Struct Matrix3d

Represents a 3x3 matrix containing 3D rotation and scale with double-precision components.

Implements

IEquatable<Matrix3d>

IFormattable

Inherited Members

object.Equals(object, object)

object.GetType()

object.ReferenceEquals(object, object)

Namespace: OpenTK.Mathematics

Assembly: OpenTK.Mathematics.dll

Syntax

[Serializable]
public struct Matrix3d : IEquatable<Matrix3d>, IFormattable

Constructors

Matrix3d(Matrix4d)

Initializes a new instance of the Matrix3d struct.

Declaration

public Matrix3d(Matrix4d matrix)

Parameters

Type	Name	Description
Matrix4d	matrix	A Matrix4d to take the upper-left 3x3 from.

Matrix3d(Vector3d, Vector3d, Vector3d)

Initializes a new instance of the Matrix3d struct.

Declaration

public Matrix3d(Vector3d row0, Vector3d row1, Vector3d row2)

Parameters

Type	Name	Description
Vector3d	row0	Top row of the matrix.
Vector3d	row1	Second row of the matrix.
Vector3d	row2	Bottom row of the matrix.

Matrix3d(double, double, double, double, double, double, double, double, double)

Initializes a new instance of the Matrix3d struct.

Declaration

public Matrix3d(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)

Parameters

Type	Name	Description
double	m00	First item of the first row of the matrix.
double	m01	Second item of the first row of the matrix.
double	m02	Third item of the first row of the matrix.
double	m10	First item of the second row of the matrix.
double	m11	Second item of the second row of the matrix.
double	m12	Third item of the second row of the matrix.
double	m20	First item of the third row of the matrix.
double	m21	Second item of the third row of the matrix.
double	m22	Third item of the third row of the matrix.

Fields

Identity

The identity matrix.

Declaration

public static readonly Matrix3d Identity

Field Value

Type	Description
Matrix3d

Row0

First row of the matrix.

Declaration

public Vector3d Row0

Field Value

Type	Description
Vector3d

Row1

Second row of the matrix.

Declaration

public Vector3d Row1

Field Value

Type	Description
Vector3d

Row2

Third row of the matrix.

Declaration

public Vector3d Row2

Field Value

Type	Description
Vector3d

Zero

The zero matrix.

Declaration

public static readonly Matrix3d Zero

Field Value

Type	Description
Matrix3d

Properties

Column0

Gets the first column of this matrix.

Declaration

public Vector3d Column0 { readonly get; set; }

Property Value

Type	Description
Vector3d

Column1

Gets the second column of this matrix.

Declaration

public Vector3d Column1 { readonly get; set; }

Property Value

Type	Description
Vector3d

Column2

Gets the third column of this matrix.

Declaration

public Vector3d Column2 { readonly get; set; }

Property Value

Type	Description
Vector3d

Determinant

Gets the determinant of this matrix.

Declaration

public readonly double Determinant { get; }

Property Value

Type	Description
double

Diagonal

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

Declaration

public Vector3d Diagonal { readonly get; set; }

Property Value

Type	Description
Vector3d

this[int, int]

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

Declaration

public double 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
double

M11

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

Declaration

public double M11 { readonly get; set; }

Property Value

Type	Description
double

M12

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

Declaration

public double M12 { readonly get; set; }

Property Value

Type	Description
double

M13

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

Declaration

public double M13 { readonly get; set; }

Property Value

Type	Description
double

M21

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

Declaration

public double M21 { readonly get; set; }

Property Value

Type	Description
double

M22

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

Declaration

public double M22 { readonly get; set; }

Property Value

Type	Description
double

M23

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

Declaration

public double M23 { readonly get; set; }

Property Value

Type	Description
double

M31

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

Declaration

public double M31 { readonly get; set; }

Property Value

Type	Description
double

M32

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

Declaration

public double M32 { readonly get; set; }

Property Value

Type	Description
double

M33

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

Declaration

public double M33 { readonly get; set; }

Property Value

Type	Description
double

Trace

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

Declaration

public readonly double Trace { get; }

Property Value

Type	Description
double

Methods

Add(Matrix3d, Matrix3d)

Adds two instances.

Declaration

[Pure]
public static Matrix3d Add(Matrix3d left, Matrix3d right)

Parameters

Type	Name	Description
Matrix3d	left	The left operand of the addition.
Matrix3d	right	The right operand of the addition.

Returns

Type	Description
Matrix3d	A new instance that is the result of the addition.

Add(in Matrix3d, in Matrix3d, out Matrix3d)

Adds two instances.

Declaration

public static void Add(in Matrix3d left, in Matrix3d right, out Matrix3d result)

Parameters

Type	Name	Description
Matrix3d	left	The left operand of the addition.
Matrix3d	right	The right operand of the addition.
Matrix3d	result	A new instance that is the result of the addition.

ClearRotation()

Returns a copy of this Matrix3 without rotation.

Declaration

public readonly Matrix3d ClearRotation()

Returns

Type	Description
Matrix3d	The matrix without rotation.

ClearScale()

Returns a copy of this Matrix3 without scale.

Declaration

public readonly Matrix3d ClearScale()

Returns

Type	Description
Matrix3d	The matrix without scaling.

CreateFromAxisAngle(Vector3d, double)

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

Declaration

[Pure]
public static Matrix3d CreateFromAxisAngle(Vector3d axis, double angle)

Parameters

Type	Name	Description
Vector3d	axis	The axis to rotate about.
double	angle	Angle in radians to rotate counter-clockwise (looking in the direction of the given axis).

Returns

Type	Description
Matrix3d	A matrix instance.

CreateFromAxisAngle(Vector3d, double, out Matrix3d)

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

Declaration

public static void CreateFromAxisAngle(Vector3d axis, double angle, out Matrix3d result)

Parameters

Type	Name	Description
Vector3d	axis	The axis to rotate about.
double	angle	Angle in radians to rotate counter-clockwise (looking in the direction of the given axis).
Matrix3d	result	A matrix instance.

CreateFromQuaternion(Quaterniond)

Build a rotation matrix from the specified quaternion.

Declaration

[Pure]
public static Matrix3d CreateFromQuaternion(Quaterniond q)

Parameters

Type	Name	Description
Quaterniond	q	Quaternion to translate.

Returns

Type	Description
Matrix3d	A matrix instance.

CreateFromQuaternion(in Quaterniond, out Matrix3d)

Build a rotation matrix from the specified quaternion.

Declaration

public static void CreateFromQuaternion(in Quaterniond q, out Matrix3d result)

Parameters

Type	Name	Description
Quaterniond	q	Quaternion to translate.
Matrix3d	result	Matrix result.

CreateRotationX(double)

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

Declaration

[Pure]
public static Matrix3d CreateRotationX(double angle)

Parameters

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

Returns

Type	Description
Matrix3d	The resulting Matrix3d instance.

CreateRotationX(double, out Matrix3d)

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

Declaration

public static void CreateRotationX(double angle, out Matrix3d result)

Parameters

Type	Name	Description
double	angle	The counter-clockwise angle in radians.
Matrix3d	result	The resulting Matrix3d instance.

CreateRotationY(double)

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

Declaration

[Pure]
public static Matrix3d CreateRotationY(double angle)

Parameters

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

Returns

Type	Description
Matrix3d	The resulting Matrix3d instance.

CreateRotationY(double, out Matrix3d)

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

Declaration

public static void CreateRotationY(double angle, out Matrix3d result)

Parameters

Type	Name	Description
double	angle	The counter-clockwise angle in radians.
Matrix3d	result	The resulting Matrix3d instance.

CreateRotationZ(double)

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

Declaration

[Pure]
public static Matrix3d CreateRotationZ(double angle)

Parameters

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

Returns

Type	Description
Matrix3d	The resulting Matrix3d instance.

CreateRotationZ(double, out Matrix3d)

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

Declaration

public static void CreateRotationZ(double angle, out Matrix3d result)

Parameters

Type	Name	Description
double	angle	The counter-clockwise angle in radians.
Matrix3d	result	The resulting Matrix3d instance.

CreateScale(Vector3d)

Creates a scale matrix.

Declaration

[Pure]
public static Matrix3d CreateScale(Vector3d scale)

Parameters

Type	Name	Description
Vector3d	scale	Scale factors for the x, y, and z axes.

Returns

Type	Description
Matrix3d	A scale matrix.

CreateScale(in Vector3d, out Matrix3d)

Creates a scale matrix.

Declaration

public static void CreateScale(in Vector3d scale, out Matrix3d result)

Parameters

Type	Name	Description
Vector3d	scale	Scale factors for the x, y, and z axes.
Matrix3d	result	A scale matrix.

CreateScale(double)

Creates a scale matrix.

Declaration

[Pure]
public static Matrix3d CreateScale(double scale)

Parameters

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

Returns

Type	Description
Matrix3d	A scale matrix.

CreateScale(double, out Matrix3d)

Creates a scale matrix.

Declaration

public static void CreateScale(double scale, out Matrix3d result)

Parameters

Type	Name	Description
double	scale	Single scale factor for the x, y, and z axes.
Matrix3d	result	A scale matrix.

CreateScale(double, double, double)

Creates a scale matrix.

Declaration

[Pure]
public static Matrix3d CreateScale(double x, double y, double z)

Parameters

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

Returns

Type	Description
Matrix3d	A scale matrix.

CreateScale(double, double, double, out Matrix3d)

Creates a scale matrix.

Declaration

public static void CreateScale(double x, double y, double z, out Matrix3d result)

Parameters

Type	Name	Description
double	x	Scale factor for the x axis.
double	y	Scale factor for the y axis.
double	z	Scale factor for the z axis.
Matrix3d	result	A scale matrix.

CreateSwizzle(int, int, int)

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

Declaration

public static Matrix3d CreateSwizzle(int rowForRow0, int rowForRow1, int rowForRow2)

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.

Returns

Type	Description
Matrix3d	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, out Matrix3d)

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, out Matrix3d 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.
Matrix3d	result	The resulting swizzle matrix.

Remarks

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

Equals(Matrix3d)

Indicates whether the current matrix is equal to another matrix.

Declaration

[Pure]
public readonly bool Equals(Matrix3d other)

Parameters

Type	Name	Description
Matrix3d	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 readonly 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

[Pure]
public readonly Quaterniond 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
Quaterniond	The rotation.

ExtractScale()

Returns the scale component of this instance.

Declaration

public readonly Vector3d ExtractScale()

Returns

Type	Description
Vector3d	The scale components.

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(Matrix3d)

Calculate the inverse of the given matrix.

Declaration

[Pure]
public static Matrix3d Invert(Matrix3d mat)

Parameters

Type	Name	Description
Matrix3d	mat	The matrix to invert.

Returns

Type	Description
Matrix3d	The inverse of the given matrix.

Exceptions

Type	Condition
InvalidOperationException	Thrown if the Matrix4 is singular.

Invert(in Matrix3d, out Matrix3d)

Calculate the inverse of the given matrix.

Declaration

public static void Invert(in Matrix3d matrix, out Matrix3d result)

Parameters

Type	Name	Description
Matrix3d	matrix	The matrix to invert.
Matrix3d	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 Matrix3d is singular.

Inverted()

Returns an inverted copy of this instance.

Declaration

public readonly Matrix3d Inverted()

Returns

Type	Description
Matrix3d	The inverted copy.

Remarks

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

Mult(Matrix3d, Matrix3d)

Multiplies two instances.

Declaration

[Pure]
public static Matrix3d Mult(Matrix3d left, Matrix3d right)

Parameters

Type	Name	Description
Matrix3d	left	The left operand of the multiplication.
Matrix3d	right	The right operand of the multiplication.

Returns

Type	Description
Matrix3d	A new instance that is the result of the multiplication.

Mult(in Matrix3d, in Matrix3d, out Matrix3d)

Multiplies two instances.

Declaration

public static void Mult(in Matrix3d left, in Matrix3d right, out Matrix3d result)

Parameters

Type	Name	Description
Matrix3d	left	The left operand of the multiplication.
Matrix3d	right	The right operand of the multiplication.
Matrix3d	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 Matrix3d Normalized()

Returns

Type	Description
Matrix3d	The normalized copy.

Swizzle(Matrix3d, int, int, int)

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

Declaration

public static Matrix3d Swizzle(Matrix3d mat, int rowForRow0, int rowForRow1, int rowForRow2)

Parameters

Type	Name	Description
Matrix3d	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.

Returns

Type	Description
Matrix3d	The swizzled matrix.

Exceptions

Type	Condition
IndexOutOfRangeException	If any of the rows are outside of the range [0, 2].

Swizzle(in Matrix3d, int, int, int, out Matrix3d)

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

Declaration

public static void Swizzle(in Matrix3d mat, int rowForRow0, int rowForRow1, int rowForRow2, out Matrix3d result)

Parameters

Type	Name	Description
Matrix3d	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.
Matrix3d	result	The swizzled matrix.

Exceptions

Type	Condition
IndexOutOfRangeException	If any of the rows are outside of the range [0, 2].

Swizzle(int, int, int)

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

Declaration

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

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.

Swizzled(int, int, int)

Returns a swizzled copy of this instance.

Declaration

public readonly Matrix3d Swizzled(int rowForRow0, int rowForRow1, int rowForRow2)

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.

Returns

Type	Description
Matrix3d	The swizzled copy.

ToString()

Returns a System.String that represents the current Matrix3d.

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(Matrix3d)

Calculate the transpose of the given matrix.

Declaration

[Pure]
public static Matrix3d Transpose(Matrix3d mat)

Parameters

Type	Name	Description
Matrix3d	mat	The matrix to transpose.

Returns

Type	Description
Matrix3d	The transpose of the given matrix.

Transpose(in Matrix3d, out Matrix3d)

Calculate the transpose of the given matrix.

Declaration

public static void Transpose(in Matrix3d mat, out Matrix3d result)

Parameters

Type	Name	Description
Matrix3d	mat	The matrix to transpose.
Matrix3d	result	The result of the calculation.

Transposed()

Returns a transposed copy of this instance.

Declaration

public readonly Matrix3d Transposed()

Returns

Type	Description
Matrix3d	The transposed copy.

Operators

operator ==(Matrix3d, Matrix3d)

Compares two instances for equality.

Declaration

[Pure]
public static bool operator ==(Matrix3d left, Matrix3d right)

Parameters

Type	Name	Description
Matrix3d	left	The first instance.
Matrix3d	right	The second instance.

Returns

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

operator !=(Matrix3d, Matrix3d)

Compares two instances for inequality.

Declaration

[Pure]
public static bool operator !=(Matrix3d left, Matrix3d right)

Parameters

Type	Name	Description
Matrix3d	left	The first instance.
Matrix3d	right	The second instance.

Returns

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

operator *(Matrix3d, Matrix3d)

Matrix multiplication.

Declaration

[Pure]
public static Matrix3d operator *(Matrix3d left, Matrix3d right)

Parameters

Type	Name	Description
Matrix3d	left	left-hand operand.
Matrix3d	right	right-hand operand.

Returns

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

Implements

IEquatable<T>

IFormattable