Struct Matrix4x4

A structure representing 4x4 matrix.

Namespace: ISynergy.Framework.Mathematics

Assembly: ISynergy.Framework.Mathematics.dll

Syntax

public struct Matrix4x4

Remarks

The structure incapsulates elements of a 4x4 matrix and provides some operations with it.

Fields

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V00

Row 0 column 0 element of the matrix.

Declaration

public float V00

Field Value

Type	Description
System.Single

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V01

Row 0 column 1 element of the matrix.

Declaration

public float V01

Field Value

Type	Description
System.Single

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V02

Row 0 column 2 element of the matrix.

Declaration

public float V02

Field Value

Type	Description
System.Single

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V03

Row 0 column 3 element of the matrix.

Declaration

public float V03

Field Value

Type	Description
System.Single

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V10

Row 1 column 0 element of the matrix.

Declaration

public float V10

Field Value

Type	Description
System.Single

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V11

Row 1 column 1 element of the matrix.

Declaration

public float V11

Field Value

Type	Description
System.Single

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V12

Row 1 column 2 element of the matrix.

Declaration

public float V12

Field Value

Type	Description
System.Single

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V13

Row 1 column 3 element of the matrix.

Declaration

public float V13

Field Value

Type	Description
System.Single

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V20

Row 2 column 0 element of the matrix.

Declaration

public float V20

Field Value

Type	Description
System.Single

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V21

Row 2 column 1 element of the matrix.

Declaration

public float V21

Field Value

Type	Description
System.Single

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V22

Row 2 column 2 element of the matrix.

Declaration

public float V22

Field Value

Type	Description
System.Single

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V23

Row 2 column 3 element of the matrix.

Declaration

public float V23

Field Value

Type	Description
System.Single

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V30

Row 3 column 0 element of the matrix.

Declaration

public float V30

Field Value

Type	Description
System.Single

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V31

Row 3 column 1 element of the matrix.

Declaration

public float V31

Field Value

Type	Description
System.Single

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V32

Row 3 column 2 element of the matrix.

Declaration

public float V32

Field Value

Type	Description
System.Single

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V33

Row 3 column 3 element of the matrix.

Declaration

public float V33

Field Value

Type	Description
System.Single

Properties

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Identity

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

Declaration

public static readonly Matrix4x4 Identity { get; }

Property Value

Type	Description
Matrix4x4

Methods

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Add(Matrix4x4, Matrix4x4)

Adds corresponding components of two matrices.

Declaration

public static Matrix4x4 Add(Matrix4x4 matrix1, Matrix4x4 matrix2)

Parameters

Type	Name	Description
Matrix4x4	matrix1	The matrix to add to.
Matrix4x4	matrix2	The matrix to add to the first matrix.

Returns

Type	Description
Matrix4x4	Returns a matrix which components are equal to sum of corresponding components of the two specified matrices.

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CreateDiagonal(Vector4)

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

Declaration

public static Matrix4x4 CreateDiagonal(Vector4 vector)

Parameters

Type	Name	Description
Vector4	vector	Vector to use for diagonal elements of the matrix.

Returns

Type	Description
Matrix4x4	Returns a diagonal matrix.

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CreateFromColumns(Vector4, Vector4, Vector4, Vector4)

Creates a matrix from 4 columns specified as vectors.

Declaration

public static Matrix4x4 CreateFromColumns(Vector4 column0, Vector4 column1, Vector4 column2, Vector4 column3)

Parameters

Type	Name	Description
Vector4	column0	First column of the matrix to create.
Vector4	column1	Second column of the matrix to create.
Vector4	column2	Third column of the matrix to create.
Vector4	column3	Fourth column of the matrix to create.

Returns

Type	Description
Matrix4x4	Returns a matrix from specified columns.

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CreateFromRotation(Matrix3x3)

Creates 4x4 tranformation matrix from 3x3 rotation matrix.

Declaration

public static Matrix4x4 CreateFromRotation(Matrix3x3 rotationMatrix)

Parameters

Type	Name	Description
Matrix3x3	rotationMatrix	Source 3x3 rotation matrix.

Returns

Type	Description
Matrix4x4	Returns 4x4 rotation matrix.

Remarks

The source 3x3 rotation matrix is copied into the top left corner of the result 4x4 matrix, i.e. it represents 0th, 1st and 2nd row/column. The V33 element is set to 1 and the rest elements of 3rd row and 3rd column are set to zeros.

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CreateFromRows(Vector4, Vector4, Vector4, Vector4)

Creates a matrix from 4 rows specified as vectors.

Declaration

public static Matrix4x4 CreateFromRows(Vector4 row0, Vector4 row1, Vector4 row2, Vector4 row3)

Parameters

Type	Name	Description
Vector4	row0	First row of the matrix to create.
Vector4	row1	Second row of the matrix to create.
Vector4	row2	Third row of the matrix to create.
Vector4	row3	Fourth row of the matrix to create.

Returns

Type	Description
Matrix4x4	Returns a matrix from specified rows.

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CreateFromYawPitchRoll(Single, Single, Single)

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

Declaration

public static Matrix4x4 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
Matrix4x4	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.

View Source

CreateLookAt(Vector3, Vector3)

Creates a view matrix for the specified camera position and target point.

Declaration

public static Matrix4x4 CreateLookAt(Vector3 cameraPosition, Vector3 cameraTarget)

Parameters

Type	Name	Description
Vector3	cameraPosition	Position of camera.
Vector3	cameraTarget	Target point towards which camera is pointing.

Returns

Type	Description
Matrix4x4	Returns a view matrix.

Remarks

Camera's "up" vector is supposed to be (0, 1, 0).

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CreatePerspective(Single, Single, Single, Single)

Creates a perspective projection matrix.

Declaration

public static Matrix4x4 CreatePerspective(float width, float height, float nearPlaneDistance, float farPlaneDistance)

Parameters

Type	Name	Description
System.Single	width	Width of the view volume at the near view plane.
System.Single	height	Height of the view volume at the near view plane.
System.Single	nearPlaneDistance	Distance to the near view plane.
System.Single	farPlaneDistance	Distance to the far view plane.

Returns

Type	Description
Matrix4x4	Return a perspective projection matrix.

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CreateRotationX(Single)

Creates rotation matrix around X axis.

Declaration

public static Matrix4x4 CreateRotationX(float radians)

Parameters

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

Returns

Type	Description
Matrix4x4	Returns rotation matrix to rotate an object around X axis.

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CreateRotationY(Single)

Creates rotation matrix around Y axis.

Declaration

public static Matrix4x4 CreateRotationY(float radians)

Parameters

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

Returns

Type	Description
Matrix4x4	Returns rotation matrix to rotate an object around Y axis.

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CreateRotationZ(Single)

Creates rotation matrix around Z axis.

Declaration

public static Matrix4x4 CreateRotationZ(float radians)

Parameters

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

Returns

Type	Description
Matrix4x4	Returns rotation matrix to rotate an object around Z axis.

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CreateTranslation(Vector3)

Creates translation matrix for the specified movement amount.

Declaration

public static Matrix4x4 CreateTranslation(Vector3 position)

Parameters

Type	Name	Description
Vector3	position	Vector which set direction and amount of movement.

Returns

Type	Description
Matrix4x4	Returns translation matrix.

Remarks

The specified vector is copied to the 3rd column of the result matrix. All diagonal elements are set to 1. The rest of matrix is initialized with zeros.

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Equals(Matrix4x4)

Tests whether the matrix equals to the specified one.

Declaration

public bool Equals(Matrix4x4 matrix)

Parameters

Type	Name	Description
Matrix4x4	matrix	The matrix to test equality with.

Returns

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

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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.

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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;
Matrix4x4 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 );

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GetColumn(Int32)

Get column of the matrix.

Declaration

public Vector4 GetColumn(int index)

Parameters

Type	Name	Description
System.Int32	index	Column index to get, [0, 3].

Returns

Type	Description
Vector4	Returns specified column of the matrix as a vector.

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GetHashCode()

Returns the hashcode for this instance.

Declaration

public override int GetHashCode()

Returns

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

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GetRow(Int32)

Get row of the matrix.

Declaration

public Vector4 GetRow(int index)

Parameters

Type	Name	Description
System.Int32	index	Row index to get, [0, 3].

Returns

Type	Description
Vector4	Returns specified row of the matrix as a vector.

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Multiply(Matrix4x4, Matrix4x4)

Multiplies two specified matrices.

Declaration

public static Matrix4x4 Multiply(Matrix4x4 matrix1, Matrix4x4 matrix2)

Parameters

Type	Name	Description
Matrix4x4	matrix1	Matrix to multiply.
Matrix4x4	matrix2	Matrix to multiply by.

Returns

Type	Description
Matrix4x4	Return new matrix, which the result of multiplication of the two specified matrices.

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Multiply(Matrix4x4, Vector4)

Multiplies specified matrix by the specified vector.

Declaration

public static Vector4 Multiply(Matrix4x4 matrix, Vector4 vector)

Parameters

Type	Name	Description
Matrix4x4	matrix	Matrix to multiply by vector.
Vector4	vector	Vector to multiply matrix by.

Returns

Type	Description
Vector4	Returns new vector which is the result of multiplication of the specified matrix by the specified vector.

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Subtract(Matrix4x4, Matrix4x4)

Subtracts corresponding components of two matrices.

Declaration

public static Matrix4x4 Subtract(Matrix4x4 matrix1, Matrix4x4 matrix2)

Parameters

Type	Name	Description
Matrix4x4	matrix1	The matrix to subtract from.
Matrix4x4	matrix2	The matrix to subtract from the first matrix.

Returns

Type	Description
Matrix4x4	Returns a matrix which components are equal to difference of corresponding components of the two specified matrices.

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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.

Operators

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Addition(Matrix4x4, Matrix4x4)

Adds corresponding components of two matrices.

Declaration

public static Matrix4x4 operator +(Matrix4x4 matrix1, Matrix4x4 matrix2)

Parameters

Type	Name	Description
Matrix4x4	matrix1	The matrix to add to.
Matrix4x4	matrix2	The matrix to add to the first matrix.

Returns

Type	Description
Matrix4x4	Returns a matrix which components are equal to sum of corresponding components of the two specified matrices.

View Source

Equality(Matrix4x4, Matrix4x4)

Tests whether two specified matrices are equal.

Declaration

public static bool operator ==(Matrix4x4 matrix1, Matrix4x4 matrix2)

Parameters

Type	Name	Description
Matrix4x4	matrix1	The left-hand matrix.
Matrix4x4	matrix2	The right-hand matrix.

Returns

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

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Inequality(Matrix4x4, Matrix4x4)

Tests whether two specified matrices are not equal.

Declaration

public static bool operator !=(Matrix4x4 matrix1, Matrix4x4 matrix2)

Parameters

Type	Name	Description
Matrix4x4	matrix1	The left-hand matrix.
Matrix4x4	matrix2	The right-hand matrix.

Returns

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

View Source

Multiply(Matrix4x4, Matrix4x4)

Multiplies two specified matrices.

Declaration

public static Matrix4x4 operator *(Matrix4x4 matrix1, Matrix4x4 matrix2)

Parameters

Type	Name	Description
Matrix4x4	matrix1	Matrix to multiply.
Matrix4x4	matrix2	Matrix to multiply by.

Returns

Type	Description
Matrix4x4	Return new matrix, which the result of multiplication of the two specified matrices.

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Multiply(Matrix4x4, Vector4)

Multiplies specified matrix by the specified vector.

Declaration

public static Vector4 operator *(Matrix4x4 matrix, Vector4 vector)

Parameters

Type	Name	Description
Matrix4x4	matrix	Matrix to multiply by vector.
Vector4	vector	Vector to multiply matrix by.

Returns

Type	Description
Vector4	Returns new vector which is the result of multiplication of the specified matrix by the specified vector.

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Subtraction(Matrix4x4, Matrix4x4)

Subtracts corresponding components of two matrices.

Declaration

public static Matrix4x4 operator -(Matrix4x4 matrix1, Matrix4x4 matrix2)

Parameters

Type	Name	Description
Matrix4x4	matrix1	The matrix to subtract from.
Matrix4x4	matrix2	The matrix to subtract from the first matrix.

Returns

Type	Description
Matrix4x4	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>>)