CoordinateSystemBaseVectors Class Reference

This class is subject to change. Programs using this class may require changes with a new version of VirtualLab.
Class for the base vectors of a Cartesian coordinate system. This kind of triple vector is also called "trihedron". More...

Inheritance diagram for CoordinateSystemBaseVectors:

Public Member Functions
override object	Clone ()
	Deep copy.
	CoordinateSystemBaseVectors ()
	Constructor that creates a system base object with the axes ((1,0,0), (0,1,0), (0,0,1))
	CoordinateSystemBaseVectors (CoordinateSystemBaseVectors sBaseVectors)
	Copy constructor.
	CoordinateSystemBaseVectors (double eulerPsi, double eulerTheta, double eulerPhi)
	Constructor that uses Euler angles. See Bronstein et.al. "Taschenbuch der Mathematik" 2., überarb. und erw. Aufl.; Deutsch-Verlag, 1995; p.179-180.
	CoordinateSystemBaseVectors (Matrix3x3D rotationMatrix)
	Constructor that uses a rotation matrix for initializing the direction cosines.
	CoordinateSystemBaseVectors (OrientationDefinitionBase orientationDefinition)
	Constructor which gets an orientation definition.
	CoordinateSystemBaseVectors (Quaternion quaternion)
	Constructor which gets a quaternion.
	CoordinateSystemBaseVectors (SerializationInfo info, StreamingContext context)
	Deserialization constructor used for manual serialization.
	CoordinateSystemBaseVectors (Vector3D axis1, Vector3D axis2, CoordinatePlane plane)
	Constructor which gets only two base vectors. This may be helpful if one of the base vectors has already been created from a cross product, so creating the third base vector also by a cross product may produce large numerical problems.
	CoordinateSystemBaseVectors (Vector3D directionOfZAxis, double zeta, bool inclinationFirst)
	Constructs a new coordinate system base vectors object via z-rotation and the direction vector of the z-axis: The orientation of the system's axes result from 2 steps and a certain order . A) inclinationFirst = false: (i) Rotation about z-axis with angle zeta - using the right-hand-rule, (ii) Inclination of z-axis specified by new direction axis. B) inclinationFirst = true: (i) Inclination of z-axis specified by direction vector, (ii) Rotation about inclined z-axis by angle zeta - using the right-hand-rule.
	CoordinateSystemBaseVectors (Vector3D xAxis, Vector3D yAxis, Vector3D zAxis)
	Constructor that uses direction cosines. This constructor is not recommended, because there's a significant probability for numerical inaccuracies which cause orthogonality problems. Better options may be the constructors getting a OrientationDefinitionBase or getting two axes and a plane index.
bool	Equals (CoordinateSystemBaseVectors baseVectors, bool indulgentCheck)
	Method that checks whether another CoordinateSystemBaseVectors object is equivalent to this.
override bool	Equals (object obj, EqualityIntent equalityIntent)
	Method which checks for equal objects.
Matrix3x3D	GetInverseRotationMatrix ()
	Get the corresponding rotation matrix build up from the direction cosines, i.e. the coordinates of the unit vectors of the three axes. If local and reference coordinate system have the same origin, a multiplication with this matrix would perform a coordinate transformation from the reference (external) cs to the local (internal) coordinate system.
OrientationDefinitionBase	GetOrientation (OrientationDefinitionType type)
	Get the orientation of this, described by an IOrientationDefinition object of a given type. As this method doesn't know whether the z-axis rotation shall be done first or last, it assumes the z-axis rotation has to be done at last.
AxisRotationSequence	GetOrientationByAxisRotationSequence ()
	Get the orientation of this, described by a sequence of axis rotations.
OrientationByCartesianAngles	GetOrientationByCartesianAngles (bool cartesianAnglesApplicationBeforeZetaRotation)
	Get the orientation of this, described by the Cartesian angles of the z-axis and an additional rotation about the z-axis. As this method doesn't know whether the z-axis rotation shall be done first or last, it assumes the z-axis rotation has to be done at last.
OrientationByDirectionAngles	GetOrientationByDirectionAngles (bool directionAnglesApplicationBeforeZetaRotation)
	Get the orientation of this, described by the direction angles of the z-axis and an additional rotation about the z-axis.
OrientationByEulerAngles	GetOrientationByEulerAngles ()
	Get the orientation of this coordinate system base expressed in Euler angles (Psi, Theta, Phi). For the definition of the Euler angles see Bronstein et.al. "Taschenbuch der Mathematik" 2., überarb. und erw. Aufl.; Deutsch-Verlag, 1995; p.179-180.
OrientationBySphereAngles	GetOrientationBySphereAngles (bool sphereAnglesApplicationBeforeZetaRotation)
	Get the orientation of this, described by the sphere angles of the z-axis and an additional rotation about the z-axis.
Matrix3x3D	GetRotationMatrix ()
	Get the corresponding rotation matrix build up from the direction cosines, i.e. the coordinates of the unit vectors of the three axes. If local and reference coordinate system have the same origin, a multiplication with this matrix would perform a coordinate transformation from the local (internal) coordinate system to the reference (external) cs.
override string	ToString ()
	Gives the axes of this base vectors object as one string.

Static Public Member Functions
static CoordinateSystemBaseVectors	GetDefinedSystemBaseForZVector (Vector3D zVector)
	Constructs a new system of base vectors from one vector serving as z-axis. The x-axis is defined as being the orthogonal projection of the reference system's x-axis onto the plane on which the given (z-)vector is orthogonal.
static bool	operator!= (CoordinateSystemBaseVectors bv1, CoordinateSystemBaseVectors bv2)
	Overloaded inequality operator.
static bool	operator== (CoordinateSystemBaseVectors bv1, CoordinateSystemBaseVectors bv2)
	Overloaded equality operator.
static Matrix3x3D	RotationMatrixForArbitraryAxis (Vector3D rotationAxis, double angle)
	Calculates the rotation matrix for a arbitrary rotation axis and a rotation angle (by using the right-hand-rule). If a coordinate system shall be rotated, the transposed matrix has to be used. Please note: Using the constructor of Quaternion with the same parameters could be a better choice regarding performance.
static Matrix3x3D	RotationMatrixForXAxis (double angle)
	Calculates the rotation matrix for a rotation about the x-axis.
static Matrix3x3D	RotationMatrixForYAxis (double angle)
	Calculates the rotation matrix for a rotation about the y-axis.
static Matrix3x3D	RotationMatrixForZAxis (double angle)
	Calculates the rotation matrix for a rotation about the z-axis.

Properties
Quaternion	Quaternion [get, set]
	Quaternion which represents the orientation of the base vectors in the reference coordinate system.
Vector3D	XAxis [get]
	Direction cosines of the x-Axis.
Vector3D	YAxis [get]
	Direction cosines of the y-Axis.
Vector3D	ZAxis [get]
	Direction cosines of the z-Axis.

Detailed Description

This class is subject to change. Programs using this class may require changes with a new version of VirtualLab.
Class for the base vectors of a Cartesian coordinate system. This kind of triple vector is also called "trihedron".

Constructor & Destructor Documentation

CoordinateSystemBaseVectors() [1/9]

CoordinateSystemBaseVectors

(

Quaternion

quaternion

)

Constructor which gets a quaternion.

Parameters

quaternion

CoordinateSystemBaseVectors() [2/9]

CoordinateSystemBaseVectors	(	Vector3D	xAxis,
		Vector3D	yAxis,
		Vector3D	zAxis
	)

Constructor that uses direction cosines. This constructor is not recommended, because there's a significant probability for numerical inaccuracies which cause orthogonality problems. Better options may be the constructors getting a OrientationDefinitionBase or getting two axes and a plane index.

Parameters

xAxis	Direction cosine of the x-axis.
yAxis	Direction cosine of the y-axis.
zAxis	Direction cosine of the z-axis.

CoordinateSystemBaseVectors() [3/9]

CoordinateSystemBaseVectors	(	Vector3D	axis1,
		Vector3D	axis2,
		CoordinatePlane	plane
	)

Constructor which gets only two base vectors. This may be helpful if one of the base vectors has already been created from a cross product, so creating the third base vector also by a cross product may produce large numerical problems.

Parameters

axis1	First base vector (meaning is set by planeIndex).
axis2	Second base vector (meaning is set by planeIndex).
plane	Sets the meaning of axis1 and axis2 by defining which plane is spanned by the given axes.

CoordinateSystemBaseVectors() [4/9]

CoordinateSystemBaseVectors

(

OrientationDefinitionBase

orientationDefinition

)

Constructor which gets an orientation definition.

Parameters

orientationDefinition

Orientation definition to create a new CoordinateSystemBaseVectors object from.

CoordinateSystemBaseVectors() [5/9]

CoordinateSystemBaseVectors

(

Matrix3x3D

rotationMatrix

)

Constructor that uses a rotation matrix for initializing the direction cosines.

Parameters

rotationMatrix

Rotation matrix R (i.e. R orthogonal and det(R)=1) that describes the rotation of the axes of the reference coordinate system to this Also (another interpretation of R): R defines a coordinate transformation from the coordinate system spanned by this base vectors (coordinates x') to the reference coordinate system (coordinates x) by x = Rx' (and therefore x' = R^Tx) - where both systems have the same origin.

CoordinateSystemBaseVectors() [6/9]

CoordinateSystemBaseVectors	(	double	eulerPsi,
		double	eulerTheta,
		double	eulerPhi
	)

Constructor that uses Euler angles. See Bronstein et.al. "Taschenbuch der Mathematik" 2., überarb. und erw. Aufl.; Deutsch-Verlag, 1995; p.179-180.

Parameters

eulerPsi	Angle Psi
eulerTheta	Angle Theta
eulerPhi	Angle Phi

CoordinateSystemBaseVectors() [7/9]

CoordinateSystemBaseVectors	(	Vector3D	directionOfZAxis,
		double	zeta,
		bool	inclinationFirst
	)

Constructs a new coordinate system base vectors object via z-rotation and the direction vector of the z-axis: The orientation of the system's axes result from 2 steps and a certain order . A) inclinationFirst = false: (i) Rotation about z-axis with angle zeta - using the right-hand-rule, (ii) Inclination of z-axis specified by new direction axis. B) inclinationFirst = true: (i) Inclination of z-axis specified by direction vector, (ii) Rotation about inclined z-axis by angle zeta - using the right-hand-rule.

Parameters

zeta	Angle (radian) of rotation about z-axis by using the right-hand-rule.
directionOfZAxis	Direction vector of new z-axis
inclinationFirst	Flag to signal if z-axis is inclined first (true) or after rotation of z-axis (false).

CoordinateSystemBaseVectors() [8/9]

CoordinateSystemBaseVectors

(

CoordinateSystemBaseVectors

sBaseVectors

)

Copy constructor.

Parameters

sBaseVectors

SystemBaseVectors to copy

CoordinateSystemBaseVectors() [9/9]

CoordinateSystemBaseVectors	(	SerializationInfo	info,
		StreamingContext	context
	)

Deserialization constructor used for manual serialization.

Parameters

info	the info object used for deserialization
context	the streaming context

Member Function Documentation

Clone()

override object Clone

(

)

Deep copy.

Returns

Copy of this

Equals() [1/2]

bool Equals	(	CoordinateSystemBaseVectors	baseVectors,
		bool	indulgentCheck
	)

Method that checks whether another CoordinateSystemBaseVectors object is equivalent to this.

Parameters

baseVectors	CoordinateSystemBaseVectors object to check
indulgentCheck	Flag that indicates whether an indulgent check is to be done (like in NumericalChecks) or if an exact check has to be done.

Returns

Is CoordinateSystemBaseVectors object equivalent?

Equals() [2/2]

override bool Equals	(	object	obj,
		EqualityIntent	equalityIntent
	)

Method which checks for equal objects.

Parameters

obj	The System.Object to compare with this instance.
equalityIntent	The equality intent.

Returns

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

GetDefinedSystemBaseForZVector()

static CoordinateSystemBaseVectors GetDefinedSystemBaseForZVector ( Vector3D  zVector )

static

Constructs a new system of base vectors from one vector serving as z-axis. The x-axis is defined as being the orthogonal projection of the reference system's x-axis onto the plane on which the given (z-)vector is orthogonal.

Parameters

zVector

Vector to create a system of base vectors from.

Returns

A new system of base vectors, created from the given vector serving as z-axis.

GetInverseRotationMatrix()

Matrix3x3D GetInverseRotationMatrix

(

)

Get the corresponding rotation matrix build up from the direction cosines, i.e. the coordinates of the unit vectors of the three axes. If local and reference coordinate system have the same origin, a multiplication with this matrix would perform a coordinate transformation from the reference (external) cs to the local (internal) coordinate system.

Returns

The inverse rotation matrix.

GetOrientation()

OrientationDefinitionBase GetOrientation

(

OrientationDefinitionType

type

)

Get the orientation of this, described by an IOrientationDefinition object of a given type. As this method doesn't know whether the z-axis rotation shall be done first or last, it assumes the z-axis rotation has to be done at last.

Parameters

type	Type of the IOrientationDefinition object to give.

Returns

Orientation of this as IOrientationDefinition

GetOrientationByAxisRotationSequence()

AxisRotationSequence GetOrientationByAxisRotationSequence

(

)

Get the orientation of this, described by a sequence of axis rotations.

Returns

Orientation of this as AxisRotationSequence

GetOrientationByCartesianAngles()

OrientationByCartesianAngles GetOrientationByCartesianAngles

(

bool

cartesianAnglesApplicationBeforeZetaRotation

)

Get the orientation of this, described by the Cartesian angles of the z-axis and an additional rotation about the z-axis. As this method doesn't know whether the z-axis rotation shall be done first or last, it assumes the z-axis rotation has to be done at last.

Parameters

cartesianAnglesApplicationBeforeZetaRotation

If set to true the Cartesian angles are applied before an eventual zeta rotation.

Returns

Orientation of this as OrientationByCartesianAngles

GetOrientationByDirectionAngles()

OrientationByDirectionAngles GetOrientationByDirectionAngles

(

bool

directionAnglesApplicationBeforeZetaRotation

)

Get the orientation of this, described by the direction angles of the z-axis and an additional rotation about the z-axis.

Parameters

directionAnglesApplicationBeforeZetaRotation

if set to true the direction angles are applied before an eventual zeta rotation.

Returns

Orientation of this as OrientationByDirectionAngles

GetOrientationByEulerAngles()

OrientationByEulerAngles GetOrientationByEulerAngles

(

)

Get the orientation of this coordinate system base expressed in Euler angles (Psi, Theta, Phi). For the definition of the Euler angles see Bronstein et.al. "Taschenbuch der Mathematik" 2., überarb. und erw. Aufl.; Deutsch-Verlag, 1995; p.179-180.

Returns

Orientation of this as OrientationByEulerAngles

GetOrientationBySphereAngles()

OrientationBySphereAngles GetOrientationBySphereAngles

(

bool

sphereAnglesApplicationBeforeZetaRotation

)

Get the orientation of this, described by the sphere angles of the z-axis and an additional rotation about the z-axis.

Parameters

sphereAnglesApplicationBeforeZetaRotation

If set to true the sphere angles are applied before an eventual zeta rotation.

Returns

Orientation of this as OrientationBySphereAngles

GetRotationMatrix()

Matrix3x3D GetRotationMatrix

(

)

Get the corresponding rotation matrix build up from the direction cosines, i.e. the coordinates of the unit vectors of the three axes. If local and reference coordinate system have the same origin, a multiplication with this matrix would perform a coordinate transformation from the local (internal) coordinate system to the reference (external) cs.

Returns

The rotation matrix.

operator!=()

static bool operator!= ( CoordinateSystemBaseVectors  bv1, CoordinateSystemBaseVectors  bv2  )

static

Overloaded inequality operator.

Parameters

bv1	First SystemBaseVectors object to compare
bv2	Second SystemBaseVectors object to compare

Returns

Are both SystemBaseVectors objects unequal?

operator==()

static bool operator== ( CoordinateSystemBaseVectors  bv1, CoordinateSystemBaseVectors  bv2  )

static

Overloaded equality operator.

Parameters

bv1	First SystemBaseVectors object to compare
bv2	Second SystemBaseVectors object to compare

Returns

Are both SystemBaseVectors objects equal?

RotationMatrixForArbitraryAxis()

static Matrix3x3D RotationMatrixForArbitraryAxis ( Vector3D  rotationAxis, double  angle  )

static

Calculates the rotation matrix for a arbitrary rotation axis and a rotation angle (by using the right-hand-rule). If a coordinate system shall be rotated, the transposed matrix has to be used. Please note: Using the constructor of Quaternion with the same parameters could be a better choice regarding performance.

See also

VirtualLabAPI.Core.Numerics.Quaternion

Parameters

rotationAxis	Rotation axis (unit vector)
angle	Rotation angle.

Returns

The rotation matrix for the rotation about the given axis with the given angle (right-hand-rule).

RotationMatrixForXAxis()

static Matrix3x3D RotationMatrixForXAxis ( double  angle )

static

Calculates the rotation matrix for a rotation about the x-axis.

Parameters

angle

Rotation angle

Returns

The rotation matrix for the rotation of a coordinate system about the x-axis.

RotationMatrixForYAxis()

static Matrix3x3D RotationMatrixForYAxis ( double  angle )

static

Calculates the rotation matrix for a rotation about the y-axis.

Parameters

angle

Rotation angle

Returns

The rotation matrix for the rotation of a coordinate system about the y-axis.

RotationMatrixForZAxis()

static Matrix3x3D RotationMatrixForZAxis ( double  angle )

static

Calculates the rotation matrix for a rotation about the z-axis.

Parameters

angle

Rotation angle

Returns

The rotation matrix for the rotation of a coordinate system about the z-axis

ToString()

override string ToString

(

)

Gives the axes of this base vectors object as one string.

Returns