Struct Matrix4

4x4 matrix, typically used to describe a transformation (rotation and translation).

Namespace: ABB.Robotics.Math

Assembly: ABB.Robotics.Math.dll

Syntax

public struct Matrix4

Constructors

Matrix4(Matrix3, Vector3)

Constructs a matrix from a 3x3 orientation matrix and a translation.

Declaration

public Matrix4(Matrix3 orientation, Vector3 translation)

Parameters

Type	Name	Description
Matrix3	orientation
Vector3	translation

Matrix4(Vector3)

Creates a matrix with unit rotation and a specified translation.

Declaration

public Matrix4(Vector3 translation)

Parameters

Type	Name	Description
Vector3	translation	Translation vector

Matrix4(Vector3, Quaternion)

Creates a matrix from a translation vector and a quaternion.

Declaration

public Matrix4(Vector3 translation, Quaternion quat)

Parameters

Type	Name	Description
Vector3	translation	Translation vector
Quaternion	quat	Quaternion

Matrix4(Vector3, Vector3)

Creates a matrix from a translation vector and Euler angles (zyx).

Declaration

public Matrix4(Vector3 translation, Vector3 eulerZYX)

Parameters

Type	Name	Description
Vector3	translation	Translation vector
Vector3	eulerZYX	Euler angles (zyx order)

Matrix4(Vector3, Vector3, Vector3, Vector3)

Creates an affine matrix from four vectors

Declaration

public Matrix4(Vector3 x0, Vector3 y0, Vector3 z0, Vector3 t0)

Parameters

Type	Name	Description
Vector3	x0	X axis
Vector3	y0	Y axis
Vector3	z0	Z axis
Vector3	t0	Translation

Matrix4(Vector3, double)

Creates a matrix from a rotation axis and angle, with unit translation.

Declaration

public Matrix4(Vector3 axis, double angle)

Parameters

Type	Name	Description
Vector3	axis	Rotation axis
double	angle	Rotation angle

Exceptions

Type	Condition
ArgumentException	Invalid rotation axis

Matrix4(Vector4, Vector4, Vector4, Vector4)

Creates a matrix from four column vectors.

Declaration

public Matrix4(Vector4 x0, Vector4 y0, Vector4 z0, Vector4 t0)

Parameters

Type	Name	Description
Vector4	x0	First column
Vector4	y0	Second column
Vector4	z0	Third column
Vector4	t0	Fourth column

Matrix4(double[], bool)

Creates a matrix from an array of 16 values.

Declaration

public Matrix4(double[] values, bool rowMajor)

Parameters

Type	Name	Description
double[]	values
bool	rowMajor

Fields

Identity

Identity matrix.

Declaration

public static readonly Matrix4 Identity

Field Value

Type	Description
Matrix4

t

Column vector.

Declaration

public Vector4 t

Field Value

Type	Description
Vector4

x

Column vector.

Declaration

public Vector4 x

Field Value

Type	Description
Vector4

y

Column vector.

Declaration

public Vector4 y

Field Value

Type	Description
Vector4

z

Column vector.

Declaration

public Vector4 z

Field Value

Type	Description
Vector4

Properties

AxisAngle

Gets/sets the rotation as axis/angle (represented by a 4-vector [axis,angle]).

Declaration

public Vector4 AxisAngle { get; set; }

Property Value

Type	Description
Vector4

Exceptions

Type	Condition
ArgumentException	Invalid rotation axis

Elements

Returns an array of all elements in column-first order.

Declaration

public double[] Elements { get; }

Property Value

Type	Description
double[]

EulerXYZ

Gets/sets the rotation as Euler angles (xyz order).

Declaration

public Vector3 EulerXYZ { get; set; }

Property Value

Type	Description
Vector3

EulerZYX

Gets/sets the rotation as Euler angles (zyx order).
Note: the vector contains the angles as [rx,ry,rz].

Declaration

public Vector3 EulerZYX { get; set; }

Property Value

Type	Description
Vector3

IsNaN

Returns a value indicating whether any elements evaluates to a value that is not a number (NaN).

Declaration

public bool IsNaN { get; }

Property Value

Type	Description
bool

this[int]

Column vector access.

Declaration

public Vector4 this[int index] { get; set; }

Parameters

Type	Name	Description
int	index

Property Value

Type	Description
Vector4

Quaternion

Gets/sets the rotation as a quaternion.

Declaration

public Quaternion Quaternion { get; set; }

Property Value

Type	Description
Quaternion

Translation

Gets/sets the translation vector.

Declaration

public Vector3 Translation { get; set; }

Property Value

Type	Description
Vector3

UpperLeft

Gets/sets the rotation as a 3x3 matrix.

Declaration

public Matrix3 UpperLeft { get; set; }

Property Value

Type	Description
Matrix3

Methods

Align(Matrix4, Matrix4)

Rotates a matrix so that its rotation axes coincide with the closest arbitrary (negative or positive) rotation axes of a reference matrix.

Declaration

public static Matrix4 Align(Matrix4 matrix, Matrix4 reference)

Parameters

Type	Name	Description
Matrix4	matrix	The matrix to rotate
Matrix4	reference	Reference matrix

Returns

Type	Description
Matrix4	The aligned matrix

AlmostEquals(Matrix4)

Comparison method for matrices with default tolerance

Declaration

public bool AlmostEquals(Matrix4 rhs)

Parameters

Type	Name	Description
Matrix4	rhs	Matrix to compare with

Returns

Type	Description
bool	true if equals within tolerance

AlmostEquals(Matrix4, double)

Comparison method for matrices with tolerance

Declaration

public bool AlmostEquals(Matrix4 rhs, double tolerance)

Parameters

Type	Name	Description
Matrix4	rhs	Matrix to compare with
double	tolerance	tolerance

Returns

Type	Description
bool	true if equals within tolerance

CheckRigid()

Throws an exception if this matrix is not rigid.

Declaration

public void CheckRigid()

Clean()

Zeroes any values smaller than Globals.EPS.

Declaration

public void Clean()

CleanRigid()

Ensures this is a valid rigid matrix

Declaration

public void CleanRigid()

Determinant()

Returns the determinant.

Declaration

public double Determinant()

Returns

Type	Description
double

FromAxis(Axis, Vector3, Vector3)

Returns a matrix with one given axis. The other two axes are arbitrarily chosen to form a right-handed coordinate system.

Declaration

public static Matrix4 FromAxis(Axis axis, Vector3 axisDirection, Vector3 translation)

Parameters

Type	Name	Description
Axis	axis
Vector3	axisDirection
Vector3	translation

Returns

Type	Description
Matrix4

FromThreePoint(Vector3, Vector3, Vector3)

Creates a matrix from three points.

Declaration

public static Matrix4 FromThreePoint(Vector3 x1, Vector3 x2, Vector3 y1)

Parameters

Type	Name	Description
Vector3	x1	First point on x axis
Vector3	x2	Second point on x axis
Vector3	y1	Point on y axis

Returns

Type	Description
Matrix4

FromTwoAxes(Vector3, Vector3, DirectionAxis, Vector3, DirectionAxis)

Creates a matrix from a translation and two axis vectors

Declaration

public static Matrix4 FromTwoAxes(Vector3 translation, Vector3 axis1, DirectionAxis axis1Direction, Vector3 axis2, DirectionAxis axis2Direction)

Parameters

Type	Name	Description
Vector3	translation	Translation
Vector3	axis1	First axis
DirectionAxis	axis1Direction
Vector3	axis2	Second axis
DirectionAxis	axis2Direction

Returns

Type	Description
Matrix4

FromTwoPointXY(Vector3, Vector3, Vector3)

Creates a matrix from a translation and two points

Declaration

public static Matrix4 FromTwoPointXY(Vector3 translation, Vector3 x1, Vector3 xy)

Parameters

Type	Name	Description
Vector3	translation	Translation
Vector3	x1	Point on x axis
Vector3	xy	Point in x-y plane

Returns

Type	Description
Matrix4

FromTwoPointXZ(Vector3, Vector3, Vector3)

Creates a matrix from a translation and two points

Declaration

public static Matrix4 FromTwoPointXZ(Vector3 translation, Vector3 x1, Vector3 xz)

Parameters

Type	Name	Description
Vector3	translation	Translation
Vector3	x1	Point on x axis
Vector3	xz	Point in x-z plane

Returns

Type	Description
Matrix4

GetAxisVector(Axis)

Gets the axis vector from the specified axis

Declaration

public Vector3 GetAxisVector(Axis axis)

Parameters

Type	Name	Description
Axis	axis	the axis whose vector to get

Returns

Type	Description
Vector3	the axis vector

GetAxisVector(DirectionAxis)

Gets the positive or negative axis vector from the specified axis

Declaration

public Vector3 GetAxisVector(DirectionAxis axis)

Parameters

Type	Name	Description
DirectionAxis	axis	the axis whose vector to get

Returns

Type	Description
Vector3	the axis vector

Inverse()

Returns the inverse of a general matrix.

Declaration

public Matrix4 Inverse()

Returns

Type	Description
Matrix4	Inverted matrix

InverseRigid()

Returns a an inverted copy of the matrix. If the matrix is non-rigid the result is undefined.

Declaration

public Matrix4 InverseRigid()

Returns

Type	Description
Matrix4	The inverse of the matrix.

Invert()

Inverts a general matrix, using Cramer's rule.

Declaration

public void Invert()

InvertAffine()

Inverts an affine matrix.

Declaration

public void InvertAffine()

InvertRigid()

Inverts a rigid (pure translation+rotation) matrix.

Declaration

public void InvertRigid()

IsAffine()

Returns true if the matrix is affine.

Declaration

public bool IsAffine()

Returns

Type	Description
bool

IsEmpty()

Returns true if all elements in the matrix are zero.

Declaration

public bool IsEmpty()

Returns

Type	Description
bool

IsIdentity()

Returns true if the matrix is identity.

Declaration

public bool IsIdentity()

Returns

Type	Description
bool

IsRigid()

Returns true if this matrix is rigid (orthogonal), e.g. it represents a pure rotation and translation.

Declaration

public bool IsRigid()

Returns

Type	Description
bool

Multiply(Matrix4)

Matrix-Matrix multiplication method.

Declaration

public Matrix4 Multiply(Matrix4 rhs)

Parameters

Type	Name	Description
Matrix4	rhs

Returns

Type	Description
Matrix4

Multiply(Vector4)

Matrix-Vector4 multiplication method.

Declaration

public Vector4 Multiply(Vector4 rhs)

Parameters

Type	Name	Description
Vector4	rhs

Returns

Type	Description
Vector4

MultiplyPoint(Vector3)

Matrix-Vector3 (interpreted as a point) multiplication.

Declaration

public Vector3 MultiplyPoint(Vector3 rhs)

Parameters

Type	Name	Description
Vector3	rhs

Returns

Type	Description
Vector3

MultiplyVector(Vector3)

Matrix-Vector3 (interpreted as a direction) multiplication.

Declaration

public Vector3 MultiplyVector(Vector3 rhs)

Parameters

Type	Name	Description
Vector3	rhs

Returns

Type	Description
Vector3

RelativeMatrix(Matrix4, Matrix4)

Returns a matrix representing the relative transform, between the two specified matrices.

Declaration

public static Matrix4 RelativeMatrix(Matrix4 from, Matrix4 to)

Parameters

Type	Name	Description
Matrix4	from
Matrix4	to

Returns

Type	Description
Matrix4

Rotate(Vector3, Vector3, double)

Rotates the matrix around an axis through a point.

Declaration

public void Rotate(Vector3 point, Vector3 axis, double angle)

Parameters

Type	Name	Description
Vector3	point
Vector3	axis
double	angle

Exceptions

Type	Condition
ArgumentException	Invalid rotation axis

Rotate(Vector3, double)

Rotates the matrix around an axis through the origin.

Declaration

public void Rotate(Vector3 axis, double angle)

Parameters

Type	Name	Description
Vector3	axis
double	angle

Exceptions

Type	Condition
ArgumentException	Invalid rotation axis

Scale(Vector3)

Scale by vector about origin.

Declaration

public void Scale(Vector3 scalevec)

Parameters

Type	Name	Description
Vector3	scalevec

Scale(Vector3, Vector3)

Scale by vector about a point.

Declaration

public void Scale(Vector3 scalevec, Vector3 point)

Parameters

Type	Name	Description
Vector3	scalevec
Vector3	point

Scale(double)

Scale uniformly about origin.

Declaration

public void Scale(double amount)

Parameters

Type	Name	Description
double	amount

ToString()

Returns a string in the format
[[x.x x.y x.z x.w] [y.x y.y y.z y.w] [z.x z.y z.z z.w] [t.x t.y t.z t.w]]

Declaration

public override string ToString()

Returns

Type	Description
string

Overrides

ValueType.ToString()

ToString(IFormatProvider)

Returns a string in the format
[[x.x x.y x.z x.w] [y.x y.y y.z y.w] [z.x z.y z.z z.w] [t.x t.y t.z t.w]]

Declaration

public string ToString(IFormatProvider formatProvider)

Parameters

Type	Name	Description
IFormatProvider	formatProvider

Returns

Type	Description
string

Translate(Vector3)

Translates the matrix by a vector.

Declaration

public void Translate(Vector3 translation)

Parameters

Type	Name	Description
Vector3	translation

Translate(double, double, double)

Translates the matrix by x,y,z.

Declaration

public void Translate(double dx, double dy, double dz)

Parameters

Type	Name	Description
double	dx
double	dy
double	dz

TranslateLocal(Vector3)

Translates the matrix by a vector in its own coordinate system.

Declaration

public void TranslateLocal(Vector3 translation)

Parameters

Type	Name	Description
Vector3	translation

TranslateLocal(double, double, double)

Translates the matrix by x,y,z in its own coordinate system.

Declaration

public void TranslateLocal(double dx, double dy, double dz)

Parameters

Type	Name	Description
double	dx
double	dy
double	dz

Transpose()

Transposes the matrix.

Declaration

public void Transpose()

TryParse(string, out Matrix4)

Converts the string representation to its Matrix4 equivalent.

Declaration

public static bool TryParse(string value, out Matrix4 result)

Parameters

Type	Name	Description
string	value
Matrix4	result

Returns

Type	Description
bool	A value indicating whether the conversion succeeded

TryParse(string, IFormatProvider, out Matrix4)

Converts the string representation to its Matrix4 equivalent.

Declaration

public static bool TryParse(string value, IFormatProvider formatProvider, out Matrix4 result)

Parameters

Type	Name	Description
string	value
IFormatProvider	formatProvider
Matrix4	result

Returns

Type	Description
bool	A value indicating whether the conversion succeeded

WithEulerZYX(Vector3)

Returns a new Matrix4 with the given Euler ZYX orientation

Declaration

public Matrix4 WithEulerZYX(Vector3 eulerZYX)

Parameters

Type	Name	Description
Vector3	eulerZYX

Returns

Type	Description
Matrix4

WithTranslation(Vector3)

Returns a new Matrix4 with the given translation

Declaration

public Matrix4 WithTranslation(Vector3 translation)

Parameters

Type	Name	Description
Vector3	translation

Returns

Type	Description
Matrix4

Operators

operator *(Matrix4, Matrix4)

Matrix-Matrix multiplication operator.

Declaration

public static Matrix4 operator *(Matrix4 lhs, Matrix4 rhs)

Parameters

Type	Name	Description
Matrix4	lhs
Matrix4	rhs

Returns

Type	Description
Matrix4

operator *(Matrix4, Vector4)

Matrix-Vector4 multiplication operator.

Declaration

public static Vector4 operator *(Matrix4 lhs, Vector4 rhs)

Parameters

Type	Name	Description
Matrix4	lhs
Vector4	rhs

Returns

Type	Description
Vector4