matrix4 left, Matrix4x2 right)

Parameters

Type	Name	Description
Matrix4	left	left-hand operand.
Matrix4x2	right	right-hand operand.

Returns

Type	Description
Matrix4x2	A new Matrix4x2 which holds the result of the multiplication.

operator *(Matrix4, Matrix4x3)

Matrix multiplication.

Declaration

[Pure]
public static Matrix4x3 operator *(Matrix4 left, Matrix4x3 right)

Parameters

Type	Name	Description
Matrix4	left	left-hand operand.
Matrix4x3	right	right-hand operand.

Returns

Type	Description
Matrix4x3	A new Matrix4x3 which holds the result of the multiplication.

operator *(Matrix4, Vector4)

Transform a Vector by the given Matrix using right-handed notation.

Declaration

[Pure]
public static Vector4 operator *(Matrix4 mat, Vector4 vec)

Parameters

Type	Name	Description
Matrix4	mat	The desired transformation.
Vector4	vec	The vector to transform.

Returns

Type	Description
Vector4	The transformed vector.

operator *(Matrix4, float)

Matrix-scalar multiplication.

Declaration

[Pure]
public static Matrix4 operator *(Matrix4 left, float right)

Parameters

Type	Name	Description
Matrix4	left	left-hand operand.
float	right	right-hand operand.

Returns

Type	Description
Matrix4	A new Matrix4 which holds the result of the multiplication.

operator -(Matrix4, Matrix4)

Matrix subtraction.

Declaration

[Pure]
public static Matrix4 operator -(Matrix4 left, Matrix4 right)

Parameters

Type	Name	Description
Matrix4	left	left-hand operand.
Matrix4	right	right-hand operand.

Returns

Type	Description
Matrix4	A new Matrix4 which holds the result of the subtraction.

Implements

IEquatable<T>

IFormattable

IMultiplyOperators<TSelf, TOther, TResult>

IMultiplyOperators<TSelf, TOther, TResult>

IMultiplyOperators<TSelf, TOther, TResult>

IMultiplyOperators<TSelf, TOther, TResult>

IMultiplyOperators<TSelf, TOther, TResult>

IAdditionOperators<TSelf, TOther, TResult>

ISubtractionOperators<TSelf, TOther, TResult>

IEqualityOperators<TSelf, TOther, TResult>

IAdditiveIdentity<TSelf, TResult>

IMultiplicativeIdentity<TSelf, TResult>

See Also

Matrix4d