Struct float4x4

Represents a 4x4 Matrix typically used in ComputerGraphics algorithms.

Implements

System.IEquatable<float4x4>

Inherited Members

System.Object.Equals(System.Object, System.Object)

System.Object.GetType()

System.Object.ReferenceEquals(System.Object, System.Object)

Namespace: Fusee.Math.Core

Assembly: Fusee.Math.Core.dll

Syntax

public struct float4x4 : IEquatable<float4x4>

Remarks

float4x4 objects represent matrices used in column-vector-notation, that means when used in common matrix-vector-multiplication scenarios, the vector should be multiplied from the right to the matrix (M * v). Concatenations of matrices from left to right represent a transformation where the rightmost matrix is applied first and the leftmost matrix is applied last, for example in (M3 * M2 * M1) * v the vector v is first transformed by M1, then by M2 and finally by M3. The translation part of a 4x4 matrix used in homogeneous coordinate calculations can be found in the leftmost column (M14 - x-translation, M24 - y-translation, M34 - z-translation).

Note that although float4x4 objects represent matrices in COLUMN-vector-NOTATION as found in math books, the objects' contents is physically stored in ROW-major-ORDER, meaning that in physical memory, a float4x4's components are stored contiguously in the following order: first row (M11, M12, M13, M14), then second row (M21, M22, M21, M24), and so on. When exchanging matrix contents with libraries like graphics engines (OpenGL, Direct3D), physics engines, file formats, etc. make sure to convert to and from the given Matrix layout of the API you are exchanging data with.

float4x4 contains convenience construction methods to create matrices commonly used in Computer Graphics. Most of these application matrices are handedness-agnostic, meaning that the resulting matrices can be used in both, left-handed and right-handed coordinate systems. This does not hold for LookAt and Projection matrices where the viewing direction plays a role. In left-handed coordinate systems the viewing direction is positive, meaning positions further away have bigger positive z-coordinates whereas in right-handed coordinate systems positions further away have smaller negative z-coordinates. By default, float4x4 will assume a left-handed coordinate system, but contains convenience construction methods to also create right-handed matrices if necessary. The right-handed versions of methods are postfixed with "RH".

Constructors

float4x4(double4x4)

Constructs a new float4x4 by converting from a double4x4.

Declaration

public float4x4(double4x4 d4x4)

Parameters

Type	Name	Description
double4x4	d4x4	The double4x4 to copy components from.

float4x4(float3x3)

Constructs a new float4x4 from a float3x3 by setting the 4th column and row to UnitW respectively.

Declaration

public float4x4(float3x3 f3x3)

Parameters

Type	Name	Description
float3x3	f3x3	The float3x3 matrix to copy components from.

float4x4(float4, float4, float4, float4)

Constructs a new instance.

Declaration

public float4x4(float4 row1, float4 row2, float4 row3, float4 row4)

Parameters

Type	Name	Description
float4	row1	Top row of the matrix
float4	row2	Second row of the matrix
float4	row3	Third row of the matrix
float4	row4	Bottom row of the matrix

float4x4(Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single, Single)

Constructs a new instance.

Declaration

public float4x4(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

Type	Name	Description
System.Single	m11	First item of the first row of the matrix.
System.Single	m12	Second item of the first row of the matrix.
System.Single	m13	Third item of the first row of the matrix.
System.Single	m14	Fourth item of the first row of the matrix.
System.Single	m21	First item of the second row of the matrix.
System.Single	m22	Second item of the second row of the matrix.
System.Single	m23	Third item of the second row of the matrix.
System.Single	m24	Fourth item of the second row of the matrix.
System.Single	m31	First item of the third row of the matrix.
System.Single	m32	Second item of the third row of the matrix.
System.Single	m33	Third item of the third row of the matrix.
System.Single	m34	First item of the third row of the matrix.
System.Single	m41	Fourth item of the fourth row of the matrix.
System.Single	m42	Second item of the fourth row of the matrix.
System.Single	m43	Third item of the fourth row of the matrix.
System.Single	m44	Fourth item of the fourth row of the matrix.

Fields

Identity

The identity matrix

Declaration

public static readonly float4x4 Identity

Field Value

Type	Description
float4x4

Row1

Top row of the matrix

Declaration

public float4 Row1

Field Value

Type	Description
float4

Row2

2nd row of the matrix

Declaration

public float4 Row2

Field Value

Type	Description
float4

Row3

3rd row of the matrix

Declaration

public float4 Row3

Field Value

Type	Description
float4

Row4

Bottom row of the matrix

Declaration

public float4 Row4

Field Value

Type	Description
float4

Zero

The zero matrix

Declaration

public static readonly float4x4 Zero

Field Value

Type	Description
float4x4

Properties

Column1

The first column of this matrix

Declaration

public float4 Column1 { get; set; }

Property Value

Type	Description
float4

Column2

The second column of this matrix

Declaration

public float4 Column2 { get; set; }

Property Value

Type	Description
float4

Column3

The third column of this matrix

Declaration

public float4 Column3 { get; set; }

Property Value

Type	Description
float4

Column4

The fourth column of this matrix

Declaration

public float4 Column4 { get; set; }

Property Value

Type	Description
float4

Determinant

The determinant of this matrix

Declaration

public readonly float Determinant { get; }

Property Value

Type	Description
System.Single

IsAffine

Checks whether row three (the projection part) of the matrix is equal to (0, 0, 0, 1). If this is the case the matrix is affine.

Declaration

public readonly bool IsAffine { get; }

Property Value

Type	Description
System.Boolean

Item[Int32, Int32]

Sets/Gets value from given index

Declaration

public float this[int i, int j] { get; set; }

Parameters

Type	Name	Description
System.Int32	i	The ROW index
System.Int32	j	The COLUMN index

Property Value

Type	Description
System.Single

M11

Gets and sets the value at row 1, column 1 of this instance.

Declaration

public float M11 { get; set; }

Property Value

Type	Description
System.Single

M12

Gets and sets the value at row 1, column 2 of this instance.

Declaration

public float M12 { get; set; }

Property Value

Type	Description
System.Single

M13

Gets and sets the value at row 1, column 3 of this instance.

Declaration

public float M13 { get; set; }

Property Value

Type	Description
System.Single

M14

Gets and sets the value at row 1, column 4 of this instance.

Declaration

public float M14 { get; set; }

Property Value

Type	Description
System.Single

M21

Gets and sets the value at row 2, column 1 of this instance.

Declaration

public float M21 { get; set; }

Property Value

Type	Description
System.Single

M22

Gets and sets the value at row 2, column 2 of this instance.

Declaration

public float M22 { get; set; }

Property Value

Type	Description
System.Single

M23

Gets and sets the value at row 2, column 3 of this instance.

Declaration

public float M23 { get; set; }

Property Value

Type	Description
System.Single

M24

Gets and sets the value at row 2, column 4 of this instance.

Declaration

public float M24 { get; set; }

Property Value

Type	Description
System.Single

M31

Gets and sets the value at row 3, column 1 of this instance.

Declaration

public float M31 { get; set; }

Property Value

Type	Description
System.Single

M32

Gets and sets the value at row 3, column 2 of this instance.

Declaration

public float M32 { get; set; }

Property Value

Type	Description
System.Single

M33

Gets and sets the value at row 3, column 3 of this instance.

Declaration

public float M33 { get; set; }

Property Value

Type	Description
System.Single

M34

Gets and sets the value at row 3, column 4 of this instance.

Declaration

public float M34 { get; set; }

Property Value

Type	Description
System.Single

M41

Gets and sets the value at row 4, column 1 of this instance.

Declaration

public float M41 { get; set; }

Property Value

Type	Description
System.Single

M42

Gets and sets the value at row 4, column 2 of this instance.

Declaration

public float M42 { get; set; }

Property Value

Type	Description
System.Single

M43

Gets and sets the value at row 4, column 3 of this instance.

Declaration

public float M43 { get; set; }

Property Value

Type	Description
System.Single

M44

Gets and sets the value at row 4, column 4 of this instance.

Declaration

public float M44 { get; set; }

Property Value

Type	Description
System.Single

Offset

Gets the offset part of the matrix as a float3 instance.

Declaration

public readonly float3 Offset { get; }

Property Value

Type	Description
float3

Remarks

The offset part of the matrix consists of the M14, M24 and M34 components (in row major order notation).

ParseConverter

Gets and sets the Converter object. Has the ability to convert a string to a float4x4.

Declaration

public static Converter<string, float4x4> ParseConverter { get; set; }

Property Value

Type	Description
Converter<System.String, float4x4>	The parse property.

Trace

Returns the trace of this matrix

Declaration

public readonly float Trace { get; }

Property Value

Type	Description
System.Single

Methods

Add(in float4x4, in float4x4)

Adds two instances.

Declaration

public static float4x4 Add(in float4x4 left, in float4x4 right)

Parameters

Type	Name	Description
float4x4	left	The left operand of the addition.
float4x4	right	The right operand of the addition.

Returns

Type	Description
float4x4	A new instance that is the result of the addition.

CreateFromAxisAngle(float3, Single)

Build a rotation matrix from the specified axis/angle rotation.

Declaration

public static float4x4 CreateFromAxisAngle(float3 axis, float angle)

Parameters

Type	Name	Description
float3	axis	The axis to rotate about.
System.Single	angle	Angle to rotate counter-clockwise (looking in the direction of the given axis).

Returns

Type	Description
float4x4	A matrix instance.

CreateOrthographic(Single, Single, Single, Single)

Creates a left handed orthographic projection matrix.

Declaration

public static float4x4 CreateOrthographic(float width, float height, float zNear, float zFar)

Parameters

Type	Name	Description
System.Single	width	The width of the projection volume.
System.Single	height	The height of the projection volume.
System.Single	zNear	The near edge of the projection volume.
System.Single	zFar	The far edge of the projection volume.

Returns

Type	Description
float4x4	The resulting float4x4 instance.

CreateOrthographicOffCenter(Single, Single, Single, Single, Single, Single)

Creates a left handed orthographic projection matrix.

Declaration

public static float4x4 CreateOrthographicOffCenter(float left, float right, float bottom, float top, float zNear, float zFar)

Parameters

Type	Name	Description
System.Single	left	The left edge of the projection volume.
System.Single	right	The right edge of the projection volume.
System.Single	bottom	The bottom edge of the projection volume.
System.Single	top	The top edge of the projection volume.
System.Single	zNear	The near edge of the projection volume.
System.Single	zFar	The far edge of the projection volume.

Returns

Type	Description
float4x4	The resulting float4x4 instance.

CreateOrthographicOffCenterRH(Single, Single, Single, Single, Single, Single)

Creates a right handed orthographic projection matrix.

Declaration

public static float4x4 CreateOrthographicOffCenterRH(float left, float right, float bottom, float top, float zNear, float zFar)

Parameters

Type	Name	Description
System.Single	left	The left edge of the projection volume.
System.Single	right	The right edge of the projection volume.
System.Single	bottom	The bottom edge of the projection volume.
System.Single	top	The top edge of the projection volume.
System.Single	zNear	The near edge of the projection volume.
System.Single	zFar	The far edge of the projection volume.

Returns

Type	Description
float4x4	The resulting float4x4 instance.

CreatePerspectiveFieldOfView(Single, Single, Single, Single)

Creates a left handed perspective projection matrix.

Declaration

public static float4x4 CreatePerspectiveFieldOfView(float fovy, float aspect, float zNear, float zFar)

Parameters

Type	Name	Description
System.Single	fovy	Angle of the field of view in the y direction (in radians)
System.Single	aspect	Aspect ratio of the view (width / height)
System.Single	zNear	Distance to the near clip plane
System.Single	zFar	Distance to the far clip plane

Returns

Type	Description
float4x4	A projection matrix that transforms camera space to raster space

Exceptions

Type	Condition
System.ArgumentOutOfRangeException	Thrown under the following conditions: fovy is zero, less than zero or larger than MathF.PI aspect is negative or zero zNear is negative or zero zFar is negative or zero zNear is larger than zFar

CreatePerspectiveOffCenter(Single, Single, Single, Single, Single, Single)

Creates an left handed perspective projection matrix.

Declaration

public static float4x4 CreatePerspectiveOffCenter(float left, float right, float bottom, float top, float zNear, float zFar)

Parameters

Type	Name	Description
System.Single	left	Left edge of the view frustum
System.Single	right	Right edge of the view frustum
System.Single	bottom	Bottom edge of the view frustum
System.Single	top	Top edge of the view frustum
System.Single	zNear	Distance to the near clip plane
System.Single	zFar	Distance to the far clip plane

Returns

Type	Description
float4x4	A projection matrix that transforms camera space to raster space

Exceptions

Type	Condition
System.ArgumentOutOfRangeException	Thrown under the following conditions: zNear is negative or zero zFar is negative or zero zNear is larger than zFar

CreatePerspectiveOffCenterRH(Single, Single, Single, Single, Single, Single)

Creates a right handed perspective projection matrix.

Declaration

public static float4x4 CreatePerspectiveOffCenterRH(float left, float right, float bottom, float top, float zNear, float zFar)

Parameters

Type	Name	Description
System.Single	left	Left edge of the view frustum
System.Single	right	Right edge of the view frustum
System.Single	bottom	Bottom edge of the view frustum
System.Single	top	Top edge of the view frustum
System.Single	zNear	Distance to the near clip plane
System.Single	zFar	Distance to the far clip plane

Returns

Type	Description
float4x4	A right handed projection matrix that transforms camera space to raster space

Remarks

Generates a matrix mapping a frustum shaped volume (the viewing frustum) to the unit cube (ranging from -1 to 1 in each dimension, also in z). The sign of the z-value will be flipped for vectors multiplied with this matrix. Given that the underlying rendering platform interprets z-values returned by the vertex shader to be in left-handed coordinates, where increasing z-values indicate locations further away from the view point (as BOTH, Direct3D AND OpenGL do), this type of matrix is widely called to be a "right handed" projection matrix as it assumes a right-handed camera coordinate system.

Exceptions

Type	Condition
System.ArgumentOutOfRangeException	Thrown under the following conditions: zNear is negative or zero zFar is negative or zero zNear is larger than zFar

CreateRotationX(Single)

Builds a rotation matrix for a rotation around the x-axis.

Declaration

public static float4x4 CreateRotationX(float angle)

Parameters

Type	Name	Description
System.Single	angle	The counter-clockwise angle in radians.

Returns

Type	Description
float4x4	The resulting float4x4 instance.

CreateRotationXY(float2)

Builds a rotation matrix for a rotation around the y and x-axis.

Declaration

public static float4x4 CreateRotationXY(float2 xy)

Parameters

Type	Name	Description
float2	xy	counter-clockwise angles in radians.

Returns

Type	Description
float4x4

CreateRotationXY(Single, Single)

Builds a rotation matrix for a rotation around the y and x-axis.

Declaration

public static float4x4 CreateRotationXY(float x, float y)

Parameters

Type	Name	Description
System.Single	x	counter-clockwise angles in radians.
System.Single	y	counter-clockwise angles in radians.

Returns

Type	Description
float4x4

CreateRotationY(Single)

Builds a rotation matrix for a rotation around the y-axis.

Declaration

public static float4x4 CreateRotationY(float angle)

Parameters

Type	Name	Description
System.Single	angle	The counter-clockwise angle in radians.

Returns

Type	Description
float4x4	The resulting float4x4 instance.

CreateRotationZ(Single)

Builds a rotation matrix for a rotation around the z-axis.

Declaration

public static float4x4 CreateRotationZ(float angle)

Parameters

Type	Name	Description
System.Single	angle	The counter-clockwise angle in radians.

Returns

Type	Description
float4x4	The resulting float4x4 instance.

CreateRotationZX(float2)

Builds a rotation matrix for a rotation around the y and x-axis.

Declaration

public static float4x4 CreateRotationZX(float2 xz)

Parameters

Type	Name	Description
float2	xz	counter-clockwise angles in radians.

Returns

Type	Description
float4x4

CreateRotationZX(Single, Single)

Builds a rotation matrix for a rotation around the y and x-axis.

Declaration

public static float4x4 CreateRotationZX(float x, float z)

Parameters

Type	Name	Description
System.Single	x	counter-clockwise angles in radians.
System.Single	z	counter-clockwise angles in radians.

Returns

Type	Description
float4x4

CreateRotationZXY(float3)

Builds a rotation matrix for a rotation around the y and x-axis.

Declaration

public static float4x4 CreateRotationZXY(float3 xyz)

Parameters

Type	Name	Description
float3	xyz	counter-clockwise angles in radians.

Returns

Type	Description
float4x4

CreateRotationZXY(Single, Single, Single)

Builds a rotation matrix for a rotation around the y and x-axis.

Declaration

public static float4x4 CreateRotationZXY(float x, float y, float z)

Parameters

Type	Name	Description
System.Single	x	counter-clockwise angles in radians.
System.Single	y	counter-clockwise angles in radians.
System.Single	z	counter-clockwise angles in radians.

Returns

Type	Description
float4x4

CreateRotationZY(float2)

Builds a rotation matrix for a rotation around the y and z-axis.

Declaration

public static float4x4 CreateRotationZY(float2 yz)

Parameters

Type	Name	Description
float2	yz	counter-clockwise angles in radians.

Returns

Type	Description
float4x4

CreateRotationZY(Single, Single)

Builds a rotation matrix for a rotation around the y and x-axis.

Declaration

public static float4x4 CreateRotationZY(float y, float z)

Parameters

Type	Name	Description
System.Single	y	counter-clockwise angles in radians.
System.Single	z	counter-clockwise angles in radians.

Returns

Type	Description
float4x4

CreateScale(float3)

Creates a scale matrix.

Declaration

public static float4x4 CreateScale(float3 vector)

Parameters

Type	Name	Description
float3	vector	The scale vector.

Returns

Type	Description
float4x4	The resulting float4x4 instance.

CreateScale(Single)

Creates a uniform scale matrix with the same scale value along all three dimensions.

Declaration

public static float4x4 CreateScale(float scale)

Parameters

Type	Name	Description
System.Single	scale	The value to scale about x, y, and z.

Returns

Type	Description
float4x4	The resulting float4x4 instance.

CreateScale(Single, Single, Single)

Creates a scale matrix.

Declaration

public static float4x4 CreateScale(float x, float y, float z)

Parameters

Type	Name	Description
System.Single	x	X scale.
System.Single	y	Y scale.
System.Single	z	Z scale.

Returns

Type	Description
float4x4	The resulting float4x4 instance.

CreateTranslation(float3)

Creates a translation matrix.

Declaration

public static float4x4 CreateTranslation(float3 vector)

Parameters

Type	Name	Description
float3	vector	The translation vector.

Returns

Type	Description
float4x4	The resulting float4x4 instance.

CreateTranslation(Single, Single, Single)

Creates a translation matrix.

Declaration

public static float4x4 CreateTranslation(float x, float y, float z)

Parameters

Type	Name	Description
System.Single	x	X translation.
System.Single	y	Y translation.
System.Single	z	Z translation.

Returns

Type	Description
float4x4	The resulting float4x4 instance.

Equals(float4x4)

Indicates whether the current matrix is equal to another matrix.

Declaration

public readonly bool Equals(float4x4 other)

Parameters

Type	Name	Description
float4x4	other	A matrix to compare with this matrix.

Returns

Type	Description
System.Boolean	true if the current matrix is equal to the matrix parameter; otherwise, false.

Equals(Object)

Indicates whether this instance and a specified object are equal.

Declaration

public override readonly bool Equals(object obj)

Parameters

Type	Name	Description
System.Object	obj	The object to compare tresult.

Returns

Type	Description
System.Boolean	True if the instances are equal; false otherwise.

Overrides

System.ValueType.Equals(System.Object)

GetHashCode()

Returns the hashcode for this instance.

Declaration

public override int GetHashCode()

Returns

Type	Description
System.Int32	A System.Int32 containing the unique hashcode for this instance.

Overrides

System.ValueType.GetHashCode()

GetScale(float4x4)

Calculates the scale factor of the given float4x4 and returns it as a float3 vector.

Declaration

public static float3 GetScale(float4x4 mat)

Parameters

Type	Name	Description
float4x4	mat

Returns

Type	Description
float3

GetTranslation(float4x4)

Calculates translation of the given float4x4 matrix and returns it as a float3 vector.

Declaration

public static float3 GetTranslation(float4x4 mat)

Parameters

Type	Name	Description
float4x4	mat

Returns

Type	Description
float3

Invert()

Converts this instance into its inverse.

Declaration

public float4x4 Invert()

Returns

Type	Description
float4x4

Invert(in float4x4)

Calculate the inverse of the given matrix. If you are unsure whether the matrix is invertible, check it with IsInvertable() first.

Declaration

public static float4x4 Invert(in float4x4 matrix)

Parameters

Type	Name	Description
float4x4	matrix	The matrix to invert.

Returns

Type	Description
float4x4	The inverse of the given matrix.

IsInvertable(float4x4)

Checks if this matrix is invertible.

Declaration

public static bool IsInvertable(float4x4 mat)

Parameters

Type	Name	Description
float4x4	mat	The matrix.

Returns

Type	Description
System.Boolean

IsInvertable(float4x4, out Single)

Checks if this matrix is invertible.

Declaration

public static bool IsInvertable(float4x4 mat, out float det)

Parameters

Type	Name	Description
float4x4	mat	The matrix.
System.Single	det	The determinant of the matrix.

Returns

Type	Description
System.Boolean

LookAt(float3, float3, float3)

Build a left handed world space to camera space matrix

Declaration

public static float4x4 LookAt(float3 eye, float3 target, float3 up)

Parameters

Type	Name	Description
float3	eye	Eye (camera) position in world space
float3	target	Target position in world space
float3	up	Up vector in world space (should not be parallel to the camera direction, that is target - eye)

Returns

Type	Description
float4x4	A Matrix4 that transforms world space to camera space

LookAt(Single, Single, Single, Single, Single, Single, Single, Single, Single)

Build a world space to camera space matrix

Declaration

public static float4x4 LookAt(float eyeX, float eyeY, float eyeZ, float targetX, float targetY, float targetZ, float upX, float upY, float upZ)

Parameters

Type	Name	Description
System.Single	eyeX	Eye (camera) position in world space
System.Single	eyeY	Eye (camera) position in world space
System.Single	eyeZ	Eye (camera) position in world space
System.Single	targetX	Target position in world space
System.Single	targetY	Target position in world space
System.Single	targetZ	Target position in world space
System.Single	upX	Up vector in world space (should not be parallel to the camera direction, that is target - eye)
System.Single	upY	Up vector in world space (should not be parallel to the camera direction, that is target - eye)
System.Single	upZ	Up vector in world space (should not be parallel to the camera direction, that is target - eye)

Returns

Type	Description
float4x4	A float4x4 that transforms world space to camera space

LookAtRH(float3, float3, float3)

Build a right handed world space to camera space matrix

Declaration

public static float4x4 LookAtRH(float3 eye, float3 target, float3 up)

Parameters

Type	Name	Description
float3	eye	Eye (camera) position in world space
float3	target	Target position in world space
float3	up	Up vector in world space (should not be parallel to the camera direction, that is target - eye)

Returns

Type	Description
float4x4	A float4x4 that transforms world space to camera space

Mult(in float4x4, in float4x4)

Multiplies two instances.

Declaration

public static float4x4 Mult(in float4x4 left, in float4x4 right)

Parameters

Type	Name	Description
float4x4	left	The left operand of the multiplication.
float4x4	right	The right operand of the multiplication.

Returns

Type	Description
float4x4	A new instance that is the result of the multiplication

Parse(String, IFormatProvider)

Parses a string into a float4x4.

Declaration

public static float4x4 Parse(string source, IFormatProvider provider = null)

Parameters

Type	Name	Description
System.String	source
System.IFormatProvider	provider

Returns

Type	Description
float4x4

RotationComponent()

The rotation component of this matrix.

Declaration

public float4x4 RotationComponent()

Returns

Type	Description
float4x4

RotationDecomposition(float4x4)

Calculates and returns the rotation component of the given float4x4 matrix.

Declaration

public static float4x4 RotationDecomposition(float4x4 mat)

Parameters

Type	Name	Description
float4x4	mat

Returns

Type	Description
float4x4

RotMatToEuler(float4x4)

Returns the euler angles from a given rotation matrix.

Declaration

public static float3 RotMatToEuler(float4x4 rotMat)

Parameters

Type	Name	Description
float4x4	rotMat	The roation matrix.

Returns

Type	Description
float3

Round()

Rounds this instance to 6 digits (max float precision).

Declaration

public float4x4 Round()

Returns

Type	Description
float4x4

Round(float4x4)

Rounds the given matrix to 6 digits (max float precision).

Declaration

public static float4x4 Round(float4x4 mat)

Parameters

Type	Name	Description
float4x4	mat	The matrix to round.

Returns

Type	Description
float4x4	The rounded matrix.

Scale()

The scale factors of this matrix.

Declaration

public float3 Scale()

Returns

Type	Description
float3

Scale(float3)

Build a scaling matrix

Declaration

public static float4x4 Scale(float3 scale)

Parameters

Type	Name	Description
float3	scale	Scale factors for x,y and z axes

Returns

Type	Description
float4x4	A scaling matrix

Scale(Single)

Build a scaling matrix

Declaration

public static float4x4 Scale(float scale)

Parameters

Type	Name	Description
System.Single	scale	Single scale factor for x,y and z axes

Returns

Type	Description
float4x4	A scaling matrix

Scale(Single, Single, Single)

Build a scaling matrix

Declaration

public static float4x4 Scale(float x, float y, float z)

Parameters

Type	Name	Description
System.Single	x	Scale factor for x-axis
System.Single	y	Scale factor for y-axis
System.Single	z	Scale factor for z-axis

Returns

Type	Description
float4x4	A scaling matrix

ScaleComponent()

The scale component of this matrix.

Declaration

public float4x4 ScaleComponent()

Returns

Type	Description
float4x4

ScaleDecomposition(float4x4)

Calculates and returns the scale component of the given float4x4 matrix.

Declaration

public static float4x4 ScaleDecomposition(float4x4 mat)

Parameters

Type	Name	Description
float4x4	mat

Returns

Type	Description
float4x4

Subtract(in float4x4, in float4x4)

Subtracts the right instance from the left instance.

Declaration

public static float4x4 Subtract(in float4x4 left, in float4x4 right)

Parameters

Type	Name	Description
float4x4	left	The left operand of the subtraction.
float4x4	right	The right operand of the subtraction.

Returns

Type	Description
float4x4	A new instance that is the result of the subtraction.

ToArray()

Returns the matrix as float array.

Declaration

public float[] ToArray()

Returns

Type	Description
System.Single[]

ToString()

Returns a System.String that represents the current float4x4.

Declaration

public override string ToString()

Returns

Type	Description
System.String	A string.

Overrides

System.ValueType.ToString()

ToString(IFormatProvider)

Returns a System.String that represents the current float4x4.

Declaration

public string ToString(IFormatProvider provider)

Parameters

Type	Name	Description
System.IFormatProvider	provider	Provides information about a specific culture.

Returns

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

Transform(float4x4, float3)

Transforms a given 3D vector by a matrix using perspective division via matrix*vector (Postmultiplication of the vector).

Declaration

public static float3 Transform(float4x4 matrix, float3 vector)

Parameters

Type	Name	Description
float4x4	matrix	A float4x4 instance.
float3	vector	A float3 instance.

Returns

Type	Description
float3	A new float3 instance containing the result.

Remarks

Before the matrix multiplication the 3D vector is extended to 4D by setting its W component to 1. After the matrix multiplication the resulting 4D vector is transformed to 3D by dividing X, Y, and Z by W. (perspective division).

Transform(float4x4, float4)

Transforms a given vector by a matrix via matrix*vector (Postmultiplication of the vector).

Declaration

public static float4 Transform(float4x4 matrix, float4 vector)

Parameters

Type	Name	Description
float4x4	matrix	A float4x4 instance.
float4	vector	A float4 instance.

Returns

Type	Description
float4	A new float4 instance containing the result.

TransformPerspective(float4x4, float3)

Transforms a given 3D vector by a matrix, and projects the resulting float4 back to a float3.

Declaration

public static float3 TransformPerspective(float4x4 mat, float3 vec)

Parameters

Type	Name	Description
float4x4	mat	The desired transformation matrix.
float3	vec	The given vector.

Returns

Type	Description
float3	The transformed vector.

TransformPerspective(float4x4, float4)

Transforms the given vector by the given matrix and applies a perspective division.

Declaration

public static float4 TransformPerspective(float4x4 mat, float4 vec)

Parameters

Type	Name	Description
float4x4	mat	The desired transformation.
float4	vec	The given vector.

Returns

Type	Description
float4	The transformed vector.

TransformPremult(float3, float4x4)

Transforms a given 3D vector by a matrix using perspective division via vector*matrix (Premultiplication of the vector).

Declaration

public static float3 TransformPremult(float3 vector, float4x4 matrix)

Parameters

Type	Name	Description
float3	vector	A float3 instance.
float4x4	matrix	A float4x4 instance.

Returns

Type	Description
float3	A new float3 instance containing the result.

Remarks

Before the matrix multiplication the 3D vector is extended to 4D by setting its W component to 1. After the matrix multiplication the resulting 4D vector is transformed to 3D by dividing X, Y, and Z by W. (perspective division).

TransformPremult(float4, float4x4)

Transforms a given vector by a matrix via vector*matrix (Premultiplication of the vector).

Declaration

public static float4 TransformPremult(float4 vector, float4x4 matrix)

Parameters

Type	Name	Description
float4	vector	A float4 instance.
float4x4	matrix	A float4x4 instance.

Returns

Type	Description
float4	A new float4 instance containing the result.

Translation()

The translation of this matrix.

Declaration

public float3 Translation()

Returns

Type	Description
float3

TranslationComponent()

The translation component of this matrix.

Declaration

public float4x4 TranslationComponent()

Returns

Type	Description
float4x4

TranslationDecomposition(float4x4)

Calculates and returns only the translation component of the given float4x4 matrix.

Declaration

public static float4x4 TranslationDecomposition(float4x4 mat)

Parameters

Type	Name	Description
float4x4	mat

Returns

Type	Description
float4x4

Transpose()

Converts this instance into its transpose.

Declaration

public float4x4 Transpose()

Returns

Type	Description
float4x4

Transpose(float4x4)

Calculate the transpose of the given matrix

Declaration

public static float4x4 Transpose(float4x4 matrix)

Parameters

Type	Name	Description
float4x4	matrix	The matrix to transpose

Returns

Type	Description
float4x4	The transpose of the given matrix

Operators

Addition(float4x4, float4x4)

Matrix addition

Declaration

public static float4x4 operator +(float4x4 left, float4x4 right)

Parameters

Type	Name	Description
float4x4	left	left-hand operand
float4x4	right	right-hand operand

Returns

Type	Description
float4x4	A new float4x4 which holds the result of the multiplication

Equality(float4x4, float4x4)

Compares two instances for equality.

Declaration

public static bool operator ==(float4x4 left, float4x4 right)

Parameters

Type	Name	Description
float4x4	left	The first instance.
float4x4	right	The second instance.

Returns

Type	Description
System.Boolean	True, if left equals right; false otherwise.

Explicit(double4x4 to float4x4)

Explicit cast operator to cast a double4x4 into a float4x4 value.

Declaration

public static explicit operator float4x4(double4x4 d4x4)

Parameters

Type	Name	Description
double4x4	d4x4	The double4x4 value to cast.

Returns

Type	Description
float4x4	A float4x4 value.

Inequality(float4x4, float4x4)

Compares two instances for inequality.

Declaration

public static bool operator !=(float4x4 left, float4x4 right)

Parameters

Type	Name	Description
float4x4	left	The first instance.
float4x4	right	The second instance.

Returns

Type	Description
System.Boolean	True, if left does not equal right; false otherwise.

Multiply(float3, float4x4)

Transforms a given three dimensional vector by a matrix via vector*matrix (pre-multiplication of the vector).

Declaration

public static float3 operator *(float3 vector, float4x4 matrix)

Parameters

Type	Name	Description
float3	vector	A float3 instance.
float4x4	matrix	A float4x4 instance.

Returns

Type	Description
float3	A new float4 instance containing the result.

Remarks

Before the matrix multiplication the 3D vector is extended to 4D by setting its W component to 1. After the matrix multiplication the resulting 4D vector is transformed to 3D by dividing X, Y, and Z by W. (perspective division).

Multiply(float4, float4x4)

Transforms a given vector by a matrix via vector*matrix (pre-multiplication of the vector).

Declaration

public static float4 operator *(float4 vector, float4x4 matrix)

Parameters

Type	Name	Description
float4	vector	A float4 instance.
float4x4	matrix	A float4x4 instance.

Returns

Type	Description
float4	A new float4 instance containing the result.

Multiply(float4x4, float3)

Transforms a given three dimensional vector by a matrix via matrix*vector (post-multiplication of the vector).

Declaration

public static float3 operator *(float4x4 matrix, float3 vector)

Parameters

Type	Name	Description
float4x4	matrix	A float4x4 instance.
float3	vector	A float3 instance.

Returns

Type	Description
float3	A new float4 instance containing the result.

Remarks

Before the matrix multiplication the 3D vector is extended to 4D by setting its W component to 1. After the matrix multiplication the resulting 4D vector is transformed to 3D by dividing X, Y, and Z by W. (perspective division).

Multiply(float4x4, float4)

Transforms a given vector by a matrix via matrix*vector (post-multiplication of the vector).

Declaration

public static float4 operator *(float4x4 matrix, float4 vector)

Parameters

Type	Name	Description
float4x4	matrix	A float4x4 instance.
float4	vector	A float4 instance.

Returns

Type	Description
float4	A new float4 instance containing the result.

Multiply(float4x4, float4x4)

Matrix multiplication

Declaration

public static float4x4 operator *(float4x4 left, float4x4 right)

Parameters

Type	Name	Description
float4x4	left	left-hand operand
float4x4	right	right-hand operand

Returns

Type	Description
float4x4	A new Matrix44 which holds the result of the multiplication

Subtraction(float4x4, float4x4)

Matrix subtraction

Declaration

public static float4x4 operator -(float4x4 left, float4x4 right)

Parameters

Type	Name	Description
float4x4	left	left-hand operand
float4x4	right	right-hand operand

Returns

Type	Description
float4x4	A new float2x2 which holds the result of the multiplication

Implements

System.IEquatable<T>