Struct Matrix3x3

A structure representing 3x3 matrix.

Namespace: ISynergy.Framework.Mathematics

Assembly: ISynergy.Framework.Mathematics.dll

Syntax

public struct Matrix3x3

Remarks

The structure incapsulates elements of a 3x3 matrix and provides some operations with it.

Fields

V00

Row 0 column 0 element of the matrix.

Declaration

public float V00

Field Value

Type	Description
System.Single

V01

Row 0 column 1 element of the matrix.

Declaration

public float V01

Field Value

Type	Description
System.Single

V02

Row 0 column 2 element of the matrix.

Declaration

public float V02

Field Value

Type	Description
System.Single

V10

Row 1 column 0 element of the matrix.

Declaration

public float V10

Field Value

Type	Description
System.Single

V11

Row 1 column 1 element of the matrix.

Declaration

public float V11

Field Value

Type	Description
System.Single

V12

Row 1 column 2 element of the matrix.

Declaration

public float V12

Field Value

Type	Description
System.Single

V20

Row 2 column 0 element of the matrix.

Declaration

public float V20

Field Value

Type	Description
System.Single

V21

Row 2 column 1 element of the matrix.

Declaration

public float V21

Field Value

Type	Description
System.Single

V22

Row 2 column 2 element of the matrix.

Declaration

public float V22

Field Value

Type	Description
System.Single

Properties

Determinant

Calculates determinant of the matrix.

Declaration

public readonly float Determinant { get; }

Property Value

Type	Description
System.Single

Identity

Provides an identity matrix with all diagonal elements set to 1.

Declaration

public static readonly Matrix3x3 Identity { get; }

Property Value

Type	Description
Matrix3x3

Methods

Add(Matrix3x3, Matrix3x3)

Adds corresponding components of two matrices.

Declaration

public static Matrix3x3 Add(Matrix3x3 matrix1, Matrix3x3 matrix2)

Parameters

Type	Name	Description
Matrix3x3	matrix1	The matrix to add to.
Matrix3x3	matrix2	The matrix to add to the first matrix.

Returns

Type	Description
Matrix3x3	Returns a matrix which components are equal to sum of corresponding components of the two specified matrices.

Add(Matrix3x3, Single)

Adds specified value to all components of the specified matrix.

Declaration

public static Matrix3x3 Add(Matrix3x3 matrix, float value)

Parameters

Type	Name	Description
Matrix3x3	matrix	Matrix to add value to.
System.Single	value	Value to add to all components of the specified matrix.

Returns

Type	Description
Matrix3x3	Returns new matrix with all components equal to corresponding components of the specified matrix increased by the specified value.

Adjugate()

Calculate adjugate of the matrix, adj(A).

Declaration

public Matrix3x3 Adjugate()

Returns

Type	Description
Matrix3x3	Returns adjugate of the matrix.

CreateDiagonal(Vector3)

Creates a diagonal matrix using the specified vector as diagonal elements.

Declaration

public static Matrix3x3 CreateDiagonal(Vector3 vector)

Parameters

Type	Name	Description
Vector3	vector	Vector to use for diagonal elements of the matrix.

Returns

Type	Description
Matrix3x3	Returns a diagonal matrix.

CreateFromColumns(Vector3, Vector3, Vector3)

Creates a matrix from 3 columns specified as vectors.

Declaration

public static Matrix3x3 CreateFromColumns(Vector3 column0, Vector3 column1, Vector3 column2)

Parameters

Type	Name	Description
Vector3	column0	First column of the matrix to create.
Vector3	column1	Second column of the matrix to create.
Vector3	column2	Third column of the matrix to create.

Returns

Type	Description
Matrix3x3	Returns a matrix from specified columns.

CreateFromRows(Vector3, Vector3, Vector3)

Creates a matrix from 3 rows specified as vectors.

Declaration

public static Matrix3x3 CreateFromRows(Vector3 row0, Vector3 row1, Vector3 row2)

Parameters

Type	Name	Description
Vector3	row0	First row of the matrix to create.
Vector3	row1	Second row of the matrix to create.
Vector3	row2	Third row of the matrix to create.

Returns

Type	Description
Matrix3x3	Returns a matrix from specified rows.

CreateFromYawPitchRoll(Single, Single, Single)

Creates rotation matrix to rotate an object around X, Y and Z axes.

Declaration

public static Matrix3x3 CreateFromYawPitchRoll(float yaw, float pitch, float roll)

Parameters

Type	Name	Description
System.Single	yaw	Rotation angle around Y axis in radians.
System.Single	pitch	Rotation angle around X axis in radians.
System.Single	roll	Rotation angle around Z axis in radians.

Returns

Type	Description
Matrix3x3	Returns rotation matrix to rotate an object around all 3 axes.

Remarks

note

The routine assumes roll-pitch-yaw rotation order, when creating rotation matrix, i.e. an object is first rotated around Z axis, then around X axis and finally around Y axis.

CreateRotationX(Single)

Creates rotation matrix around X axis.

Declaration

public static Matrix3x3 CreateRotationX(float radians)

Parameters

Type	Name	Description
System.Single	radians	Rotation angle around X axis in radians.

Returns

Type	Description
Matrix3x3	Returns rotation matrix to rotate an object around X axis.

CreateRotationY(Single)

Creates rotation matrix around Y axis.

Declaration

public static Matrix3x3 CreateRotationY(float radians)

Parameters

Type	Name	Description
System.Single	radians	Rotation angle around Y axis in radians.

Returns

Type	Description
Matrix3x3	Returns rotation matrix to rotate an object around Y axis.

CreateRotationZ(Single)

Creates rotation matrix around Z axis.

Declaration

public static Matrix3x3 CreateRotationZ(float radians)

Parameters

Type	Name	Description
System.Single	radians	Rotation angle around Z axis in radians.

Returns

Type	Description
Matrix3x3	Returns rotation matrix to rotate an object around Z axis.

Equals(Matrix3x3)

Tests whether the matrix equals to the specified one.

Declaration

public bool Equals(Matrix3x3 matrix)

Parameters

Type	Name	Description
Matrix3x3	matrix	The matrix to test equality with.

Returns

Type	Description
System.Boolean	Returns true if the two matrices are equal or false otherwise.

Equals(Object)

Tests whether the matrix equals to the specified object.

Declaration

public override bool Equals(object obj)

Parameters

Type	Name	Description
System.Object	obj	The object to test equality with.

Returns

Type	Description
System.Boolean	Returns true if the matrix equals to the specified object or false otherwise.

ExtractYawPitchRoll(out Single, out Single, out Single)

Extract rotation angles from the rotation matrix.

Declaration

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

Parameters

Type	Name	Description
System.Single	yaw	Extracted rotation angle around Y axis in radians.
System.Single	pitch	Extracted rotation angle around X axis in radians.
System.Single	roll	Extracted rotation angle around Z axis in radians.

Remarks

note

The routine assumes roll-pitch-yaw rotation order when extracting rotation angle. Using extracted angles with the CreateFromYawPitchRoll(Single, Single, Single) should provide same rotation matrix.

note

The method assumes the provided matrix represent valid rotation matrix.

Sample usage:

// assume we have a rotation matrix created like this
float yaw   = 10.0f / 180 * Math.PI;
float pitch = 30.0f / 180 * Math.PI;
float roll  = 45.0f / 180 * Math.PI;
Matrix3x3 rotationMatrix = Matrix3x3.CreateFromYawPitchRoll( yaw, pitch, roll );
// ...
// now somewhere in the code you may want to get rotation
// angles back from a matrix assuming same rotation order
float extractedYaw;
float extractedPitch;
float extractedRoll;
rotation.ExtractYawPitchRoll( out extractedYaw, out extractedPitch, out extractedRoll );

GetColumn(Int32)

Get column of the matrix.

Declaration

public Vector3 GetColumn(int index)

Parameters

Type	Name	Description
System.Int32	index	Column index to get, [0, 2].

Returns

Type	Description
Vector3	Returns specified column of the matrix as a vector.

GetHashCode()

Returns the hashcode for this instance.

Declaration

public override int GetHashCode()

Returns

Type	Description
System.Int32	A 32-bit signed integer hash code.

GetRow(Int32)

Get row of the matrix.

Declaration

public Vector3 GetRow(int index)

Parameters

Type	Name	Description
System.Int32	index	Row index to get, [0, 2].

Returns

Type	Description
Vector3	Returns specified row of the matrix as a vector.

Inverse()

Calculate inverse of the matrix, A^-1.

Declaration

public Matrix3x3 Inverse()

Returns

Type	Description
Matrix3x3	Returns inverse of the matrix.

Multiply(Matrix3x3, Matrix3x3)

Multiplies two specified matrices.

Declaration

public static Matrix3x3 Multiply(Matrix3x3 matrix1, Matrix3x3 matrix2)

Parameters

Type	Name	Description
Matrix3x3	matrix1	Matrix to multiply.
Matrix3x3	matrix2	Matrix to multiply by.

Returns

Type	Description
Matrix3x3	Return new matrix, which the result of multiplication of the two specified matrices.

Multiply(Matrix3x3, Vector3)

Multiplies specified matrix by the specified vector.

Declaration

public static Vector3 Multiply(Matrix3x3 matrix, Vector3 vector)

Parameters

Type	Name	Description
Matrix3x3	matrix	Matrix to multiply by vector.
Vector3	vector	Vector to multiply matrix by.

Returns

Type	Description
Vector3	Returns new vector which is the result of multiplication of the specified matrix by the specified vector.

Multiply(Matrix3x3, Single)

Multiplies matrix by the specified factor.

Declaration

public static Matrix3x3 Multiply(Matrix3x3 matrix, float factor)

Parameters

Type	Name	Description
Matrix3x3	matrix	Matrix to multiply.
System.Single	factor	Factor to multiple the specified matrix by.

Returns

Type	Description
Matrix3x3	Returns new matrix with all components equal to corresponding components of the specified matrix multiples by the specified factor.

MultiplySelfByTranspose()

Multiply the matrix by its transposition, A*A^T.

Declaration

public Matrix3x3 MultiplySelfByTranspose()

Returns

Type	Description
Matrix3x3	Returns a matrix which is the result of multiplying this matrix by its transposition.

MultiplyTransposeBySelf()

Multiply transposition of this matrix by itself, A^T*A.

Declaration

public Matrix3x3 MultiplyTransposeBySelf()

Returns

Type	Description
Matrix3x3	Returns a matrix which is the result of multiplying this matrix's transposition by itself.

PseudoInverse()

Calculate pseudo inverse of the matrix, A⁺.

Declaration

public Matrix3x3 PseudoInverse()

Returns

Type	Description
Matrix3x3	Returns pseudo inverse of the matrix.

Remarks

The pseudo inverse of the matrix is calculate through its SVD(out Matrix3x3, out Vector3, out Matrix3x3) as V*E⁺*U^T.

Subtract(Matrix3x3, Matrix3x3)

Subtracts corresponding components of two matrices.

Declaration

public static Matrix3x3 Subtract(Matrix3x3 matrix1, Matrix3x3 matrix2)

Parameters

Type	Name	Description
Matrix3x3	matrix1	The matrix to subtract from.
Matrix3x3	matrix2	The matrix to subtract from the first matrix.

Returns

Type	Description
Matrix3x3	Returns a matrix which components are equal to difference of corresponding components of the two specified matrices.

SVD(out Matrix3x3, out Vector3, out Matrix3x3)

Calculate Singular Value Decomposition (SVD) of the matrix, such as A=UEV^T.

Declaration

public void SVD(out Matrix3x3 u, out Vector3 e, out Matrix3x3 v)

Parameters

Type	Name	Description
Matrix3x3	u	Output parameter which gets 3x3 U matrix.
Vector3	e	Output parameter which gets diagonal elements of the E matrix.
Matrix3x3	v	Output parameter which gets 3x3 V matrix.

Remarks

Having components U, E and V the source matrix can be reproduced using below code:

Matrix3x3 source = u * Matrix3x3.Diagonal( e ) * v.Transpose( );

ToArray()

Returns array representation of the matrix.

Declaration

public float[] ToArray()

Returns

Type	Description
System.Single[]	Returns array which contains all elements of the matrix in the row-major order.

Transpose()

Transpose the matrix, A^T.

Declaration

public Matrix3x3 Transpose()

Returns

Type	Description
Matrix3x3	Return a matrix which equals to transposition of this matrix.

Operators

Addition(Matrix3x3, Matrix3x3)

Adds corresponding components of two matrices.

Declaration

public static Matrix3x3 operator +(Matrix3x3 matrix1, Matrix3x3 matrix2)

Parameters

Type	Name	Description
Matrix3x3	matrix1	The matrix to add to.
Matrix3x3	matrix2	The matrix to add to the first matrix.

Returns

Type	Description
Matrix3x3	Returns a matrix which components are equal to sum of corresponding components of the two specified matrices.

Addition(Matrix3x3, Single)

Adds specified value to all components of the specified matrix.

Declaration

public static Matrix3x3 operator +(Matrix3x3 matrix, float value)

Parameters

Type	Name	Description
Matrix3x3	matrix	Matrix to add value to.
System.Single	value	Value to add to all components of the specified matrix.

Returns

Type	Description
Matrix3x3	Returns new matrix with all components equal to corresponding components of the specified matrix increased by the specified value.

Equality(Matrix3x3, Matrix3x3)

Tests whether two specified matrices are equal.

Declaration

public static bool operator ==(Matrix3x3 matrix1, Matrix3x3 matrix2)

Parameters

Type	Name	Description
Matrix3x3	matrix1	The left-hand matrix.
Matrix3x3	matrix2	The right-hand matrix.

Returns

Type	Description
System.Boolean	Returns true if the two matrices are equal or false otherwise.

Inequality(Matrix3x3, Matrix3x3)

Tests whether two specified matrices are not equal.

Declaration

public static bool operator !=(Matrix3x3 matrix1, Matrix3x3 matrix2)

Parameters

Type	Name	Description
Matrix3x3	matrix1	The left-hand matrix.
Matrix3x3	matrix2	The right-hand matrix.

Returns

Type	Description
System.Boolean	Returns true if the two matrices are not equal or false otherwise.

Multiply(Matrix3x3, Matrix3x3)

Multiplies two specified matrices.

Declaration

public static Matrix3x3 operator *(Matrix3x3 matrix1, Matrix3x3 matrix2)

Parameters

Type	Name	Description
Matrix3x3	matrix1	Matrix to multiply.
Matrix3x3	matrix2	Matrix to multiply by.

Returns

Type	Description
Matrix3x3	Return new matrix, which the result of multiplication of the two specified matrices.

Multiply(Matrix3x3, Vector3)

Multiplies specified matrix by the specified vector.

Declaration

public static Vector3 operator *(Matrix3x3 matrix, Vector3 vector)

Parameters

Type	Name	Description
Matrix3x3	matrix	Matrix to multiply by vector.
Vector3	vector	Vector to multiply matrix by.

Returns

Type	Description
Vector3	Returns new vector which is the result of multiplication of the specified matrix by the specified vector.

Multiply(Matrix3x3, Single)

Multiplies matrix by the specified factor.

Declaration

public static Matrix3x3 operator *(Matrix3x3 matrix, float factor)

Parameters

Type	Name	Description
Matrix3x3	matrix	Matrix to multiply.
System.Single	factor	Factor to multiple the specified matrix by.

Returns

Type	Description
Matrix3x3	Returns new matrix with all components equal to corresponding components of the specified matrix multiples by the specified factor.

Subtraction(Matrix3x3, Matrix3x3)

Subtracts corresponding components of two matrices.

Declaration

public static Matrix3x3 operator -(Matrix3x3 matrix1, Matrix3x3 matrix2)

Parameters

Type	Name	Description
Matrix3x3	matrix1	The matrix to subtract from.
Matrix3x3	matrix2	The matrix to subtract from the first matrix.

Returns

Type	Description
Matrix3x3	Returns a matrix which components are equal to difference of corresponding components of the two specified matrices.

Extension Methods

EnumExtensions.GetSymbol<T>(T)

ArrayExtensions.Concatenate<T>(T, T[])

CollectionExtensions.FromHierarchy<TSource>(TSource, Func<TSource, TSource>, Func<TSource, Boolean>)

ObjectExtensions.Clone<T>(T)

ObjectExtensions.AddressOf<T>(T)

ObjectExtensions.ToByteArray<T>(T)

ReflectionExtensions.GetPropertyInfo<T, TValue>(T, Expression<Func<T, TValue>>)