Class Matrix3x3

Represents a 3x3 mathematical matrix.

Inheritance

System.Object

Matrix3x3

Implements

System.IEquatable<Matrix3x3>

System.IFormattable

Namespace: FlaxEngine

Assembly: FlaxEngine.CSharp.dll

Syntax

[Unmanaged]
public sealed class Matrix3x3 : ValueType, IEquatable<Matrix3x3>, IFormattable

Constructors

Matrix3x3(Matrix)

Initializes a new instance of the Matrix3x3 struct.

Declaration

public Matrix3x3(Matrix m)

Parameters

Matrix m The rotation/scale matrix.

Matrix3x3(Single)

Initializes a new instance of the Matrix3x3 struct.

Declaration

public Matrix3x3(float value)

Parameters

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

Matrix3x3(Single, Single, Single, Single, Single, Single, Single, Single, Single)

Initializes a new instance of the Matrix3x3 struct.

Declaration

public Matrix3x3(float m11, float m12, float m13, float m21, float m22, float m23, float m31, float m32, float m33)

Parameters

System.Single m11 The value to assign at row 1 column 1 of the Matrix3x3.

System.Single m12 The value to assign at row 1 column 2 of the Matrix3x3.

System.Single m13 The value to assign at row 1 column 3 of the Matrix3x3.

System.Single m21 The value to assign at row 2 column 1 of the Matrix3x3.

System.Single m22 The value to assign at row 2 column 2 of the Matrix3x3.

System.Single m23 The value to assign at row 2 column 3 of the Matrix3x3.

System.Single m31 The value to assign at row 3 column 1 of the Matrix3x3.

System.Single m32 The value to assign at row 3 column 2 of the Matrix3x3.

System.Single m33 The value to assign at row 3 column 3 of the Matrix3x3.

Matrix3x3(Single[])

Initializes a new instance of the Matrix3x3 struct.

Declaration

public Matrix3x3(float[] values)

Parameters

System.Single[] values The values to assign to the components of the Matrix3x3. This must be an array with nine elements.

Exceptions

System.ArgumentNullException Thrown when values is null.

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

Fields

Identity

The identity Matrix3x3.

Declaration

public static readonly Matrix3x3 Identity

Field Value

Matrix3x3

M11

Value at row 1 column 1 of the Matrix3x3.

Declaration

public float M11

Field Value

System.Single

M12

Value at row 1 column 2 of the Matrix3x3.

Declaration

public float M12

Field Value

System.Single

M13

Value at row 1 column 3 of the Matrix3x3.

Declaration

public float M13

Field Value

System.Single

M21

Value at row 2 column 1 of the Matrix3x3.

Declaration

public float M21

Field Value

System.Single

M22

Value at row 2 column 2 of the Matrix3x3.

Declaration

public float M22

Field Value

System.Single

M23

Value at row 2 column 3 of the Matrix3x3.

Declaration

public float M23

Field Value

System.Single

M31

Value at row 3 column 1 of the Matrix3x3.

Declaration

public float M31

Field Value

System.Single

M32

Value at row 3 column 2 of the Matrix3x3.

Declaration

public float M32

Field Value

System.Single

M33

Value at row 3 column 3 of the Matrix3x3.

Declaration

public float M33

Field Value

System.Single

SizeInBytes

The size of the Matrix3x3 type, in bytes.

Declaration

public static readonly int SizeInBytes

Field Value

System.Int32

Zero

A Matrix3x3 with all of its components set to zero.

Declaration

public static readonly Matrix3x3 Zero

Field Value

Matrix3x3

Properties

Column1

Gets or sets the first column in the Matrix3x3; that is M11, M21, M31

Declaration

public Float3 Column1 { get; set; }

Property Value

Float3

Column2

Gets or sets the second column in the Matrix3x3; that is M12, M22, M32

Declaration

public Float3 Column2 { get; set; }

Property Value

Float3

Column3

Gets or sets the third column in the Matrix3x3; that is M13, M23, M33

Declaration

public Float3 Column3 { get; set; }

Property Value

Float3

Default

The default Matrix3x3.

Declaration

public static Matrix3x3 Default { get; }

Property Value

Matrix3x3

IsIdentity

Gets a value indicating whether this instance is an identity Matrix3x3.

Declaration

public bool IsIdentity { get; }

Property Value

System.Boolean true if this instance is an identity Matrix3x3; otherwise, false.

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 Matrix3x3 component, depending on the 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 Matrix3x3 to access.

System.Int32 column The column of the Matrix3x3 to access.

Property Value

System.Single The value of the Matrix3x3 component, depending on the index.

Exceptions

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

Row1

Gets or sets the first row in the Matrix3x3; that is M11, M12, M13

Declaration

public Float3 Row1 { get; set; }

Property Value

Float3

Row2

Gets or sets the second row in the Matrix3x3; that is M21, M22, M23

Declaration

public Float3 Row2 { get; set; }

Property Value

Float3

Row3

Gets or sets the third row in the Matrix3x3; that is M31, M32, M33

Declaration

public Float3 Row3 { get; set; }

Property Value

Float3

ScaleVector

Gets or sets the scale of the Matrix3x3; that is M11, M22, and M33.

Declaration

public Float3 ScaleVector { get; set; }

Property Value

Float3

Methods

Add(Matrix3x3, Matrix3x3)

Determines the sum of two matrices.

Declaration

public static Matrix3x3 Add(Matrix3x3 left, Matrix3x3 right)

Parameters

Matrix3x3 left The first Matrix3x3 to add.

Matrix3x3 right The second Matrix3x3 to add.

Returns

Matrix3x3 The sum of the two matrices.

Add(ref Matrix3x3, ref Matrix3x3, out Matrix3x3)

Determines the sum of two matrices.

Declaration

public static void Add(ref Matrix3x3 left, ref Matrix3x3 right, out Matrix3x3 result)

Parameters

Matrix3x3 left The first Matrix3x3 to add.

Matrix3x3 right The second Matrix3x3 to add.

Matrix3x3 result When the method completes, contains the sum of the two matrices.

Billboard(Float3, Float3, Float3, Float3)

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

Declaration

public static Matrix3x3 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

Matrix3x3 The created billboard Matrix3x3.

Billboard(ref Float3, ref Float3, ref Float3, ref Float3, out Matrix3x3)

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 Matrix3x3 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.

Matrix3x3 result When the method completes, contains the created billboard Matrix3x3.

Decompose(out Float3, out Quaternion)

Decomposes a Matrix3x3 into a scale, rotation, and translation.

Declaration

public bool Decompose(out Float3 scale, out Quaternion rotation)

Parameters

Float3 scale When the method completes, contains the scaling component of the decomposed Matrix3x3.

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

Returns

System.Boolean

Remarks

This method is designed to decompose an SRT transformation Matrix3x3 only.

DecomposeLQ(out Matrix3x3, out Matrix3x3)

Decomposes a Matrix3x3 into a lower triangular Matrix3x3 l and an orthonormalized Matrix3x3 q.

Declaration

public void DecomposeLQ(out Matrix3x3 l, out Matrix3x3 q)

Parameters

Matrix3x3 l When the method completes, contains the lower triangular Matrix3x3 of the decomposition.

Matrix3x3 q When the method completes, contains the orthonormalized Matrix3x3 of the decomposition.

DecomposeQR(out Matrix3x3, out Matrix3x3)

Decomposes a Matrix3x3 into an orthonormalized Matrix3x3 q and a right triangular Matrix3x3 r.

Declaration

public void DecomposeQR(out Matrix3x3 q, out Matrix3x3 r)

Parameters

Matrix3x3 q When the method completes, contains the orthonormalized Matrix3x3 of the decomposition.

Matrix3x3 r When the method completes, contains the right triangular Matrix3x3 of the decomposition.

DecomposeUniformScale(out Single, out Quaternion)

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

Declaration

public bool DecomposeUniformScale(out float scale, out Quaternion rotation)

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.

Returns

System.Boolean

Remarks

This method is designed to decompose only an SRT transformation matrix that has the same scale in every axis.

Determinant()

Calculates the determinant of the Matrix3x3.

Declaration

public float Determinant()

Returns

System.Single The determinant of the Matrix3x3.

Divide(Matrix3x3, Matrix3x3)

Determines the quotient of two matrices.

Declaration

public static Matrix3x3 Divide(Matrix3x3 left, Matrix3x3 right)

Parameters

Matrix3x3 left The first Matrix3x3 to divide.

Matrix3x3 right The second Matrix3x3 to divide.

Returns

Matrix3x3 The quotient of the two matrices.

Divide(Matrix3x3, Single)

Scales a Matrix3x3 by the given value.

Declaration

public static Matrix3x3 Divide(Matrix3x3 left, float right)

Parameters

Matrix3x3 left The Matrix3x3 to scale.

System.Single right The amount by which to scale.

Returns

Matrix3x3 The scaled Matrix3x3.

Divide(ref Matrix3x3, ref Matrix3x3, out Matrix3x3)

Determines the quotient of two matrices.

Declaration

public static void Divide(ref Matrix3x3 left, ref Matrix3x3 right, out Matrix3x3 result)

Parameters

Matrix3x3 left The first Matrix3x3 to divide.

Matrix3x3 right The second Matrix3x3 to divide.

Matrix3x3 result When the method completes, contains the quotient of the two matrices.

Divide(ref Matrix3x3, Single, out Matrix3x3)

Scales a Matrix3x3 by the given value.

Declaration

public static void Divide(ref Matrix3x3 left, float right, out Matrix3x3 result)

Parameters

Matrix3x3 left The Matrix3x3 to scale.

System.Single right The amount by which to scale.

Matrix3x3 result When the method completes, contains the scaled Matrix3x3.

Equals(Matrix3x3)

Determines whether the specified Matrix3x3 is equal to this instance.

Declaration

public bool Equals(Matrix3x3 other)

Parameters

Matrix3x3 other The Matrix3x3 to compare with this instance.

Returns

System.Boolean true if the specified Matrix3x3 is equal to this instance; otherwise, false.

Equals(ref Matrix3x3)

Determines whether the specified Matrix3x3 is equal to this instance.

Declaration

public bool Equals(ref Matrix3x3 other)

Parameters

Matrix3x3 other The Matrix3x3 to compare with this instance.

Returns

System.Boolean true if the specified Matrix3x3 is equal to this instance; otherwise, false.

Equals(ref Matrix3x3, ref Matrix3x3)

Determines whether the specified Matrix3x3 are equal.

Declaration

public static bool Equals(ref Matrix3x3 a, ref Matrix3x3 b)

Parameters

Matrix3x3 a

Matrix3x3 b

Returns

System.Boolean

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 Matrix3x3.

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 Matrix3x3.

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(Matrix3x3, Int32)

Performs the exponential operation on a Matrix3x3.

Declaration

public static Matrix3x3 Exponent(Matrix3x3 value, int exponent)

Parameters

Matrix3x3 value The Matrix3x3 to perform the operation on.

System.Int32 exponent The exponent to raise the Matrix3x3 to.

Returns

Matrix3x3 The exponential Matrix3x3.

Exceptions

System.ArgumentOutOfRangeException Thrown when the exponent is negative.

Exponent(ref Matrix3x3, Int32, out Matrix3x3)

Performs the exponential operation on a Matrix3x3.

Declaration

public static void Exponent(ref Matrix3x3 value, int exponent, out Matrix3x3 result)

Parameters

Matrix3x3 value The Matrix3x3 to perform the operation on.

System.Int32 exponent The exponent to raise the Matrix3x3 to.

Matrix3x3 result When the method completes, contains the exponential Matrix3x3.

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 Matrix3x3.

Declaration

public void Invert()

Invert(Matrix3x3)

Calculates the inverse of the specified Matrix3x3.

Declaration

public static Matrix3x3 Invert(Matrix3x3 value)

Parameters

Matrix3x3 value The Matrix3x3 whose inverse is to be calculated.

Returns

Matrix3x3 The inverse of the specified Matrix3x3.

Invert(ref Matrix3x3, out Matrix3x3)

Calculates the inverse of the specified Matrix3x3.

Declaration

public static void Invert(ref Matrix3x3 value, out Matrix3x3 result)

Parameters

Matrix3x3 value The Matrix3x3 whose inverse is to be calculated.

Matrix3x3 result When the method completes, contains the inverse of the specified Matrix3x3.

Lerp(Matrix3x3, Matrix3x3, Single)

Performs a linear interpolation between two matrices.

Declaration

public static Matrix3x3 Lerp(Matrix3x3 start, Matrix3x3 end, float amount)

Parameters

Matrix3x3 start Start Matrix3x3.

Matrix3x3 end End Matrix3x3.

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

Returns

Matrix3x3 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 Matrix3x3, ref Matrix3x3, Single, out Matrix3x3)

Performs a linear interpolation between two matrices.

Declaration

public static void Lerp(ref Matrix3x3 start, ref Matrix3x3 end, float amount, out Matrix3x3 result)

Parameters

Matrix3x3 start Start Matrix3x3.

Matrix3x3 end End Matrix3x3.

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

Matrix3x3 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 Matrix3x3.

Declaration

public static Matrix3x3 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

Matrix3x3 The created look-at Matrix3x3.

LookAt(ref Float3, ref Float3, ref Float3, out Matrix3x3)

Creates a left-handed, look-at Matrix3x3.

Declaration

public static void LookAt(ref Float3 eye, ref Float3 target, ref Float3 up, out Matrix3x3 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.

Matrix3x3 result When the method completes, contains the created look-at Matrix3x3.

LowerTriangularForm(Matrix3x3)

Brings the Matrix3x3 into lower triangular form using elementary row operations.

Declaration

public static Matrix3x3 LowerTriangularForm(Matrix3x3 value)

Parameters

Matrix3x3 value The Matrix3x3 to put into lower triangular form.

Returns

Matrix3x3 The lower triangular Matrix3x3.

Remarks

If the Matrix3x3 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 Matrix3x3 represents a system of linear equations, than this often means that either no solution exists or an infinite number of solutions exist.

LowerTriangularForm(ref Matrix3x3, out Matrix3x3)

Brings the Matrix3x3 into lower triangular form using elementary row operations.

Declaration

public static void LowerTriangularForm(ref Matrix3x3 value, out Matrix3x3 result)

Parameters

Matrix3x3 value The Matrix3x3 to put into lower triangular form.

Matrix3x3 result When the method completes, contains the lower triangular Matrix3x3.

Remarks

If the Matrix3x3 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 Matrix3x3 represents a system of linear equations, than this often means that either no solution exists or an infinite number of solutions exist.

Multiply(Matrix3x3, Matrix3x3)

Determines the product of two matrices.

Declaration

public static Matrix3x3 Multiply(Matrix3x3 left, Matrix3x3 right)

Parameters

Matrix3x3 left The first Matrix3x3 to multiply.

Matrix3x3 right The second Matrix3x3 to multiply.

Returns

Matrix3x3 The product of the two matrices.

Multiply(Matrix3x3, Single)

Scales a Matrix3x3 by the given value.

Declaration

public static Matrix3x3 Multiply(Matrix3x3 left, float right)

Parameters

Matrix3x3 left The Matrix3x3 to scale.

System.Single right The amount by which to scale.

Returns

Matrix3x3 The scaled Matrix3x3.

Multiply(ref Matrix3x3, ref Matrix3x3, out Matrix3x3)

Determines the product of two matrices.

Declaration

public static void Multiply(ref Matrix3x3 left, ref Matrix3x3 right, out Matrix3x3 result)

Parameters

Matrix3x3 left The first Matrix3x3 to multiply.

Matrix3x3 right The second Matrix3x3 to multiply.

Matrix3x3 result The product of the two matrices.

Multiply(ref Matrix3x3, Single, out Matrix3x3)

Scales a Matrix3x3 by the given value.

Declaration

public static void Multiply(ref Matrix3x3 left, float right, out Matrix3x3 result)

Parameters

Matrix3x3 left The Matrix3x3 to scale.

System.Single right The amount by which to scale.

Matrix3x3 result When the method completes, contains the scaled Matrix3x3.

Negate(Matrix3x3)

Negates a Matrix3x3.

Declaration

public static Matrix3x3 Negate(Matrix3x3 value)

Parameters

Matrix3x3 value The Matrix3x3 to be negated.

Returns

Matrix3x3 The negated Matrix3x3.

Negate(ref Matrix3x3, out Matrix3x3)

Negates a Matrix3x3.

Declaration

public static void Negate(ref Matrix3x3 value, out Matrix3x3 result)

Parameters

Matrix3x3 value The Matrix3x3 to be negated.

Matrix3x3 result When the method completes, contains the negated Matrix3x3.

Orthogonalize()

Orthogonalizes the specified Matrix3x3.

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 Matrix3x3 will be orthogonal to any other given row in the Matrix3x3.

Because this method uses the modified Gram-Schmidt process, the resulting Matrix3x3 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 Matrix3x3 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(Matrix3x3)

Orthogonalizes the specified Matrix3x3.

Declaration

public static Matrix3x3 Orthogonalize(Matrix3x3 value)

Parameters

Matrix3x3 value The Matrix3x3 to orthogonalize.

Returns

Matrix3x3 The orthogonalized Matrix3x3.

Remarks

Orthogonalization is the process of making all rows orthogonal to each other. This means that any given row in the Matrix3x3 will be orthogonal to any other given row in the Matrix3x3.

Because this method uses the modified Gram-Schmidt process, the resulting Matrix3x3 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 Matrix3x3 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 Matrix3x3, out Matrix3x3)

Orthogonalizes the specified Matrix3x3.

Declaration

public static void Orthogonalize(ref Matrix3x3 value, out Matrix3x3 result)

Parameters

Matrix3x3 value The Matrix3x3 to orthogonalize.

Matrix3x3 result When the method completes, contains the orthogonalized Matrix3x3.

Remarks

Orthogonalization is the process of making all rows orthogonal to each other. This means that any given row in the Matrix3x3 will be orthogonal to any other given row in the Matrix3x3.

Because this method uses the modified Gram-Schmidt process, the resulting Matrix3x3 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 Matrix3x3 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 Matrix3x3.

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 Matrix3x3 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 Matrix3x3 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(Matrix3x3)

Orthonormalizes the specified Matrix3x3.

Declaration

public static Matrix3x3 Orthonormalize(Matrix3x3 value)

Parameters

Matrix3x3 value The Matrix3x3 to orthonormalize.

Returns

Matrix3x3 The orthonormalized Matrix3x3.

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 Matrix3x3 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 Matrix3x3 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 Matrix3x3, out Matrix3x3)

Orthonormalizes the specified Matrix3x3.

Declaration

public static void Orthonormalize(ref Matrix3x3 value, out Matrix3x3 result)

Parameters

Matrix3x3 value The Matrix3x3 to orthonormalize.

Matrix3x3 result When the method completes, contains the orthonormalized Matrix3x3.

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 Matrix3x3 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 Matrix3x3 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.

RotationAxis(Float3, Single)

Creates a Matrix3x3 that rotates around an arbitrary axis.

Declaration

public static Matrix3x3 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

Matrix3x3 The created rotation Matrix3x3.

RotationAxis(ref Float3, Single, out Matrix3x3)

Creates a Matrix3x3 that rotates around an arbitrary axis.

Declaration

public static void RotationAxis(ref Float3 axis, float angle, out Matrix3x3 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.

Matrix3x3 result When the method completes, contains the created rotation Matrix3x3.

RotationQuaternion(Quaternion)

Creates a rotation Matrix3x3 from a quaternion.

Declaration

public static Matrix3x3 RotationQuaternion(Quaternion rotation)

Parameters

Quaternion rotation The quaternion to use to build the Matrix3x3.

Returns

Matrix3x3 The created rotation Matrix3x3.

RotationQuaternion(ref Quaternion, out Matrix3x3)

Creates a rotation Matrix3x3 from a quaternion.

Declaration

public static void RotationQuaternion(ref Quaternion rotation, out Matrix3x3 result)

Parameters

Quaternion rotation The quaternion to use to build the Matrix3x3.

Matrix3x3 result The created rotation Matrix3x3.

RotationX(Single)

Creates a Matrix3x3 that rotates around the x-axis.

Declaration

public static Matrix3x3 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

Matrix3x3 The created rotation Matrix3x3.

RotationX(Single, out Matrix3x3)

Creates a Matrix3x3 that rotates around the x-axis.

Declaration

public static void RotationX(float angle, out Matrix3x3 result)

Parameters

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

Matrix3x3 result When the method completes, contains the created rotation Matrix3x3.

RotationY(Single)

Creates a Matrix3x3 that rotates around the y-axis.

Declaration

public static Matrix3x3 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

Matrix3x3 The created rotation Matrix3x3.

RotationY(Single, out Matrix3x3)

Creates a Matrix3x3 that rotates around the y-axis.

Declaration

public static void RotationY(float angle, out Matrix3x3 result)

Parameters

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

Matrix3x3 result When the method completes, contains the created rotation Matrix3x3.

RotationYawPitchRoll(Single, Single, Single)

Creates a rotation Matrix3x3 with a specified yaw, pitch, and roll.

Declaration

public static Matrix3x3 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

Matrix3x3 The created rotation Matrix3x3.

RotationYawPitchRoll(Single, Single, Single, out Matrix3x3)

Creates a rotation Matrix3x3 with a specified yaw, pitch, and roll.

Declaration

public static void RotationYawPitchRoll(float yaw, float pitch, float roll, out Matrix3x3 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.

Matrix3x3 result When the method completes, contains the created rotation Matrix3x3.

RotationZ(Single)

Creates a Matrix3x3 that rotates around the z-axis.

Declaration

public static Matrix3x3 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

Matrix3x3 The created rotation Matrix3x3.

RotationZ(Single, out Matrix3x3)

Creates a Matrix3x3 that rotates around the z-axis.

Declaration

public static void RotationZ(float angle, out Matrix3x3 result)

Parameters

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

Matrix3x3 result When the method completes, contains the created rotation Matrix3x3.

RowEchelonForm(Matrix3x3)

Brings the Matrix3x3 into row echelon form using elementary row operations;

Declaration

public static Matrix3x3 RowEchelonForm(Matrix3x3 value)

Parameters

Matrix3x3 value The Matrix3x3 to put into row echelon form.

Returns

Matrix3x3 When the method completes, contains the row echelon form of the Matrix3x3.

RowEchelonForm(ref Matrix3x3, out Matrix3x3)

Brings the Matrix3x3 into row echelon form using elementary row operations;

Declaration

public static void RowEchelonForm(ref Matrix3x3 value, out Matrix3x3 result)

Parameters

Matrix3x3 value The Matrix3x3 to put into row echelon form.

Matrix3x3 result When the method completes, contains the row echelon form of the Matrix3x3.

Scaling(Float3)

Creates a Matrix3x3 that scales along the x-axis, y-axis, and z-axis.

Declaration

public static Matrix3x3 Scaling(Float3 scale)

Parameters

Float3 scale Scaling factor for all three axes.

Returns

Matrix3x3 The created scaling Matrix3x3.

Scaling(ref Float3, out Matrix3x3)

Creates a Matrix3x3 that scales along the x-axis, y-axis, and y-axis.

Declaration

public static void Scaling(ref Float3 scale, out Matrix3x3 result)

Parameters

Float3 scale Scaling factor for all three axes.

Matrix3x3 result When the method completes, contains the created scaling Matrix3x3.

Scaling(Single)

Creates a Matrix3x3 that uniformly scales along all three axes.

Declaration

public static Matrix3x3 Scaling(float scale)

Parameters

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

Returns

Matrix3x3 The created scaling Matrix3x3.

Scaling(Single, out Matrix3x3)

Creates a Matrix3x3 that uniformly scales along all three axes.

Declaration

public static void Scaling(float scale, out Matrix3x3 result)

Parameters

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

Matrix3x3 result When the method completes, contains the created scaling Matrix3x3.

Scaling(Single, Single, Single)

Creates a Matrix3x3 that scales along the x-axis, y-axis, and y-axis.

Declaration

public static Matrix3x3 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

Matrix3x3 The created scaling Matrix3x3.

Scaling(Single, Single, Single, out Matrix3x3)

Creates a Matrix3x3 that scales along the x-axis, y-axis, and z-axis.

Declaration

public static void Scaling(float x, float y, float z, out Matrix3x3 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.

Matrix3x3 result When the method completes, contains the created scaling Matrix3x3.

Shear(ref Float2, out Matrix3x3)

Creates the 2D shear matrix. Represented by: [1 Y 0] [X 1 0] [0 0 1]

Declaration

public static void Shear(ref Float2 shearAngles, out Matrix3x3 result)

Parameters

Float2 shearAngles The shear angles (in degrees).

Matrix3x3 result The result.

SmoothStep(Matrix3x3, Matrix3x3, Single)

Performs a cubic interpolation between two matrices.

Declaration

public static Matrix3x3 SmoothStep(Matrix3x3 start, Matrix3x3 end, float amount)

Parameters

Matrix3x3 start Start Matrix3x3.

Matrix3x3 end End Matrix3x3.

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

Returns

Matrix3x3 The cubic interpolation of the two matrices.

SmoothStep(ref Matrix3x3, ref Matrix3x3, Single, out Matrix3x3)

Performs a cubic interpolation between two matrices.

Declaration

public static void SmoothStep(ref Matrix3x3 start, ref Matrix3x3 end, float amount, out Matrix3x3 result)

Parameters

Matrix3x3 start Start Matrix3x3.

Matrix3x3 end End Matrix3x3.

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

Matrix3x3 result When the method completes, contains the cubic interpolation of the two matrices.

Subtract(Matrix3x3, Matrix3x3)

Determines the difference between two matrices.

Declaration

public static Matrix3x3 Subtract(Matrix3x3 left, Matrix3x3 right)

Parameters

Matrix3x3 left The first Matrix3x3 to subtract.

Matrix3x3 right The second Matrix3x3 to subtract.

Returns

Matrix3x3 The difference between the two matrices.

Subtract(ref Matrix3x3, ref Matrix3x3, out Matrix3x3)

Determines the difference between two matrices.

Declaration

public static void Subtract(ref Matrix3x3 left, ref Matrix3x3 right, out Matrix3x3 result)

Parameters

Matrix3x3 left The first Matrix3x3 to subtract.

Matrix3x3 right The second Matrix3x3 to subtract.

Matrix3x3 result When the method completes, contains the difference between the two matrices.

ToArray()

Creates an array containing the elements of the Matrix3x3.

Declaration

public float[] ToArray()

Returns

System.Single[] A 9-element array containing the components of the Matrix3x3.

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.

Transform2D(Float2, Matrix3x3)

Transforms given vector by the matrix (in 2D).

Declaration

public static Float2 Transform2D(Float2 vector, Matrix3x3 transform)

Parameters

Float2 vector The vector.

Matrix3x3 transform The transform.

Returns

Float2 The result.

Transform2D(ref Float2, ref Matrix3x3, out Float2)

Transforms given vector by the matrix (in 2D).

Declaration

public static void Transform2D(ref Float2 vector, ref Matrix3x3 transform, out Float2 result)

Parameters

Float2 vector The vector.

Matrix3x3 transform The transform.

Float2 result The result.

Translation2D(Float2)

Creates 2D translation matrix.

Declaration

public static Matrix3x3 Translation2D(Float2 translation)

Parameters

Float2 translation The translation vector.

Returns

Matrix3x3 The result.

Translation2D(ref Float2, out Matrix3x3)

Creates 2D translation matrix.

Declaration

public static void Translation2D(ref Float2 translation, out Matrix3x3 result)

Parameters

Float2 translation The translation vector.

Matrix3x3 result The result.

Translation2D(Single, Single)

Creates 2D translation matrix.

Declaration

public static Matrix3x3 Translation2D(float x, float y)

Parameters

System.Single x The translation vector X.

System.Single y The translation vector Y.

Returns

Matrix3x3 The result.

Transpose()

Transposes the Matrix3x3.

Declaration

public void Transpose()

Transpose(Matrix3x3)

Calculates the transpose of the specified Matrix3x3.

Declaration

public static Matrix3x3 Transpose(Matrix3x3 value)

Parameters

Matrix3x3 value The Matrix3x3 whose transpose is to be calculated.

Returns

Matrix3x3 The transpose of the specified Matrix3x3.

Transpose(ref Matrix3x3, out Matrix3x3)

Calculates the transpose of the specified Matrix3x3.

Declaration

public static void Transpose(ref Matrix3x3 value, out Matrix3x3 result)

Parameters

Matrix3x3 value The Matrix3x3 whose transpose is to be calculated.

Matrix3x3 result When the method completes, contains the transpose of the specified Matrix3x3.

TransposeByRef(ref Matrix3x3, ref Matrix3x3)

Calculates the transpose of the specified Matrix3x3.

Declaration

public static void TransposeByRef(ref Matrix3x3 value, ref Matrix3x3 result)

Parameters

Matrix3x3 value The Matrix3x3 whose transpose is to be calculated.

Matrix3x3 result When the method completes, contains the transpose of the specified Matrix3x3.

UpperTriangularForm(Matrix3x3)

Brings the Matrix3x3 into upper triangular form using elementary row operations.

Declaration

public static Matrix3x3 UpperTriangularForm(Matrix3x3 value)

Parameters

Matrix3x3 value The Matrix3x3 to put into upper triangular form.

Returns

Matrix3x3 The upper triangular Matrix3x3.

Remarks

If the Matrix3x3 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 Matrix3x3 represents a system of linear equations, than this often means that either no solution exists or an infinite number of solutions exist.

UpperTriangularForm(ref Matrix3x3, out Matrix3x3)

Brings the Matrix3x3 into upper triangular form using elementary row operations.

Declaration

public static void UpperTriangularForm(ref Matrix3x3 value, out Matrix3x3 result)

Parameters

Matrix3x3 value The Matrix3x3 to put into upper triangular form.

Matrix3x3 result When the method completes, contains the upper triangular Matrix3x3.

Remarks

If the Matrix3x3 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 Matrix3x3 represents a system of linear equations, than this often means that either no solution exists or an infinite number of solutions exist.

Operators

Addition(Matrix3x3, Matrix3x3)

Adds two matrices.

Declaration

public static Matrix3x3 operator +(Matrix3x3 left, Matrix3x3 right)

Parameters

Matrix3x3 left The first Matrix3x3 to add.

Matrix3x3 right The second Matrix3x3 to add.

Returns

Matrix3x3 The sum of the two matrices.

Division(Matrix3x3, Matrix3x3)

Divides two matrices.

Declaration

public static Matrix3x3 operator /(Matrix3x3 left, Matrix3x3 right)

Parameters

Matrix3x3 left The first Matrix3x3 to divide.

Matrix3x3 right The second Matrix3x3 to divide.

Returns

Matrix3x3 The quotient of the two matrices.

Division(Matrix3x3, Single)

Scales a Matrix3x3 by a given value.

Declaration

public static Matrix3x3 operator /(Matrix3x3 left, float right)

Parameters

Matrix3x3 left The Matrix3x3 to scale.

System.Single right The amount by which to scale.

Returns

Matrix3x3 The scaled Matrix3x3.

Equality(Matrix3x3, Matrix3x3)

Tests for equality between two objects.

Declaration

public static bool operator ==(Matrix3x3 left, Matrix3x3 right)

Parameters

Matrix3x3 left The first value to compare.

Matrix3x3 right The second value to compare.

Returns

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

Explicit(Matrix to Matrix3x3)

Convert the 4x4 Matrix to a 3x3 Matrix.

Declaration

public static explicit operator Matrix3x3(Matrix value)

Parameters

Matrix value

Returns

Matrix3x3 A 3x3 Matrix

Explicit(Matrix3x3 to Matrix)

Convert the 3x3 Matrix to a 4x4 Matrix.

Declaration

public static explicit operator Matrix(Matrix3x3 value)

Parameters

Matrix3x3 value

Returns

Matrix A 4x4 Matrix with zero translation and M44=1

Inequality(Matrix3x3, Matrix3x3)

Tests for inequality between two objects.

Declaration

public static bool operator !=(Matrix3x3 left, Matrix3x3 right)

Parameters

Matrix3x3 left The first value to compare.

Matrix3x3 right The second value to compare.

Returns

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

Multiply(Matrix3x3, Matrix3x3)

Multiplies two matrices.

Declaration

public static Matrix3x3 operator *(Matrix3x3 left, Matrix3x3 right)

Parameters

Matrix3x3 left The first Matrix3x3 to multiply.

Matrix3x3 right The second Matrix3x3 to multiply.

Returns

Matrix3x3 The product of the two matrices.

Multiply(Matrix3x3, Single)

Scales a Matrix3x3 by a given value.

Declaration

public static Matrix3x3 operator *(Matrix3x3 left, float right)

Parameters

Matrix3x3 left The Matrix3x3 to scale.

System.Single right The amount by which to scale.

Returns

Matrix3x3 The scaled Matrix3x3.

Multiply(Single, Matrix3x3)

Scales a Matrix3x3 by a given value.

Declaration

public static Matrix3x3 operator *(float left, Matrix3x3 right)

Parameters

System.Single left The amount by which to scale.

Matrix3x3 right The Matrix3x3 to scale.

Returns

Matrix3x3 The scaled Matrix3x3.

Subtraction(Matrix3x3, Matrix3x3)

Subtracts two matrices.

Declaration

public static Matrix3x3 operator -(Matrix3x3 left, Matrix3x3 right)

Parameters

Matrix3x3 left The first Matrix3x3 to subtract.

Matrix3x3 right The second Matrix3x3 to subtract.

Returns

Matrix3x3 The difference between the two matrices.

UnaryNegation(Matrix3x3)

Negates a Matrix3x3.

Declaration

public static Matrix3x3 operator -(Matrix3x3 value)

Parameters

Matrix3x3 value The Matrix3x3 to negate.

Returns

Matrix3x3 The negated Matrix3x3.

UnaryPlus(Matrix3x3)

Assert a Matrix3x3 (return it unchanged).

Declaration

public static Matrix3x3 operator +(Matrix3x3 value)

Parameters

Matrix3x3 value The Matrix3x3 to assert (unchanged).

Returns

Matrix3x3 The asserted (unchanged) Matrix3x3.

Extension Methods

Extensions.ReflectiveCompare<T>(T, T)

Extensions.RawClone<T>(T)