Class Matrix

Represents a 4x4 mathematical matrix.

Inheritance

System.Object

Matrix

Implements

System.IEquatable<Matrix>

System.IFormattable

Namespace: FlaxEngine

Assembly: FlaxEngine.CSharp.dll

Syntax

[Unmanaged]
public sealed class Matrix : ValueType, IEquatable<Matrix>, IFormattable

Constructors

Matrix(Matrix3x3)

Initializes a new instance of the Matrix struct.

Declaration

public Matrix(Matrix3x3 m)

Parameters

Matrix3x3 m The rotation/scale matrix.

Matrix(Single)

Initializes a new instance of the Matrix struct.

Declaration

public Matrix(float value)

Parameters

System.Single value The value that will be assigned to all components.

Matrix(Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single)

Initializes a new instance of the Matrix struct.

Declaration

public Matrix(float m11, float m12, float m13, float m14, float m21, float m22, float m23, float m24, float m31, float m32, float m33, float m34, float m41, float m42, float m43, float m44)

Parameters

System.Single m11 The value to assign at row 1 column 1 of the matrix.

System.Single m12 The value to assign at row 1 column 2 of the matrix.

System.Single m13 The value to assign at row 1 column 3 of the matrix.

System.Single m14 The value to assign at row 1 column 4 of the matrix.

System.Single m21 The value to assign at row 2 column 1 of the matrix.

System.Single m22 The value to assign at row 2 column 2 of the matrix.

System.Single m23 The value to assign at row 2 column 3 of the matrix.

System.Single m24 The value to assign at row 2 column 4 of the matrix.

System.Single m31 The value to assign at row 3 column 1 of the matrix.

System.Single m32 The value to assign at row 3 column 2 of the matrix.

System.Single m33 The value to assign at row 3 column 3 of the matrix.

System.Single m34 The value to assign at row 3 column 4 of the matrix.

System.Single m41 The value to assign at row 4 column 1 of the matrix.

System.Single m42 The value to assign at row 4 column 2 of the matrix.

System.Single m43 The value to assign at row 4 column 3 of the matrix.

System.Single m44 The value to assign at row 4 column 4 of the matrix.

Matrix(Single[])

Initializes a new instance of the Matrix struct.

Declaration

public Matrix(float[] values)

Parameters

System.Single[] values The values to assign to the components of the matrix. This must be an array with sixteen elements.

Exceptions

System.ArgumentNullException Thrown when values is null.

System.ArgumentOutOfRangeException Thrown when values contains more or less than sixteen elements.

Fields

Identity

The identity Matrix.

Declaration

public static readonly Matrix Identity

Field Value

Matrix

M11

Value at row 1 column 1 of the matrix.

Declaration

public float M11

Field Value

System.Single

M12

Value at row 1 column 2 of the matrix.

Declaration

public float M12

Field Value

System.Single

M13

Value at row 1 column 3 of the matrix.

Declaration

public float M13

Field Value

System.Single

M14

Value at row 1 column 4 of the matrix.

Declaration

public float M14

Field Value

System.Single

M21

Value at row 2 column 1 of the matrix.

Declaration

public float M21

Field Value

System.Single

M22

Value at row 2 column 2 of the matrix.

Declaration

public float M22

Field Value

System.Single

M23

Value at row 2 column 3 of the matrix.

Declaration

public float M23

Field Value

System.Single

M24

Value at row 2 column 4 of the matrix.

Declaration

public float M24

Field Value

System.Single

M31

Value at row 3 column 1 of the matrix.

Declaration

public float M31

Field Value

System.Single

M32

Value at row 3 column 2 of the matrix.

Declaration

public float M32

Field Value

System.Single

M33

Value at row 3 column 3 of the matrix.

Declaration

public float M33

Field Value

System.Single

M34

Value at row 3 column 4 of the matrix.

Declaration

public float M34

Field Value

System.Single

M41

Value at row 4 column 1 of the matrix.

Declaration

public float M41

Field Value

System.Single

M42

Value at row 4 column 2 of the matrix.

Declaration

public float M42

Field Value

System.Single

M43

Value at row 4 column 3 of the matrix.

Declaration

public float M43

Field Value

System.Single

M44

Value at row 4 column 4 of the matrix.

Declaration

public float M44

Field Value

System.Single

SizeInBytes

The size of the Matrix type, in bytes.

Declaration

public static readonly int SizeInBytes

Field Value

System.Int32

Zero

A Matrix with all of its components set to zero.

Declaration

public static readonly Matrix Zero

Field Value

Matrix

Properties

Backward

Gets or sets the backward Float3 of the matrix; that is -M31, -M32, and -M33.

Declaration

public Float3 Backward { get; set; }

Property Value

Float3

Column1

Gets or sets the first column in the matrix; that is M11, M21, M31, and M41.

Declaration

public Float4 Column1 { get; set; }

Property Value

Float4

Column2

Gets or sets the second column in the matrix; that is M12, M22, M32, and M42.

Declaration

public Float4 Column2 { get; set; }

Property Value

Float4

Column3

Gets or sets the third column in the matrix; that is M13, M23, M33, and M43.

Declaration

public Float4 Column3 { get; set; }

Property Value

Float4

Column4

Gets or sets the fourth column in the matrix; that is M14, M24, M34, and M44.

Declaration

public Float4 Column4 { get; set; }

Property Value

Float4

Default

The default Matrix.

Declaration

public static Matrix Default { get; }

Property Value

Matrix

Down

Gets or sets the down Float3 of the matrix; that is -M21, -M22, and -M23.

Declaration

public Float3 Down { get; set; }

Property Value

Float3

Forward

Gets or sets the forward Float3 of the matrix; that is M31, M32, and M33.

Declaration

public Float3 Forward { get; set; }

Property Value

Float3

IsIdentity

Gets a value indicating whether this instance is an identity matrix.

Declaration

public bool IsIdentity { get; }

Property Value

System.Boolean

Item[Int32]

Gets or sets the component at the specified index.

Declaration

public float this[int index] { get; set; }

Parameters

System.Int32 index The zero-based index of the component to access.

Property Value

System.Single The value of the component at the specified index.

Exceptions

System.ArgumentOutOfRangeException Thrown when the index is out of the range [0, 15].

Item[Int32, Int32]

Gets or sets the component at the specified index.

Declaration

public float this[int row, int column] { get; set; }

Parameters

System.Int32 row The row of the matrix to access.

System.Int32 column The column of the matrix to access.

Property Value

System.Single The value of the matrix component, depending on the index.

Exceptions

System.ArgumentOutOfRangeException Thrown when the row or columnis out of the range [0, 3].

Left

Gets or sets the left Float3 of the matrix; that is -M11, -M12, and -M13.

Declaration

public Float3 Left { get; set; }

Property Value

Float3

Right

Gets or sets the right Float3 of the matrix; that is M11, M12, and M13.

Declaration

public Float3 Right { get; set; }

Property Value

Float3

Row1

Gets or sets the first row in the matrix; that is M11, M12, M13, and M14.

Declaration

public Float4 Row1 { get; set; }

Property Value

Float4

Row2

Gets or sets the second row in the matrix; that is M21, M22, M23, and M24.

Declaration

public Float4 Row2 { get; set; }

Property Value

Float4

Row3

Gets or sets the third row in the matrix; that is M31, M32, M33, and M34.

Declaration

public Float4 Row3 { get; set; }

Property Value

Float4

Row4

Gets or sets the fourth row in the matrix; that is M41, M42, M43, and M44.

Declaration

public Float4 Row4 { get; set; }

Property Value

Float4

ScaleVector

Gets or sets the scale of the matrix; that is M11, M22, and M33.

Declaration

public Float3 ScaleVector { get; set; }

Property Value

Float3

TranslationVector

Gets or sets the translation of the matrix; that is M41, M42, and M43.

Declaration

public Float3 TranslationVector { get; set; }

Property Value

Float3

Up

Gets or sets the up Float3 of the matrix; that is M21, M22, and M23.

Declaration

public Float3 Up { get; set; }

Property Value

Float3

Methods

Add(Matrix, Matrix)

Determines the sum of two matrices.

Declaration

public static Matrix Add(Matrix left, Matrix right)

Parameters

Matrix left The first matrix to add.

Matrix right The second matrix to add.

Returns

Matrix The sum of the two matrices.

Add(ref Matrix, ref Matrix, out Matrix)

Determines the sum of two matrices.

Declaration

public static void Add(ref Matrix left, ref Matrix right, out Matrix result)

Parameters

Matrix left The first matrix to add.

Matrix right The second matrix to add.

Matrix result When the method completes, contains the sum of the two matrices.

AffineTransformation(Single, Float3, Quaternion, Float3)

Creates a 3D affine transformation matrix.

Declaration

public static Matrix AffineTransformation(float scaling, Float3 rotationCenter, Quaternion rotation, Float3 translation)

Parameters

System.Single scaling Scaling factor.

Float3 rotationCenter The center of the rotation.

Quaternion rotation The rotation of the transformation.

Float3 translation The translation factor of the transformation.

Returns

Matrix The created affine transformation matrix.

AffineTransformation(Single, ref Float3, ref Quaternion, ref Float3, out Matrix)

Creates a 3D affine transformation matrix.

Declaration

public static void AffineTransformation(float scaling, ref Float3 rotationCenter, ref Quaternion rotation, ref Float3 translation, out Matrix result)

Parameters

System.Single scaling Scaling factor.

Float3 rotationCenter The center of the rotation.

Quaternion rotation The rotation of the transformation.

Float3 translation The translation factor of the transformation.

Matrix result When the method completes, contains the created affine transformation matrix.

AffineTransformation(Single, Quaternion, Float3)

Creates a 3D affine transformation matrix.

Declaration

public static Matrix AffineTransformation(float scaling, Quaternion rotation, Float3 translation)

Parameters

System.Single scaling Scaling factor.

Quaternion rotation The rotation of the transformation.

Float3 translation The translation factor of the transformation.

Returns

Matrix The created affine transformation matrix.

AffineTransformation(Single, ref Quaternion, ref Float3, out Matrix)

Creates a 3D affine transformation matrix.

Declaration

public static void AffineTransformation(float scaling, ref Quaternion rotation, ref Float3 translation, out Matrix result)

Parameters

System.Single scaling Scaling factor.

Quaternion rotation The rotation of the transformation.

Float3 translation The translation factor of the transformation.

Matrix result When the method completes, contains the created affine transformation matrix.

AffineTransformation2D(Single, Float2, Single, Float2)

Creates a 2D affine transformation matrix.

Declaration

public static Matrix AffineTransformation2D(float scaling, Float2 rotationCenter, float rotation, Float2 translation)

Parameters

System.Single scaling Scaling factor.

Float2 rotationCenter The center of the rotation.

System.Single rotation The rotation of the transformation.

Float2 translation The translation factor of the transformation.

Returns

Matrix The created affine transformation matrix.

AffineTransformation2D(Single, ref Float2, Single, ref Float2, out Matrix)

Creates a 2D affine transformation matrix.

Declaration

public static void AffineTransformation2D(float scaling, ref Float2 rotationCenter, float rotation, ref Float2 translation, out Matrix result)

Parameters

System.Single scaling Scaling factor.

Float2 rotationCenter The center of the rotation.

System.Single rotation The rotation of the transformation.

Float2 translation The translation factor of the transformation.

Matrix result When the method completes, contains the created affine transformation matrix.

AffineTransformation2D(Single, Single, Float2)

Creates a 2D affine transformation matrix.

Declaration

public static Matrix AffineTransformation2D(float scaling, float rotation, Float2 translation)

Parameters

System.Single scaling Scaling factor.

System.Single rotation The rotation of the transformation.

Float2 translation The translation factor of the transformation.

Returns

Matrix The created affine transformation matrix.

AffineTransformation2D(Single, Single, ref Float2, out Matrix)

Creates a 2D affine transformation matrix.

Declaration

public static void AffineTransformation2D(float scaling, float rotation, ref Float2 translation, out Matrix result)

Parameters

System.Single scaling Scaling factor.

System.Single rotation The rotation of the transformation.

Float2 translation The translation factor of the transformation.

Matrix result When the method completes, contains the created affine transformation matrix.

Billboard(Float3, Float3, Float3, Float3)

Creates a left-handed spherical billboard that rotates around a specified object position.

Declaration

public static Matrix Billboard(Float3 objectPosition, Float3 cameraPosition, Float3 cameraUpFloat, Float3 cameraForwardFloat)

Parameters

Float3 objectPosition The position of the object around which the billboard will rotate.

Float3 cameraPosition The position of the camera.

Float3 cameraUpFloat The up vector of the camera.

Float3 cameraForwardFloat The forward vector of the camera.

Returns

Matrix The created billboard matrix.

Billboard(ref Float3, ref Float3, ref Float3, ref Float3, out Matrix)

Creates a left-handed spherical billboard that rotates around a specified object position.

Declaration

public static void Billboard(ref Float3 objectPosition, ref Float3 cameraPosition, ref Float3 cameraUpFloat, ref Float3 cameraForwardFloat, out Matrix result)

Parameters

Float3 objectPosition The position of the object around which the billboard will rotate.

Float3 cameraPosition The position of the camera.

Float3 cameraUpFloat The up vector of the camera.

Float3 cameraForwardFloat The forward vector of the camera.

Matrix result When the method completes, contains the created billboard matrix.

CreateFromAxisAngle(Float3, Single)

Creates a new matrix that rotates around an arbitrary vector.

Declaration

public static Matrix CreateFromAxisAngle(Float3 axis, float angle)

Parameters

Float3 axis The axis to rotate around.

System.Single angle The angle to rotate around the vector.

Returns

Matrix The created rotation matrix.

CreateFromAxisAngle(ref Float3, Single, out Matrix)

Creates a new matrix that rotates around an arbitrary vector.

Declaration

public static void CreateFromAxisAngle(ref Float3 axis, float angle, out Matrix result)

Parameters

Float3 axis The axis to rotate around.

System.Single angle The angle to rotate around the vector.

Matrix result When the method completes, contains the created rotation matrix.

CreateWorld(Float3, Float3, Float3)

Creates the world matrix from the specified parameters

Declaration

public static Matrix CreateWorld(Float3 position, Float3 forward, Float3 up)

Parameters

Float3 position The position of the object. This value is used in translation operations.

Float3 forward The forward direction of the object.

Float3 up The upward direction of the object; usually [0, 1, 0].

Returns

Matrix The created world matrix of given transformation world

CreateWorld(ref Float3, ref Float3, ref Float3, out Matrix)

Creates the world matrix from the specified parameters

Declaration

public static void CreateWorld(ref Float3 position, ref Float3 forward, ref Float3 up, out Matrix result)

Parameters

Float3 position The position of the object. This value is used in translation operations.

Float3 forward The forward direction of the object.

Float3 up The upward direction of the object; usually [0, 1, 0].

Matrix result When the method completes, contains the created world matrix of given transformation world.

Decompose(out Float3, out Matrix, out Float3)

Decomposes a matrix into a scale, rotation, and translation. [Deprecated on 20.02.2024, expires on 20.02.2026]

Declaration

public void Decompose(out Float3 scale, out Matrix rotation, out Float3 translation)

Parameters

Float3 scale When the method completes, contains the scaling component of the decomposed matrix.

Matrix rotation When the method completes, contains the rotation component of the decomposed matrix.

Float3 translation When the method completes, contains the translation component of the decomposed matrix.

Remarks

This method is designed to decompose an SRT transformation matrix only.

Decompose(out Float3, out Matrix3x3, out Float3)

Decomposes a matrix into a scale, rotation, and translation.

Declaration

public void Decompose(out Float3 scale, out Matrix3x3 rotation, out Float3 translation)

Parameters

Float3 scale When the method completes, contains the scaling component of the decomposed matrix.

Matrix3x3 rotation When the method completes, contains the rotation component of the decomposed matrix.

Float3 translation When the method completes, contains the translation component of the decomposed matrix.

Remarks

This method is designed to decompose an SRT transformation matrix only.

Decompose(out Float3, out Quaternion, out Float3)

Decomposes a matrix into a scale, rotation, and translation.

Declaration

public void Decompose(out Float3 scale, out Quaternion rotation, out Float3 translation)

Parameters

Float3 scale When the method completes, contains the scaling component of the decomposed matrix.

Quaternion rotation When the method completes, contains the rotation component of the decomposed matrix.

Float3 translation When the method completes, contains the translation component of the decomposed matrix.

Remarks

This method is designed to decompose an SRT transformation matrix only.

Decompose(out Transform)

Decomposes a matrix into a scale, rotation, and translation.

Declaration

public void Decompose(out Transform transform)

Parameters

Transform transform When the method completes, contains the transformation of the decomposed matrix.

Remarks

This method is designed to decompose an SRT transformation matrix only.

DecomposeLQ(out Matrix, out Matrix)

Decomposes a matrix into a lower triangular matrix L and an orthonormalized matrix Q.

Declaration

public void DecomposeLQ(out Matrix L, out Matrix Q)

Parameters

Matrix L When the method completes, contains the lower triangular matrix of the decomposition.

Matrix Q When the method completes, contains the orthonormalized matrix of the decomposition.

DecomposeQR(out Matrix, out Matrix)

Decomposes a matrix into an orthonormalized matrix Q and a right triangular matrix R.

Declaration

public void DecomposeQR(out Matrix Q, out Matrix R)

Parameters

Matrix Q When the method completes, contains the orthonormalized matrix of the decomposition.

Matrix R When the method completes, contains the right triangular matrix of the decomposition.

DecomposeUniformScale(out Single, out Quaternion, out Float3)

Decomposes a uniform scale matrix into a scale, rotation, and translation. A uniform scale matrix has the same scale in every axis.

Declaration

public void DecomposeUniformScale(out float scale, out Quaternion rotation, out Float3 translation)

Parameters

System.Single scale When the method completes, contains the scaling component of the decomposed matrix.

Quaternion rotation When the method completes, contains the rotation component of the decomposed matrix.

Float3 translation When the method completes, contains the translation component of the decomposed matrix.

Remarks

This method is designed to decompose an SRT transformation matrix only.

Determinant()

Calculates the determinant of the matrix.

Declaration

public float Determinant()

Returns

System.Single The determinant of the matrix.

Divide(Matrix, Matrix)

Determines the quotient of two matrices.

Declaration

public static Matrix Divide(Matrix left, Matrix right)

Parameters

Matrix left The first matrix to divide.

Matrix right The second matrix to divide.

Returns

Matrix The quotient of the two matrices.

Divide(Matrix, Single)

Scales a matrix by the given value.

Declaration

public static Matrix Divide(Matrix left, float right)

Parameters

Matrix left The matrix to scale.

System.Single right The amount by which to scale.

Returns

Matrix The scaled matrix.

Divide(ref Matrix, ref Matrix, out Matrix)

Determines the quotient of two matrices.

Declaration

public static void Divide(ref Matrix left, ref Matrix right, out Matrix result)

Parameters

Matrix left The first matrix to divide.

Matrix right The second matrix to divide.

Matrix result When the method completes, contains the quotient of the two matrices.

Divide(ref Matrix, Single, out Matrix)

Scales a matrix by the given value.

Declaration

public static void Divide(ref Matrix left, float right, out Matrix result)

Parameters

Matrix left The matrix to scale.

System.Single right The amount by which to scale.

Matrix result When the method completes, contains the scaled matrix.

Equals(Matrix)

Determines whether the specified Matrix is equal to this instance.

Declaration

public bool Equals(Matrix other)

Parameters

Matrix other The Matrix to compare with this instance.

Returns

System.Boolean true if the specified Matrix is equal to this instance; otherwise, false.

Equals(ref Matrix)

Determines whether the specified Matrix is equal to this instance.

Declaration

public bool Equals(ref Matrix other)

Parameters

Matrix other The Matrix to compare with this instance.

Returns

System.Boolean true if the specified Matrix is equal to this instance; otherwise, false.

Equals(Object)

Determines whether the specified System.Object is equal to this instance.

Declaration

public override bool Equals(object value)

Parameters

System.Object value The System.Object to compare with this instance.

Returns

System.Boolean true if the specified System.Object is equal to this instance; otherwise, false.

ExchangeColumns(Int32, Int32)

Exchanges two columns in the matrix.

Declaration

public void ExchangeColumns(int firstColumn, int secondColumn)

Parameters

System.Int32 firstColumn The first column to exchange. This is an index of the column starting at zero.

System.Int32 secondColumn The second column to exchange. This is an index of the column starting at zero.

ExchangeRows(Int32, Int32)

Exchanges two rows in the matrix.

Declaration

public void ExchangeRows(int firstRow, int secondRow)

Parameters

System.Int32 firstRow The first row to exchange. This is an index of the row starting at zero.

System.Int32 secondRow The second row to exchange. This is an index of the row starting at zero.

Exponent(Matrix, Int32)

Performs the exponential operation on a matrix.

Declaration

public static Matrix Exponent(Matrix value, int exponent)

Parameters

Matrix value The matrix to perform the operation on.

System.Int32 exponent The exponent to raise the matrix to.

Returns

Matrix The exponential matrix.

Exceptions

System.ArgumentOutOfRangeException Thrown when the exponent is negative.

Exponent(ref Matrix, Int32, out Matrix)

Performs the exponential operation on a matrix.

Declaration

public static void Exponent(ref Matrix value, int exponent, out Matrix result)

Parameters

Matrix value The matrix to perform the operation on.

System.Int32 exponent The exponent to raise the matrix to.

Matrix result When the method completes, contains the exponential matrix.

Exceptions

System.ArgumentOutOfRangeException Thrown when the exponent is negative.

GetHashCode()

Returns a hash code for this instance.

Declaration

public override int GetHashCode()

Returns

System.Int32 A hash code for this instance, suitable for use in hashing algorithms and data structures like a hash table.

Invert()

Inverts the matrix.

Declaration

public void Invert()

Invert(Matrix)

Calculates the inverse of the specified matrix.

Declaration

public static Matrix Invert(Matrix value)

Parameters

Matrix value The matrix whose inverse is to be calculated.

Returns

Matrix The inverse of the specified matrix.

Invert(ref Matrix, out Matrix)

Calculates the inverse of the specified matrix.

Declaration

public static void Invert(ref Matrix value, out Matrix result)

Parameters

Matrix value The matrix whose inverse is to be calculated.

Matrix result When the method completes, contains the inverse of the specified matrix.

Lerp(Matrix, Matrix, Single)

Performs a linear interpolation between two matrices.

Declaration

public static Matrix Lerp(Matrix start, Matrix end, float amount)

Parameters

Matrix start Start matrix.

Matrix end End matrix.

System.Single amount Value between 0 and 1 indicating the weight of end.

Returns

Matrix The linear interpolation of the two matrices.

Remarks

Passing amount a value of 0 will cause start to be returned; a value of 1 will cause end to be returned.

Lerp(ref Matrix, ref Matrix, Single, out Matrix)

Performs a linear interpolation between two matrices.

Declaration

public static void Lerp(ref Matrix start, ref Matrix end, float amount, out Matrix result)

Parameters

Matrix start Start matrix.

Matrix end End matrix.

System.Single amount Value between 0 and 1 indicating the weight of end.

Matrix result When the method completes, contains the linear interpolation of the two matrices.

Remarks

Passing amount a value of 0 will cause start to be returned; a value of 1 will cause end to be returned.

LookAt(Float3, Float3, Float3)

Creates a left-handed, look-at matrix.

Declaration

public static Matrix LookAt(Float3 eye, Float3 target, Float3 up)

Parameters

Float3 eye The position of the viewer's eye.

Float3 target The camera look-at target.

Float3 up The camera's up vector.

Returns

Matrix The created look-at matrix.

LookAt(ref Float3, ref Float3, ref Float3, out Matrix)

Creates a left-handed, look-at matrix.

Declaration

public static void LookAt(ref Float3 eye, ref Float3 target, ref Float3 up, out Matrix result)

Parameters

Float3 eye The position of the viewer's eye.

Float3 target The camera look-at target.

Float3 up The camera's up vector.

Matrix result When the method completes, contains the created look-at matrix.

LowerTriangularForm(Matrix)

Brings the matrix into lower triangular form using elementary row operations.

Declaration

public static Matrix LowerTriangularForm(Matrix value)

Parameters

Matrix value The matrix to put into lower triangular form.

Returns

Matrix The lower triangular matrix.

Remarks

If the matrix is not invertible (i.e. its determinant is zero) than the result of this method may produce Single.Nan and Single.Inf values. When the matrix represents a system of linear equations, than this often means that either no solution exists or an infinite number of solutions exist.

LowerTriangularForm(ref Matrix, out Matrix)

Brings the matrix into lower triangular form using elementary row operations.

Declaration

public static void LowerTriangularForm(ref Matrix value, out Matrix result)

Parameters

Matrix value The matrix to put into lower triangular form.

Matrix result When the method completes, contains the lower triangular matrix.

Remarks

If the matrix is not invertible (i.e. its determinant is zero) than the result of this method may produce Single.Nan and Single.Inf values. When the matrix represents a system of linear equations, than this often means that either no solution exists or an infinite number of solutions exist.

Multiply(Matrix, Matrix)

Determines the product of two matrices.

Declaration

public static Matrix Multiply(Matrix left, Matrix right)

Parameters

Matrix left The first matrix to multiply.

Matrix right The second matrix to multiply.

Returns

Matrix The product of the two matrices.

Multiply(Matrix, Single)

Scales a matrix by the given value.

Declaration

public static Matrix Multiply(Matrix left, float right)

Parameters

Matrix left The matrix to scale.

System.Single right The amount by which to scale.

Returns

Matrix The scaled matrix.

Multiply(ref Matrix, ref Matrix, out Matrix)

Determines the product of two matrices.

Declaration

public static void Multiply(ref Matrix left, ref Matrix right, out Matrix result)

Parameters

Matrix left The first matrix to multiply.

Matrix right The second matrix to multiply.

Matrix result The product of the two matrices.

Multiply(ref Matrix, Single, out Matrix)

Scales a matrix by the given value.

Declaration

public static void Multiply(ref Matrix left, float right, out Matrix result)

Parameters

Matrix left The matrix to scale.

System.Single right The amount by which to scale.

Matrix result When the method completes, contains the scaled matrix.

Negate(Matrix)

Negates a matrix.

Declaration

public static Matrix Negate(Matrix value)

Parameters

Matrix value The matrix to be negated.

Returns

Matrix The negated matrix.

Negate(ref Matrix, out Matrix)

Negates a matrix.

Declaration

public static void Negate(ref Matrix value, out Matrix result)

Parameters

Matrix value The matrix to be negated.

Matrix result When the method completes, contains the negated matrix.

Ortho(Single, Single, Single, Single)

Creates a left-handed, orthographic projection matrix.

Declaration

public static Matrix Ortho(float width, float height, float znear, float zfar)

Parameters

System.Single width Width of the viewing volume.

System.Single height Height of the viewing volume.

System.Single znear Minimum z-value of the viewing volume.

System.Single zfar Maximum z-value of the viewing volume.

Returns

Matrix The created projection matrix.

Ortho(Single, Single, Single, Single, out Matrix)

Creates a left-handed, orthographic projection matrix.

Declaration

public static void Ortho(float width, float height, float znear, float zfar, out Matrix result)

Parameters

System.Single width Width of the viewing volume.

System.Single height Height of the viewing volume.

System.Single znear Minimum z-value of the viewing volume.

System.Single zfar Maximum z-value of the viewing volume.

Matrix result When the method completes, contains the created projection matrix.

Orthogonalize()

Orthogonalizes the specified matrix.

Declaration

public void Orthogonalize()

Remarks

Orthogonalization is the process of making all rows orthogonal to each other. This means that any given row in the matrix will be orthogonal to any other given row in the matrix.

Because this method uses the modified Gram-Schmidt process, the resulting matrix tends to be numerically unstable. The numeric stability decreases according to the rows so that the first row is the most stable and the last row is the least stable.

This operation is performed on the rows of the matrix rather than the columns. If you wish for this operation to be performed on the columns, first transpose the input and than transpose the output.

Orthogonalize(Matrix)

Orthogonalizes the specified matrix.

Declaration

public static Matrix Orthogonalize(Matrix value)

Parameters

Matrix value The matrix to orthogonalize.

Returns

Matrix The orthogonalized matrix.

Remarks

Orthogonalization is the process of making all rows orthogonal to each other. This means that any given row in the matrix will be orthogonal to any other given row in the matrix.

Because this method uses the modified Gram-Schmidt process, the resulting matrix tends to be numerically unstable. The numeric stability decreases according to the rows so that the first row is the most stable and the last row is the least stable.

This operation is performed on the rows of the matrix rather than the columns. If you wish for this operation to be performed on the columns, first transpose the input and than transpose the output.

Orthogonalize(ref Matrix, out Matrix)

Orthogonalizes the specified matrix.

Declaration

public static void Orthogonalize(ref Matrix value, out Matrix result)

Parameters

Matrix value The matrix to orthogonalize.

Matrix result When the method completes, contains the orthogonalized matrix.

Remarks

Orthogonalization is the process of making all rows orthogonal to each other. This means that any given row in the matrix will be orthogonal to any other given row in the matrix.

Because this method uses the modified Gram-Schmidt process, the resulting matrix tends to be numerically unstable. The numeric stability decreases according to the rows so that the first row is the most stable and the last row is the least stable.

This operation is performed on the rows of the matrix rather than the columns. If you wish for this operation to be performed on the columns, first transpose the input and than transpose the output.

Orthonormalize()

Orthonormalizes the specified matrix.

Declaration

public void Orthonormalize()

Remarks

Orthonormalization is the process of making all rows and columns orthogonal to each other and making all rows and columns of unit length. This means that any given row will be orthogonal to any other given row and any given column will be orthogonal to any other given column. Any given row will not be orthogonal to any given column. Every row and every column will be of unit length.

Because this method uses the modified Gram-Schmidt process, the resulting matrix tends to be numerically unstable. The numeric stability decreases according to the rows so that the first row is the most stable and the last row is the least stable.

This operation is performed on the rows of the matrix rather than the columns. If you wish for this operation to be performed on the columns, first transpose the input and than transpose the output.

Orthonormalize(Matrix)

Orthonormalizes the specified matrix.

Declaration

public static Matrix Orthonormalize(Matrix value)

Parameters

Matrix value The matrix to orthonormalize.

Returns

Matrix The orthonormalized matrix.

Remarks

Orthonormalization is the process of making all rows and columns orthogonal to each other and making all rows and columns of unit length. This means that any given row will be orthogonal to any other given row and any given column will be orthogonal to any other given column. Any given row will not be orthogonal to any given column. Every row and every column will be of unit length.

Because this method uses the modified Gram-Schmidt process, the resulting matrix tends to be numerically unstable. The numeric stability decreases according to the rows so that the first row is the most stable and the last row is the least stable.

This operation is performed on the rows of the matrix rather than the columns. If you wish for this operation to be performed on the columns, first transpose the input and than transpose the output.

Orthonormalize(ref Matrix, out Matrix)

Orthonormalizes the specified matrix.

Declaration

public static void Orthonormalize(ref Matrix value, out Matrix result)

Parameters

Matrix value The matrix to orthonormalize.

Matrix result When the method completes, contains the orthonormalized matrix.

Remarks

Orthonormalization is the process of making all rows and columns orthogonal to each other and making all rows and columns of unit length. This means that any given row will be orthogonal to any other given row and any given column will be orthogonal to any other given column. Any given row will not be orthogonal to any given column. Every row and every column will be of unit length.

Because this method uses the modified Gram-Schmidt process, the resulting matrix tends to be numerically unstable. The numeric stability decreases according to the rows so that the first row is the most stable and the last row is the least stable.

This operation is performed on the rows of the matrix rather than the columns. If you wish for this operation to be performed on the columns, first transpose the input and than transpose the output.

OrthoOffCenter(Single, Single, Single, Single, Single, Single)

Creates a left-handed, customized orthographic projection matrix.

Declaration

public static Matrix OrthoOffCenter(float left, float right, float bottom, float top, float znear, float zfar)

Parameters

System.Single left Minimum x-value of the viewing volume.

System.Single right Maximum x-value of the viewing volume.

System.Single bottom Minimum y-value of the viewing volume.

System.Single top Maximum y-value of the viewing volume.

System.Single znear Minimum z-value of the viewing volume.

System.Single zfar Maximum z-value of the viewing volume.

Returns

Matrix The created projection matrix.

OrthoOffCenter(Single, Single, Single, Single, Single, Single, out Matrix)

Creates a left-handed, customized orthographic projection matrix.

Declaration

public static void OrthoOffCenter(float left, float right, float bottom, float top, float znear, float zfar, out Matrix result)

Parameters

System.Single left Minimum x-value of the viewing volume.

System.Single right Maximum x-value of the viewing volume.

System.Single bottom Minimum y-value of the viewing volume.

System.Single top Maximum y-value of the viewing volume.

System.Single znear Minimum z-value of the viewing volume.

System.Single zfar Maximum z-value of the viewing volume.

Matrix result When the method completes, contains the created projection matrix.

Perspective(Single, Single, Single, Single)

Creates a left-handed, perspective projection matrix.

Declaration

public static Matrix Perspective(float width, float height, float znear, float zfar)

Parameters

System.Single width Width of the viewing volume.

System.Single height Height of the viewing volume.

System.Single znear Minimum z-value of the viewing volume.

System.Single zfar Maximum z-value of the viewing volume.

Returns

Matrix The created projection matrix.

Perspective(Single, Single, Single, Single, out Matrix)

Creates a left-handed, perspective projection matrix.

Declaration

public static void Perspective(float width, float height, float znear, float zfar, out Matrix result)

Parameters

System.Single width Width of the viewing volume.

System.Single height Height of the viewing volume.

System.Single znear Minimum z-value of the viewing volume.

System.Single zfar Maximum z-value of the viewing volume.

Matrix result When the method completes, contains the created projection matrix.

PerspectiveFov(Single, Single, Single, Single)

Creates a left-handed, perspective projection matrix based on a field of view.

Declaration

public static Matrix PerspectiveFov(float fov, float aspect, float znear, float zfar)

Parameters

System.Single fov Field of view in the y direction, in radians.

System.Single aspect Aspect ratio, defined as view space width divided by height.

System.Single znear Minimum z-value of the viewing volume.

System.Single zfar Maximum z-value of the viewing volume.

Returns

Matrix The created projection matrix.

PerspectiveFov(Single, Single, Single, Single, out Matrix)

Creates a left-handed, perspective projection matrix based on a field of view.

Declaration

public static void PerspectiveFov(float fov, float aspect, float znear, float zfar, out Matrix result)

Parameters

System.Single fov Field of view in the y direction, in radians.

System.Single aspect Aspect ratio, defined as view space width divided by height.

System.Single znear Minimum z-value of the viewing volume.

System.Single zfar Maximum z-value of the viewing volume.

Matrix result When the method completes, contains the created projection matrix.

PerspectiveOffCenter(Single, Single, Single, Single, Single, Single)

Creates a left-handed, customized perspective projection matrix.

Declaration

public static Matrix PerspectiveOffCenter(float left, float right, float bottom, float top, float znear, float zfar)

Parameters

System.Single left Minimum x-value of the viewing volume.

System.Single right Maximum x-value of the viewing volume.

System.Single bottom Minimum y-value of the viewing volume.

System.Single top Maximum y-value of the viewing volume.

System.Single znear Minimum z-value of the viewing volume.

System.Single zfar Maximum z-value of the viewing volume.

Returns

Matrix The created projection matrix.

PerspectiveOffCenter(Single, Single, Single, Single, Single, Single, out Matrix)

Creates a left-handed, customized perspective projection matrix.

Declaration

public static void PerspectiveOffCenter(float left, float right, float bottom, float top, float znear, float zfar, out Matrix result)

Parameters

System.Single left Minimum x-value of the viewing volume.

System.Single right Maximum x-value of the viewing volume.

System.Single bottom Minimum y-value of the viewing volume.

System.Single top Maximum y-value of the viewing volume.

System.Single znear Minimum z-value of the viewing volume.

System.Single zfar Maximum z-value of the viewing volume.

Matrix result When the method completes, contains the created projection matrix.

ReducedRowEchelonForm(ref Matrix, ref Float4, out Matrix, out Float4)

Brings the matrix into reduced row echelon form using elementary row operations.

Declaration

public static void ReducedRowEchelonForm(ref Matrix value, ref Float4 augment, out Matrix result, out Float4 augmentResult)

Parameters

Matrix value The matrix to put into reduced row echelon form.

Float4 augment The fifth column of the matrix.

Matrix result When the method completes, contains the resultant matrix after the operation.

Float4 augmentResult When the method completes, contains the resultant fifth column of the matrix.

Remarks

The fifth column is often called the augmented part of the matrix. This is because the fifth column is really just an extension of the matrix so that there is a place to put all of the non-zero components after the operation is complete.

Often times the resultant matrix will the identity matrix or a matrix similar to the identity matrix. Sometimes, however, that is not possible and numbers other than zero and one may appear.

This method can be used to solve systems of linear equations. Upon completion of this method, the augmentResult will contain the solution for the system. It is up to the user to analyze both the input and the result to determine if a solution really exists.

RotationAxis(Float3, Single)

Creates a matrix that rotates around an arbitrary axis.

Declaration

public static Matrix RotationAxis(Float3 axis, float angle)

Parameters

Float3 axis The axis around which to rotate. This parameter is assumed to be normalized.

System.Single angle Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.

Returns

Matrix The created rotation matrix.

RotationAxis(ref Float3, Single, out Matrix)

Creates a matrix that rotates around an arbitrary axis.

Declaration

public static void RotationAxis(ref Float3 axis, float angle, out Matrix result)

Parameters

Float3 axis The axis around which to rotate. This parameter is assumed to be normalized.

System.Single angle Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.

Matrix result When the method completes, contains the created rotation matrix.

RotationQuaternion(Quaternion)

Creates a rotation matrix from a quaternion.

Declaration

public static Matrix RotationQuaternion(Quaternion rotation)

Parameters

Quaternion rotation The quaternion to use to build the matrix.

Returns

Matrix The created rotation matrix.

RotationQuaternion(ref Quaternion, out Matrix)

Creates a rotation matrix from a quaternion.

Declaration

public static void RotationQuaternion(ref Quaternion rotation, out Matrix result)

Parameters

Quaternion rotation The quaternion to use to build the matrix.

Matrix result The created rotation matrix.

RotationX(Single)

Creates a matrix that rotates around the x-axis.

Declaration

public static Matrix RotationX(float angle)

Parameters

System.Single angle Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.

Returns

Matrix The created rotation matrix.

RotationX(Single, out Matrix)

Creates a matrix that rotates around the x-axis.

Declaration

public static void RotationX(float angle, out Matrix result)

Parameters

System.Single angle Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.

Matrix result When the method completes, contains the created rotation matrix.

RotationY(Single)

Creates a matrix that rotates around the y-axis.

Declaration

public static Matrix RotationY(float angle)

Parameters

System.Single angle Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.

Returns

Matrix The created rotation matrix.

RotationY(Single, out Matrix)

Creates a matrix that rotates around the y-axis.

Declaration

public static void RotationY(float angle, out Matrix result)

Parameters

System.Single angle Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.

Matrix result When the method completes, contains the created rotation matrix.

RotationYawPitchRoll(Single, Single, Single)

Creates a rotation matrix with a specified yaw, pitch, and roll.

Declaration

public static Matrix RotationYawPitchRoll(float yaw, float pitch, float roll)

Parameters

System.Single yaw Yaw around the y-axis, in radians.

System.Single pitch Pitch around the x-axis, in radians.

System.Single roll Roll around the z-axis, in radians.

Returns

Matrix The created rotation matrix.

RotationYawPitchRoll(Single, Single, Single, out Matrix)

Creates a rotation matrix with a specified yaw, pitch, and roll.

Declaration

public static void RotationYawPitchRoll(float yaw, float pitch, float roll, out Matrix result)

Parameters

System.Single yaw Yaw around the y-axis, in radians.

System.Single pitch Pitch around the x-axis, in radians.

System.Single roll Roll around the z-axis, in radians.

Matrix result When the method completes, contains the created rotation matrix.

RotationZ(Single)

Creates a matrix that rotates around the z-axis.

Declaration

public static Matrix RotationZ(float angle)

Parameters

System.Single angle Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.

Returns

Matrix The created rotation matrix.

RotationZ(Single, out Matrix)

Creates a matrix that rotates around the z-axis.

Declaration

public static void RotationZ(float angle, out Matrix result)

Parameters

System.Single angle Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.

Matrix result When the method completes, contains the created rotation matrix.

RowEchelonForm(Matrix)

Brings the matrix into row echelon form using elementary row operations;

Declaration

public static Matrix RowEchelonForm(Matrix value)

Parameters

Matrix value The matrix to put into row echelon form.

Returns

Matrix When the method completes, contains the row echelon form of the matrix.

RowEchelonForm(ref Matrix, out Matrix)

Brings the matrix into row echelon form using elementary row operations;

Declaration

public static void RowEchelonForm(ref Matrix value, out Matrix result)

Parameters

Matrix value The matrix to put into row echelon form.

Matrix result When the method completes, contains the row echelon form of the matrix.

Scaling(Float3)

Creates a matrix that scales along the x-axis, y-axis, and y-axis.

Declaration

public static Matrix Scaling(Float3 scale)

Parameters

Float3 scale Scaling factor for all three axes.

Returns

Matrix The created scaling matrix.

Scaling(ref Float3, out Matrix)

Creates a matrix that scales along the x-axis, y-axis, and y-axis.

Declaration

public static void Scaling(ref Float3 scale, out Matrix result)

Parameters

Float3 scale Scaling factor for all three axes.

Matrix result When the method completes, contains the created scaling matrix.

Scaling(Single)

Creates a matrix that uniformly scales along all three axis.

Declaration

public static Matrix Scaling(float scale)

Parameters

System.Single scale The uniform scale that is applied along all axis.

Returns

Matrix The created scaling matrix.

Scaling(Single, out Matrix)

Creates a matrix that uniformly scales along all three axis.

Declaration

public static void Scaling(float scale, out Matrix result)

Parameters

System.Single scale The uniform scale that is applied along all axis.

Matrix result When the method completes, contains the created scaling matrix.

Scaling(Single, Single, Single)

Creates a matrix that scales along the x-axis, y-axis, and y-axis.

Declaration

public static Matrix Scaling(float x, float y, float z)

Parameters

System.Single x Scaling factor that is applied along the x-axis.

System.Single y Scaling factor that is applied along the y-axis.

System.Single z Scaling factor that is applied along the z-axis.

Returns

Matrix The created scaling matrix.

Scaling(Single, Single, Single, out Matrix)

Creates a matrix that scales along the x-axis, y-axis, and y-axis.

Declaration

public static void Scaling(float x, float y, float z, out Matrix result)

Parameters

System.Single x Scaling factor that is applied along the x-axis.

System.Single y Scaling factor that is applied along the y-axis.

System.Single z Scaling factor that is applied along the z-axis.

Matrix result When the method completes, contains the created scaling matrix.

Skew(Single, ref Float3, ref Float3, out Matrix)

Creates a skew/shear matrix by means of a translation vector, a rotation vector, and a rotation angle. shearing is performed in the direction of translation vector, where translation vector and rotation vector define the shearing plane. The effect is such that the skewed rotation vector has the specified angle with rotation itself.

Declaration

public static void Skew(float angle, ref Float3 rotationVec, ref Float3 transVec, out Matrix matrix)

Parameters

System.Single angle The rotation angle.

Float3 rotationVec The rotation vector

Float3 transVec The translation vector

Matrix matrix Contains the created skew/shear matrix.

SmoothStep(Matrix, Matrix, Single)

Performs a cubic interpolation between two matrices.

Declaration

public static Matrix SmoothStep(Matrix start, Matrix end, float amount)

Parameters

Matrix start Start matrix.

Matrix end End matrix.

System.Single amount Value between 0 and 1 indicating the weight of end.

Returns

Matrix The cubic interpolation of the two matrices.

SmoothStep(ref Matrix, ref Matrix, Single, out Matrix)

Performs a cubic interpolation between two matrices.

Declaration

public static void SmoothStep(ref Matrix start, ref Matrix end, float amount, out Matrix result)

Parameters

Matrix start Start matrix.

Matrix end End matrix.

System.Single amount Value between 0 and 1 indicating the weight of end.

Matrix result When the method completes, contains the cubic interpolation of the two matrices.

Subtract(Matrix, Matrix)

Determines the difference between two matrices.

Declaration

public static Matrix Subtract(Matrix left, Matrix right)

Parameters

Matrix left The first matrix to subtract.

Matrix right The second matrix to subtract.

Returns

Matrix The difference between the two matrices.

Subtract(ref Matrix, ref Matrix, out Matrix)

Determines the difference between two matrices.

Declaration

public static void Subtract(ref Matrix left, ref Matrix right, out Matrix result)

Parameters

Matrix left The first matrix to subtract.

Matrix right The second matrix to subtract.

Matrix result When the method completes, contains the difference between the two matrices.

ToArray()

Creates an array containing the elements of the matrix.

Declaration

public float[] ToArray()

Returns

System.Single[] A sixteen-element array containing the components of the matrix.

ToString()

Returns a System.String that represents this instance.

Declaration

public override string ToString()

Returns

System.String A System.String that represents this instance.

ToString(IFormatProvider)

Returns a System.String that represents this instance.

Declaration

public string ToString(IFormatProvider formatProvider)

Parameters

System.IFormatProvider formatProvider The format provider.

Returns

System.String A System.String that represents this instance.

ToString(String)

Returns a System.String that represents this instance.

Declaration

public string ToString(string format)

Parameters

System.String format The format.

Returns

System.String A System.String that represents this instance.

ToString(String, IFormatProvider)

Returns a System.String that represents this instance.

Declaration

public string ToString(string format, IFormatProvider formatProvider)

Parameters

System.String format The format.

System.IFormatProvider formatProvider The format provider.

Returns

System.String A System.String that represents this instance.

Transformation(Float3, Quaternion, Float3)

Creates a matrix that contains both the X, Y and Z rotation, as well as scaling and translation.

Declaration

public static Matrix Transformation(Float3 scaling, Quaternion rotation, Float3 translation)

Parameters

Float3 scaling The scaling.

Quaternion rotation Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.

Float3 translation The translation.

Returns

Matrix The created transformation matrix.

Transformation(Float3, Quaternion, Float3, Float3, Quaternion, Float3)

Creates a transformation matrix.

Declaration

public static Matrix Transformation(Float3 scalingCenter, Quaternion scalingRotation, Float3 scaling, Float3 rotationCenter, Quaternion rotation, Float3 translation)

Parameters

Float3 scalingCenter Center point of the scaling operation.

Quaternion scalingRotation Scaling rotation amount.

Float3 scaling Scaling factor.

Float3 rotationCenter The center of the rotation.

Quaternion rotation The rotation of the transformation.

Float3 translation The translation factor of the transformation.

Returns

Matrix The created transformation matrix.

Transformation(ref Float3, ref Quaternion, ref Float3, ref Float3, ref Quaternion, ref Float3, out Matrix)

Creates a transformation matrix.

Declaration

public static void Transformation(ref Float3 scalingCenter, ref Quaternion scalingRotation, ref Float3 scaling, ref Float3 rotationCenter, ref Quaternion rotation, ref Float3 translation, out Matrix result)

Parameters

Float3 scalingCenter Center point of the scaling operation.

Quaternion scalingRotation Scaling rotation amount.

Float3 scaling Scaling factor.

Float3 rotationCenter The center of the rotation.

Quaternion rotation The rotation of the transformation.

Float3 translation The translation factor of the transformation.

Matrix result When the method completes, contains the created transformation matrix.

Transformation(ref Float3, ref Quaternion, ref Float3, out Matrix)

Creates a matrix that contains both the X, Y and Z rotation, as well as scaling and translation.

Declaration

public static void Transformation(ref Float3 scaling, ref Quaternion rotation, ref Float3 translation, out Matrix result)

Parameters

Float3 scaling The scaling.

Quaternion rotation Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.

Float3 translation The translation.

Matrix result When the method completes, contains the created transformation matrix.

Transformation2D(Float2, Single, Float2, Float2, Single, Float2)

Creates a 2D transformation matrix.

Declaration

public static Matrix Transformation2D(Float2 scalingCenter, float scalingRotation, Float2 scaling, Float2 rotationCenter, float rotation, Float2 translation)

Parameters

Float2 scalingCenter Center point of the scaling operation.

System.Single scalingRotation Scaling rotation amount.

Float2 scaling Scaling factor.

Float2 rotationCenter The center of the rotation.

System.Single rotation The rotation of the transformation.

Float2 translation The translation factor of the transformation.

Returns

Matrix The created transformation matrix.

Transformation2D(ref Float2, Single, ref Float2, ref Float2, Single, ref Float2, out Matrix)

Creates a 2D transformation matrix.

Declaration

public static void Transformation2D(ref Float2 scalingCenter, float scalingRotation, ref Float2 scaling, ref Float2 rotationCenter, float rotation, ref Float2 translation, out Matrix result)

Parameters

Float2 scalingCenter Center point of the scaling operation.

System.Single scalingRotation Scaling rotation amount.

Float2 scaling Scaling factor.

Float2 rotationCenter The center of the rotation.

System.Single rotation The rotation of the transformation.

Float2 translation The translation factor of the transformation.

Matrix result When the method completes, contains the created transformation matrix.

Translation(Float3)

Creates a translation matrix using the specified offsets.

Declaration

public static Matrix Translation(Float3 value)

Parameters

Float3 value The offset for all three coordinate planes.

Returns

Matrix The created translation matrix.

Translation(ref Float3, out Matrix)

Creates a translation matrix using the specified offsets.

Declaration

public static void Translation(ref Float3 value, out Matrix result)

Parameters

Float3 value The offset for all three coordinate planes.

Matrix result When the method completes, contains the created translation matrix.

Translation(Single, Single, Single)

Creates a translation matrix using the specified offsets.

Declaration

public static Matrix Translation(float x, float y, float z)

Parameters

System.Single x X-coordinate offset.

System.Single y Y-coordinate offset.

System.Single z Z-coordinate offset.

Returns

Matrix The created translation matrix.

Translation(Single, Single, Single, out Matrix)

Creates a translation matrix using the specified offsets.

Declaration

public static void Translation(float x, float y, float z, out Matrix result)

Parameters

System.Single x X-coordinate offset.

System.Single y Y-coordinate offset.

System.Single z Z-coordinate offset.

Matrix result When the method completes, contains the created translation matrix.

Transpose()

Transposes the matrix.

Declaration

public void Transpose()

Transpose(Matrix)

Calculates the transpose of the specified matrix.

Declaration

public static Matrix Transpose(Matrix value)

Parameters

Matrix value The matrix whose transpose is to be calculated.

Returns

Matrix The transpose of the specified matrix.

Transpose(ref Matrix, out Matrix)

Calculates the transpose of the specified matrix.

Declaration

public static void Transpose(ref Matrix value, out Matrix result)

Parameters

Matrix value The matrix whose transpose is to be calculated.

Matrix result When the method completes, contains the transpose of the specified matrix.

TransposeByRef(ref Matrix, ref Matrix)

Calculates the transpose of the specified matrix.

Declaration

public static void TransposeByRef(ref Matrix value, ref Matrix result)

Parameters

Matrix value The matrix whose transpose is to be calculated.

Matrix result When the method completes, contains the transpose of the specified matrix.

UpperTriangularForm(Matrix)

Brings the matrix into upper triangular form using elementary row operations.

Declaration

public static Matrix UpperTriangularForm(Matrix value)

Parameters

Matrix value The matrix to put into upper triangular form.

Returns

Matrix The upper triangular matrix.

Remarks

If the matrix is not invertible (i.e. its determinant is zero) than the result of this method may produce Single.Nan and Single.Inf values. When the matrix represents a system of linear equations, than this often means that either no solution exists or an infinite number of solutions exist.

UpperTriangularForm(ref Matrix, out Matrix)

Brings the matrix into upper triangular form using elementary row operations.

Declaration

public static void UpperTriangularForm(ref Matrix value, out Matrix result)

Parameters

Matrix value The matrix to put into upper triangular form.

Matrix result When the method completes, contains the upper triangular matrix.

Remarks

If the matrix is not invertible (i.e. its determinant is zero) than the result of this method may produce Single.Nan and Single.Inf values. When the matrix represents a system of linear equations, than this often means that either no solution exists or an infinite number of solutions exist.

Operators

Addition(Matrix, Matrix)

Adds two matrices.

Declaration

public static Matrix operator +(Matrix left, Matrix right)

Parameters

Matrix left The first matrix to add.

Matrix right The second matrix to add.

Returns

Matrix The sum of the two matrices.

Division(Matrix, Matrix)

Divides two matrices.

Declaration

public static Matrix operator /(Matrix left, Matrix right)

Parameters

Matrix left The first matrix to divide.

Matrix right The second matrix to divide.

Returns

Matrix The quotient of the two matrices.

Division(Matrix, Single)

Scales a matrix by a given value.

Declaration

public static Matrix operator /(Matrix left, float right)

Parameters

Matrix left The matrix to scale.

System.Single right The amount by which to scale.

Returns

Matrix The scaled matrix.

Equality(Matrix, Matrix)

Tests for equality between two objects.

Declaration

public static bool operator ==(Matrix left, Matrix right)

Parameters

Matrix left The first value to compare.

Matrix right The second value to compare.

Returns

System.Boolean true if left has the same value as right; otherwise,false.

Inequality(Matrix, Matrix)

Tests for inequality between two objects.

Declaration

public static bool operator !=(Matrix left, Matrix right)

Parameters

Matrix left The first value to compare.

Matrix right The second value to compare.

Returns

System.Boolean true if left has a different value than right; otherwise,false.

Multiply(Matrix, Matrix)

Multiplies two matrices.

Declaration

public static Matrix operator *(Matrix left, Matrix right)

Parameters

Matrix left The first matrix to multiply.

Matrix right The second matrix to multiply.

Returns

Matrix The product of the two matrices.

Multiply(Matrix, Single)

Scales a matrix by a given value.

Declaration

public static Matrix operator *(Matrix left, float right)

Parameters

Matrix left The matrix to scale.

System.Single right The amount by which to scale.

Returns

Matrix The scaled matrix.

Multiply(Single, Matrix)

Scales a matrix by a given value.

Declaration

public static Matrix operator *(float left, Matrix right)

Parameters

System.Single left The amount by which to scale.

Matrix right The matrix to scale.

Returns

Matrix The scaled matrix.

Subtraction(Matrix, Matrix)

Subtracts two matrices.

Declaration

public static Matrix operator -(Matrix left, Matrix right)

Parameters

Matrix left The first matrix to subtract.

Matrix right The second matrix to subtract.

Returns

Matrix The difference between the two matrices.

UnaryNegation(Matrix)

Negates a matrix.

Declaration

public static Matrix operator -(Matrix value)

Parameters

Matrix value The matrix to negate.

Returns

Matrix The negated matrix.

UnaryPlus(Matrix)

Assert a matrix (return it unchanged).

Declaration

public static Matrix operator +(Matrix value)

Parameters

Matrix value The matrix to assert (unchanged).

Returns

Matrix The asserted (unchanged) matrix.

Extension Methods

Extensions.ReflectiveCompare<T>(T, T)

Extensions.RawClone<T>(T)