Struct Matrix3

Represents a 3x3 matrix containing 3D rotation and scale.

Implements

IEquatable<Matrix3>

IFormattable

Inherited Members

object.Equals(object, object)

object.GetType()

object.ReferenceEquals(object, object)

Namespace: OpenTK.Mathematics

Assembly: OpenTK.Mathematics.dll

Syntax

[Serializable]
public struct Matrix3 : IEquatable<Matrix3>, IFormattable

Constructors

Matrix3(Matrix4)

Initializes a new instance of the Matrix3 struct.

Declaration

public Matrix3(Matrix4 matrix)

Parameters

Type	Name	Description
Matrix4	matrix	A Matrix4 to take the upper-left 3x3 from.

Matrix3(Vector3, Vector3, Vector3)

Initializes a new instance of the Matrix3 struct.

Declaration

public Matrix3(Vector3 row0, Vector3 row1, Vector3 row2)

Parameters

Type	Name	Description
Vector3	row0	Top row of the matrix.
Vector3	row1	Second row of the matrix.
Vector3	row2	Bottom row of the matrix.

Matrix3(float, float, float, float, float, float, float, float, float)

Initializes a new instance of the Matrix3 struct.

Declaration

public Matrix3(float m00, float m01, float m02, float m10, float m11, float m12, float m20, float m21, float m22)

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	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	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.

Fields

Identity

The identity matrix.

Declaration

public static readonly Matrix3 Identity

Field Value

Type	Description
Matrix3

Row0

First row of the matrix.

Declaration

public Vector3 Row0

Field Value

Type	Description
Vector3

Row1

Second row of the matrix.

Declaration

public Vector3 Row1

Field Value

Type	Description
Vector3

Row2

Third row of the matrix.

Declaration

public Vector3 Row2

Field Value

Type	Description
Vector3

Zero

The zero matrix.

Declaration

public static readonly Matrix3 Zero

Field Value

Type	Description
Matrix3

Properties

Column0

Gets the first column of this matrix.

Declaration

public Vector3 Column0 { get; }

Property Value

Type	Description
Vector3

Column1

Gets the second column of this matrix.

Declaration

public Vector3 Column1 { get; }

Property Value

Type	Description
Vector3

Column2

Gets the third column of this matrix.

Declaration

public Vector3 Column2 { get; }

Property Value

Type	Description
Vector3

Determinant

Gets the determinant of this matrix.

Declaration

public float Determinant { get; }

Property Value

Type	Description
float

Diagonal

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

Declaration

public Vector3 Diagonal { get; set; }

Property Value

Type	Description
Vector3

this[int, int]

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

Declaration

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

Property Value

Type	Description
float

Trace

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

Declaration

public float Trace { get; }

Property Value

Type	Description
float

Methods

Add(Matrix3, Matrix3)

Adds two instances.

Declaration

[Pure]
public static Matrix3 Add(Matrix3 left, Matrix3 right)

Parameters

Type	Name	Description
Matrix3	left	The left operand of the addition.
Matrix3	right	The right operand of the addition.

Returns

Type	Description
Matrix3	A new instance that is the result of the addition.

Add(in Matrix3, in Matrix3, out Matrix3)

Adds two instances.

Declaration

public static void Add(in Matrix3 left, in Matrix3 right, out Matrix3 result)

Parameters

Type	Name	Description
Matrix3	left	The left operand of the addition.
Matrix3	right	The right operand of the addition.
Matrix3	result	A new instance that is the result of the addition.

ClearRotation()

Returns a copy of this Matrix3 without rotation.

Declaration

public Matrix3 ClearRotation()

Returns

Type	Description
Matrix3	The matrix without rotation.

ClearScale()

Returns a copy of this Matrix3 without scale.

Declaration

public Matrix3 ClearScale()

Returns

Type	Description
Matrix3	The matrix without scaling.

CreateFromAxisAngle(Vector3, float, out Matrix3)

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

Declaration

public static void CreateFromAxisAngle(Vector3 axis, float angle, out Matrix3 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).
Matrix3	result	A matrix instance.

CreateFromAxisAngle(Vector3, float)

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

Declaration

[Pure]
public static Matrix3 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
Matrix3	A matrix instance.

CreateFromQuaternion(Quaternion)

Build a rotation matrix from the specified quaternion.

Declaration

[Pure]
public static Matrix3 CreateFromQuaternion(Quaternion q)

Parameters

Type	Name	Description
Quaternion	q	Quaternion to translate.

Returns

Type	Description
Matrix3	A matrix instance.

CreateFromQuaternion(in Quaternion, out Matrix3)

Build a rotation matrix from the specified quaternion.

Declaration

public static void CreateFromQuaternion(in Quaternion q, out Matrix3 result)

Parameters

Type	Name	Description
Quaternion	q	Quaternion to translate.
Matrix3	result	Matrix result.

CreateRotationX(float, out Matrix3)

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

Declaration

public static void CreateRotationX(float angle, out Matrix3 result)

Parameters

Type	Name	Description
float	angle	The counter-clockwise angle in radians.
Matrix3	result	The resulting Matrix3 instance.

CreateRotationX(float)

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

Declaration

[Pure]
public static Matrix3 CreateRotationX(float angle)

Parameters

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

Returns

Type	Description
Matrix3	The resulting Matrix3 instance.

CreateRotationY(float, out Matrix3)

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

Declaration

public static void CreateRotationY(float angle, out Matrix3 result)

Parameters

Type	Name	Description
float	angle	The counter-clockwise angle in radians.
Matrix3	result	The resulting Matrix3 instance.

CreateRotationY(float)

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

Declaration

[Pure]
public static Matrix3 CreateRotationY(float angle)

Parameters

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

Returns

Type	Description
Matrix3	The resulting Matrix3 instance.

CreateRotationZ(float, out Matrix3)

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

Declaration

public static void CreateRotationZ(float angle, out Matrix3 result)

Parameters

Type	Name	Description
float	angle	The counter-clockwise angle in radians.
Matrix3	result	The resulting Matrix3 instance.

CreateRotationZ(float)

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

Declaration

[Pure]
public static Matrix3 CreateRotationZ(float angle)

Parameters

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

Returns

Type	Description
Matrix3	The resulting Matrix3 instance.

CreateScale(Vector3)

Creates a scale matrix.

Declaration

[Pure]
public static Matrix3 CreateScale(Vector3 scale)

Parameters

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

Returns

Type	Description
Matrix3	A scale matrix.

CreateScale(in Vector3, out Matrix3)

Creates a scale matrix.

Declaration

public static void CreateScale(in Vector3 scale, out Matrix3 result)

Parameters

Type	Name	Description
Vector3	scale	Scale factors for the x, y, and z axes.
Matrix3	result	A scale matrix.

CreateScale(float, out Matrix3)

Creates a scale matrix.

Declaration

public static void CreateScale(float scale, out Matrix3 result)

Parameters

Type	Name	Description
float	scale	Single scale factor for the x, y, and z axes.
Matrix3	result	A scale matrix.

CreateScale(float, float, float, out Matrix3)

Creates a scale matrix.

Declaration

public static void CreateScale(float x, float y, float z, out Matrix3 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.
Matrix3	result	A scale matrix.

CreateScale(float, float, float)

Creates a scale matrix.

Declaration

[Pure]
public static Matrix3 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
Matrix3	A scale matrix.

CreateScale(float)

Creates a scale matrix.

Declaration

[Pure]
public static Matrix3 CreateScale(float scale)

Parameters

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

Returns

Type	Description
Matrix3	A scale matrix.

Equals(Matrix3)

Indicates whether the current matrix is equal to another matrix.

Declaration

[Pure]
public bool Equals(Matrix3 other)

Parameters

Type	Name	Description
Matrix3	other	A 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 bool Equals(object obj)

Parameters

Type	Name	Description
object	obj	The object to compare to.

Returns

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

Overrides

ValueType.Equals(object)

ExtractRotation(bool)

Returns the rotation component of this instance. Quite slow.

Declaration

public 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 Vector3 ExtractScale()

Returns

Type	Description
Vector3	The scale components.

GetHashCode()

Returns the hashcode for this instance.

Declaration

public override 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(Matrix3)

Calculate the inverse of the given matrix.

Declaration

[Pure]
public static Matrix3 Invert(Matrix3 mat)

Parameters

Type	Name	Description
Matrix3	mat	The matrix to invert.

Returns

Type	Description
Matrix3	The inverse of the given matrix.

Exceptions

Type	Condition
InvalidOperationException	Thrown if the Matrix4 is singular.

Invert(in Matrix3, out Matrix3)

Calculate the inverse of the given matrix.

Declaration

public static void Invert(in Matrix3 matrix, out Matrix3 result)

Parameters

Type	Name	Description
Matrix3	matrix	The matrix to invert.
Matrix3	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 Matrix3 is singular.

Inverted()

Returns an inverted copy of this instance.

Declaration

public Matrix3 Inverted()

Returns

Type	Description
Matrix3	The inverted copy.

Mult(Matrix3, Matrix3)

Multiplies two instances.

Declaration

[Pure]
public static Matrix3 Mult(Matrix3 left, Matrix3 right)

Parameters

Type	Name	Description
Matrix3	left	The left operand of the multiplication.
Matrix3	right	The right operand of the multiplication.

Returns

Type	Description
Matrix3	A new instance that is the result of the multiplication.

Mult(in Matrix3, in Matrix3, out Matrix3)

Multiplies two instances.

Declaration

public static void Mult(in Matrix3 left, in Matrix3 right, out Matrix3 result)

Parameters

Type	Name	Description
Matrix3	left	The left operand of the multiplication.
Matrix3	right	The right operand of the multiplication.
Matrix3	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 Matrix3 Normalized()

Returns

Type	Description
Matrix3	The normalized copy.

ToString()

Returns a System.String that represents the current Matrix3d.

Declaration

public override string ToString()

Returns

Type	Description
string	The string representation of the matrix.

Overrides

ValueType.ToString()

ToString(IFormatProvider)

Declaration

public string ToString(IFormatProvider formatProvider)

Parameters

Type	Name	Description
IFormatProvider	formatProvider

Returns

Type	Description
string

ToString(string, IFormatProvider)

Declaration

public string ToString(string format, IFormatProvider formatProvider)

Parameters

Type	Name	Description
string	format
IFormatProvider	formatProvider

Returns

Type	Description
string

ToString(string)

Declaration

public string ToString(string format)

Parameters

Type	Name	Description
string	format

Returns

Type	Description
string

Transpose()

Converts this instance into its transpose.

Declaration

public void Transpose()

Transpose(Matrix3)

Calculate the transpose of the given matrix.

Declaration

[Pure]
public static Matrix3 Transpose(Matrix3 mat)

Parameters

Type	Name	Description
Matrix3	mat	The matrix to transpose.

Returns

Type	Description
Matrix3	The transpose of the given matrix.

Transpose(in Matrix3, out Matrix3)

Calculate the transpose of the given matrix.

Declaration

public static void Transpose(in Matrix3 mat, out Matrix3 result)

Parameters

Type	Name	Description
Matrix3	mat	The matrix to transpose.
Matrix3	result	The result of the calculation.

Operators

operator ==(Matrix3, Matrix3)

Compares two instances for equality.

Declaration

[Pure]
public static bool operator ==(Matrix3 left, Matrix3 right)

Parameters

Type	Name	Description
Matrix3	left	The first instance.
Matrix3	right	The second instance.

Returns

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

operator !=(Matrix3, Matrix3)

Compares two instances for inequality.

Declaration

[Pure]
public static bool operator !=(Matrix3 left, Matrix3 right)

Parameters

Type	Name	Description
Matrix3	left	The first instance.
Matrix3	right	The second instance.

Returns

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

operator *(Matrix3, Matrix3)

Matrix multiplication.

Declaration

[Pure]
public static Matrix3 operator *(Matrix3 left, Matrix3 right)

Parameters

Type	Name	Description
Matrix3	left	left-hand operand.
Matrix3	right	right-hand operand.

Returns

Type	Description
Matrix3	A new Matrix3d which holds the result of the multiplication.

Implements

IEquatable<T>

IFormattable