Matrix33 Class

Namespace:: Maroontress.Euclid

Assembly:: Euclid.dll

Represents the 3x3 square matrix.

public sealed class Matrix33

Inheritance: object
Matrix33

Constructors

Matrix33(Position, Position, Position)	Initializes a new instance of the Matrix33 class.
Matrix33((float X, float Y, float Z), (float X, float Y, float Z), (float X, float Y, float Z))	Initializes a new instance of the Matrix33 class.

Properties

Identity

Gets the identity matrix.

Methods

Transpose()	Gets the transpose matrix.
Map(Position)	Translate the specified position.
Map((float X, float Y, float Z))	Translate the specified position.
Mul(Matrix33)	Gets the matrix product of `this` and `a`.
ToWxyzTuple()	Gets the quaternion representation when this matrix is the rotation matrix.
Determinant()	Gets the determinant of this matrix.
Column1()	Gets the first column vector.
Column2()	Gets the second column vector.
Column3()	Gets the third column vector.
Column1Tuple()	Gets the tuple representing the first column vector.
Column2Tuple()	Gets the tuple representing the second column vector.
Column3Tuple()	Gets the tuple representing the third column vector.
EigenvaluesAndVectors(float)	Gets the eigenvalues and eigenvectors by the Jacobi eigenvalue algorithm when this is a symmetric matrix.
Equals(object)	(Inherited from object)
GetHashCode()	(Inherited from object)
GetType()	(Inherited from object)
MemberwiseClone()	(Inherited from object)
ToString()	(Inherited from object)

Constructors Detail

Matrix33(Position, Position, Position)

Initializes a new instance of the Matrix33 class.

public Matrix33(Position cx, Position cy, Position cz)

Parameters

cx: Position

The first column vector.

cy: Position

The second column vector.

cz: Position

The third column vector.

Matrix33((float X, float Y, float Z), (float X, float Y, float Z), (float X, float Y, float Z))

Initializes a new instance of the Matrix33 class.

public Matrix33(in (float X, float Y, float Z) cx, in (float X, float Y, float Z) cy, in (float X, float Y, float Z) cz)

Parameters

cx: (float X, float Y, float Z)

The first column vector.

cy: (float X, float Y, float Z)

The second column vector.

cz: (float X, float Y, float Z)

The third column vector.

Properties Detail

Identity

Gets the identity matrix.

public static Matrix33 Identity { get; }

Property Value

Matrix33

Methods Detail

Transpose()

Gets the transpose matrix.

public Matrix33 Transpose()

Returns

Matrix33

The new transpose matrix.

Map(Position)

Translate the specified position.

public Position Map(Position p)

Parameters

p: Position

The position, which represents the column vector.

Returns

Position

The position representing the result of the matrix product.

Map((float X, float Y, float Z))

Translate the specified position.

public (float X, float Y, float Z) Map((float X, float Y, float Z) p)

Parameters

p: (float X, float Y, float Z)

The position, which represents the column vector.

Returns

(float X, float Y, float Z)

The position representing the result of the matrix product.

Mul(Matrix33)

Gets the matrix product of this and a.

public Matrix33 Mul(Matrix33 a)

Parameters

a: Matrix33

Another matrix.

Returns

Matrix33

The matrix product this matrix and a.

ToWxyzTuple()

Gets the quaternion representation when this matrix is the rotation matrix.

public (float W, float X, float Y, float Z) ToWxyzTuple()

Returns

(float W, float X, float Y, float Z)

The WXYZ tuple representing the quaternion.

Determinant()

Gets the determinant of this matrix.

public float Determinant()

Returns

float

The determinant.

Column1()

Gets the first column vector.

public Position Column1()

Returns

Position

The first column vector, which is equivalent to the result of this.Map(Position.XUnit).

Column2()

Gets the second column vector.

public Position Column2()

Returns

Position

The second column vector, which is equivalent to the result of this.Map(Position.YUnit).

Column3()

Gets the third column vector.

public Position Column3()

Returns

Position

The third column vector, which is equivalent to the result of this.Map(Position.ZUnit).

Column1Tuple()

Gets the tuple representing the first column vector.

public (float X, float Y, float Z) Column1Tuple()

Returns

(float X, float Y, float Z)

The first column vector, which is equivalent to the result of this.Map((1f, 0f, 0f)).

Column2Tuple()

Gets the tuple representing the second column vector.

public (float X, float Y, float Z) Column2Tuple()

Returns

(float X, float Y, float Z)

The second column vector, which is equivalent to the result of this.Map((0f, 1f, 0f)).

Column3Tuple()

Gets the tuple representing the third column vector.

public (float X, float Y, float Z) Column3Tuple()

Returns

(float X, float Y, float Z)

The third column vector, which is equivalent to the result of this.Map((0f, 0f, 1f)).

EigenvaluesAndVectors(float)

Gets the eigenvalues and eigenvectors by the Jacobi eigenvalue algorithm when this is a symmetric matrix.

public (Matrix33 D, Matrix33 V) EigenvaluesAndVectors(float threshold)

Parameters

threshold: float

All absolute values of off-diagonal entries in D are less than this threshold.

Returns

(Matrix33 D, Matrix33 V)

The tuple containing a diagonal matrix D and an orthogonal matrix V. The diagonal entries in D and the column vectors in V represent the eigenvalues and eigenvectors of this symmetric matrix, respectively.