base::Orient Class Reference

Orientation in 3D. More...

Collaboration diagram for base::Orient:

[legend]List of all members.

Public Types
typedef Byte	Representation
Public Member Functions
	Orient ()
	construct a zero orientation. (like the identify transform - defaults to EulerRPY vector 0)
	Orient (Representation representation)
	construct a zero orientation. (like the identify transform)
	Orient (const Quat4 &q)
	construct from a quaternion (x,y,z,w)
	Orient (Real roll, Real pitch, Real yaw)
	construct from EulerRPY
	Orient (const Vector &v, Representation representation=EulerRPY)
	construct from a Vector.
	Orient (const Matrix3 &m3)
	construct from a 3x3 rotation transformation matrix
	Orient (const Matrix &m)
	construct from a 3x3 rotation transformation matrix
	Orient (const Orient &copy)
	~Orient ()
Representation	representation () const
bool	isEuler () const
Int	size () const
Real &	operator[] (Int i)
const Real &	operator[] (Int i) const
Orient &	operator= (const Quat4 &q)
Orient &	operator= (const Matrix3 &mt)
Orient &	operator= (const Orient &copy) throw ()
void	setIdentity (Representation representation=Quat)
void	setFromRotationComponent (const Matrix4 &mt)
bool	operator== (const Orient &o) const throw ()
	equality.
bool	operator!= (const Orient &o) const throw ()
bool	equals (const Orient &o, Real epsilon=consts::epsilon) const throw ()
void	rotatePoint (Point3 &p) const
Point3	rotate (const Point3 &p) const
void	rotatePoint (Point4 &p) const
Point4	rotate (const Point4 &p) const
Orient &	invert ()
	invert the rotation (i.e. switch to the reverse rotation)
Matrix	getRotationMatrix () const
Matrix3	getRotationMatrix3 () const
Quat4	getQuat4 () const
Vector	getVector (Representation representation) const
Vector3	getVector3 (Representation representation) const
	operator Vector () const
	automatic conversion to a Vector
	operator Matrix3 () const
	automatic conversion to a rotation matrix
	operator Quat4 () const
	automatic conversion to a Quat4
void	changeRepresentation (Representation newRepresentation)
	request change the internal representation (which may or may not be honored)
Matrix	getBinv () const
	returns the inverse of B, such that omega = B(v)^-1 . dv/dt, where omega is angular velocity and v is this orientation
void	serialize (Serializer &s)
	read or write object state to Serializer
Static Public Member Functions
String	representationString (Representation rep)
bool	isEuler (Representation rep)
Int	size (Representation rep)
Orient	interpolate (const Orient &lower, const Orient &upper, Real t)
	interpolate between the orientations lower and upper t:[0..1]
Static Public Attributes
const Representation	EulerXYZs
const Representation	EulerXYXs
const Representation	EulerXZYs
const Representation	EulerXZXs
const Representation	EulerYZXs
const Representation	EulerYZYs
const Representation	EulerYXZs
const Representation	EulerYXYs
const Representation	EulerZXYs
const Representation	EulerZXZs
const Representation	EulerZYXs
const Representation	EulerZYZs
const Representation	EulerZYXr
const Representation	EulerXYXr
const Representation	EulerYZXr
const Representation	EulerXZXr
const Representation	EulerXZYr
const Representation	EulerYZYr
const Representation	EulerZXYr
const Representation	EulerYXYr
const Representation	EulerYXZr
const Representation	EulerZXZr
const Representation	EulerXYZr
const Representation	EulerZYZr
const Representation	LastEuler = 23
const Representation	EulerRPY
const Representation	Quat = 24
const Representation	Mat = 25
const Representation	Rodriguez = 26
const Representation	RepEnd = 27
Protected Types
typedef Matrix *	MatrixRef
enum	Axis { X = 0, Y = 1, Z = 2, W = 3 }
enum	Frame { Static = 0, Rotating = 1 }
enum	Repetition { NonRepeating = 0, Repeating = 1 }
enum	Parity { Even = 0, Odd = 1 }
Protected Member Functions
void	changeRep (Representation newRep) const
	change the current internal representation to that specified.
Static Protected Member Functions
Representation	eulerRep (Axis axis, Parity parity, Repetition repetition, Frame frame)
Frame	frame (Representation rep)
Repetition	repetition (Representation rep)
Parity	parity (Representation rep)
Axis	axisI (Representation rep)
Axis	axisJ (Representation rep)
Axis	axisK (Representation rep)
Axis	axisH (Representation rep)
void	getRep (Representation rep, Axis &i, Axis &j, Axis &k, Axis &h, Parity &n, Repetition &s, Frame &f)
Protected Attributes
Representation	rep
Vector	v
	component of vector-based representations (Quat, Euler, etc.)
MatrixRef	m
	Matrix(3,3) ref if rep==Mat.
Static Protected Attributes
Byte	EulSafe [4]
Byte	EulNext [4]
Friends
std::ostream &	operator<< (std::ostream &out, const Orient &o)

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Detailed Description

Orientation in 3D.

Represents an orientation in 3D using various internal representations.

There are many parameterizations and terms in use for rotations and orientation/attitude. Some of the more common are:

• 3x3 transformation matrices. As this has 9 direction cosine values, it contains redundant information. Consequently, without care, roundoff errors can yield matrices that contain unwanted effects (e.g. scaling, skew) There are no singularities. This is the representation used by OpenGL.

• Euler parameters. A vector of 4 components - not to be confused with Euler angles. The mathematics corresponds to unit Quaternions - hence this representation is often refered to as such. No singularities, hence useful for interpolation. Roundoff error often results in non-normalized vectors. Some formulations place the scalar component as the first component and some as the last component (it is placed last here)

• Cardan-Bryant angles. These are a 3 component vectors that represents rotations about 3 principle axes (anti-cyclic). The possibilities are XYZ, XZY, YZX, YXZ, ZYX and ZXY. i.e. rotation about the first axis, followed by a rotation about the (now transformed) second axis and finally about the (now twice transformed) third axis. Commonly refered to as Euler angles (although technically they are not). Has a singularity (gimble-lock) when 2nd rotation is 90 or 270deg. Often the terms Roll, Pitch and Yaw (RPY) are used, where Roll is roation about the forward axis by phi, Pitch is about the right axis by theta and Yaw is about the up axis by psi. For aeronautics, and the manipulator DH notation frames, the axes are assigned x-forward, y-right & z-up. In this case RPY is equivelent to EulerXYZ applied in the order Roll,Pitch,Yaw Note that For the OpenSim world frame the assignments are x-back, y-right & z-up.

• Euler angles. A 3 component vector similar to Cardan-Bryant angles, but where the first and last rotation axis are the same (cyclic). Possibilities are XYX, XZX, YXY, YZY, ZXZ and ZYZ. Has a singularity when the 2nd rotation is 0 or 180deg. Euler used ZXZ, which is the most common - and also called 'x-convention'.

• Rodriguez parameters. A 3 component vector. Also known as a Rotation Vector (Benati, Rodriguez-Hamilton), or Gibbs Vector. Defined by gamma = v.tan(theta/2), where v is the axis of rotation and theta is the angle. Has a gimble-lock singularity at 180deg.

Todo:

finish implementing and testing this class!

Definition at line 93 of file Orient.

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Member Typedef Documentation

typedef Matrix* base::Orient::MatrixRef [protected]

Definition at line 311 of file Orient.

typedef Byte base::Orient::Representation

Quat - Euler parameters expressed as a quaternion (v.x,v.y,v.z,w) Mat - 3x3 transformation matrix of direction cosines. EulerABC - Euler (possibly Cardan-Bryant) angles about the axes A, B & C in that order. EulerRPY - Euler (Cardan-Bryant) Roll, Pitch, Yaw angles (alpha,beta,gamma). This is equivelent to EulerXYZ and assumes that the x-axis points forward, y-axis points right and the z-axis up. (Aeronautical convention) Euler - alias for EulerZXZ Rodriguez - Rodriguez parameters (gamma1, gamma2, gamma3) Definition at line 108 of file Orient. Referenced by axisH(), axisI(), axisJ(), axisK(), changeRepresentation(), eulerRep(), frame(), getRep(), isEuler(), parity(), repetition(), representation(), and size().

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Member Enumeration Documentation

enum base::Orient::Axis [protected]

Enumeration values: X  Y  Z  W  Definition at line 314 of file Orient. Referenced by axisH(), axisI(), axisJ(), axisK(), and getRep().

enum base::Orient::Frame [protected]

Enumeration values: Static  Rotating  Definition at line 315 of file Orient. Referenced by frame(), and getRep().

enum base::Orient::Parity [protected]

Enumeration values: Even  Odd  Definition at line 317 of file Orient. Referenced by getRep(), and parity().

enum base::Orient::Repetition [protected]

Enumeration values: NonRepeating  Repeating  Definition at line 316 of file Orient. Referenced by getRep(), and repetition().

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Constructor & Destructor Documentation

base::Orient::Orient (   )

construct a zero orientation. (like the identify transform - defaults to EulerRPY vector 0)

base::Orient::Orient (  Representation  representation  )

construct a zero orientation. (like the identify transform)

base::Orient::Orient (  const Quat4 &  q  )

construct from a quaternion (x,y,z,w)

base::Orient::Orient (  Real  roll, Real  pitch, Real  yaw )

construct from EulerRPY

base::Orient::Orient (  const Vector &  v, Representation  representation = EulerRPY )  [explicit]

construct from a Vector.

base::Orient::Orient (  const Matrix3 &  m3  )

construct from a 3x3 rotation transformation matrix

base::Orient::Orient (  const Matrix &  m  )

construct from a 3x3 rotation transformation matrix

base::Orient::Orient (  const Orient &  copy  )

base::Orient::~Orient (   )

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Member Function Documentation

Axis base::Orient::axisH (  Representation  rep  )  [inline, static, protected]

Definition at line 329 of file Orient. References Axis, axisI(), axisK(), NonRepeating, repetition(), and Representation.

Axis base::Orient::axisI (  Representation  rep  )  [inline, static, protected]

Definition at line 326 of file Orient. References Axis, base::Byte, EulSafe, and Representation. Referenced by axisH(), axisJ(), and axisK().

Axis base::Orient::axisJ (  Representation  rep  )  [inline, static, protected]

Definition at line 327 of file Orient. References Axis, axisI(), base::Byte, EulNext, Odd, parity(), and Representation.

Axis base::Orient::axisK (  Representation  rep  )  [inline, static, protected]

Definition at line 328 of file Orient. References Axis, axisI(), base::Byte, EulNext, Odd, parity(), and Representation. Referenced by axisH().

void base::Orient::changeRep (  Representation  newRep  )  const [protected]

change the current internal representation to that specified. Referenced by changeRepresentation().

void base::Orient::changeRepresentation (  Representation  newRepresentation  )  [inline]

request change the internal representation (which may or may not be honored) Definition at line 299 of file Orient. References changeRep(), and Representation.

bool base::Orient::equals (  const Orient &  o, Real  epsilon = consts::epsilon )  const throw ()

Representation base::Orient::eulerRep (  Axis  axis, Parity  parity, Repetition  repetition, Frame  frame )  [inline, static, protected]

Definition at line 319 of file Orient. References base::Byte, and Representation.

Frame base::Orient::frame (  Representation  rep  )  [inline, static, protected]

Definition at line 322 of file Orient. References base::Byte, Frame, and Representation.

Matrix base::Orient::getBinv (   )  const

returns the inverse of B, such that omega = B(v)^-1 . dv/dt, where omega is angular velocity and v is this orientation

Quat4 base::Orient::getQuat4 (   )  const

Referenced by operator Quat4(), rotate(), base::LineSegPathRep::rotate(), rotatePoint(), and base::LineSegPathRep::transform().

void base::Orient::getRep (  Representation  rep, Axis &  i, Axis &  j, Axis &  k, Axis &  h, Parity &  n, Repetition &  s, Frame &  f )  [inline, static, protected]

Definition at line 330 of file Orient. References Axis, base::Byte, EulNext, EulSafe, f, Frame, Parity, Repetition, and Representation.

Matrix base::Orient::getRotationMatrix (   )  const

Matrix3 base::Orient::getRotationMatrix3 (   )  const

Referenced by operator Matrix3().

Vector base::Orient::getVector (  Representation  representation  )  const

Referenced by operator Vector().

Vector3 base::Orient::getVector3 (  Representation  representation  )  const

Orient base::Orient::interpolate (  const Orient &  lower, const Orient &  upper, Real  t )  [static]

interpolate between the orientations lower and upper t:[0..1]

Orient& base::Orient::invert (   )

invert the rotation (i.e. switch to the reverse rotation)

bool base::Orient::isEuler (   )  const [inline]

Definition at line 179 of file Orient. References LastEuler, and rep.

bool base::Orient::isEuler (  Representation  rep  )  [inline, static]

Definition at line 178 of file Orient. References LastEuler, and Representation.

base::Orient::operator Matrix3 (   )  const [inline]

automatic conversion to a rotation matrix Definition at line 290 of file Orient. References getRotationMatrix3().

base::Orient::operator Quat4 (   )  const [inline]

automatic conversion to a Quat4 Definition at line 294 of file Orient. References getQuat4().

base::Orient::operator Vector (   )  const [inline]

automatic conversion to a Vector Definition at line 286 of file Orient. References getVector(), Mat, and rep.

bool base::Orient::operator!= (  const Orient &  o  )  const throw () [inline]

Definition at line 239 of file Orient. References operator==().

Orient& base::Orient::operator= (  const Orient &  copy  )  throw ()

Orient& base::Orient::operator= (  const Matrix3 &  mt  )

Orient& base::Orient::operator= (  const Quat4 &  q  )  [inline]

Definition at line 216 of file Orient. References Mat, Quat, rep, base::vector< T >::resize(), base::Quat4::v, base::Quat4::w, base::Vector3::x, base::Vector3::y, and base::Vector3::z.

bool base::Orient::operator== (  const Orient &  o  )  const throw ()

equality. NB: expensive if representations are not the same (conversion attempted) Referenced by operator!=().

const Real& base::Orient::operator[] (  Int  i  )  const [inline]

Definition at line 205 of file Orient. References base::Int, Mat, base::Real, and rep.

Real& base::Orient::operator[] (  Int  i  )  [inline]

Definition at line 194 of file Orient. References base::Int, Mat, base::Real, and rep.

Parity base::Orient::parity (  Representation  rep  )  [inline, static, protected]

Definition at line 324 of file Orient. References base::Byte, Parity, and Representation. Referenced by axisJ(), and axisK().

Repetition base::Orient::repetition (  Representation  rep  )  [inline, static, protected]

Definition at line 323 of file Orient. References base::Byte, Repetition, and Representation. Referenced by axisH().

Representation base::Orient::representation (   )  const [inline]

Definition at line 174 of file Orient. References rep, and Representation.

String base::Orient::representationString (  Representation  rep  )  [static]

Point4 base::Orient::rotate (  const Point4 &  p  )  const [inline]

Definition at line 264 of file Orient. References getQuat4(), base::Point4, and base::Quat4::rotate().

Point3 base::Orient::rotate (  const Point3 &  p  )  const [inline]

Definition at line 252 of file Orient. References getQuat4(), base::Point3, and base::Quat4::rotate().

void base::Orient::rotatePoint (  Point4 &  p  )  const [inline]

Definition at line 258 of file Orient. References getQuat4(), base::Point4, and base::Quat4::rotatePoint().

void base::Orient::rotatePoint (  Point3 &  p  )  const [inline]

Definition at line 246 of file Orient. References getQuat4(), base::Point3, and base::Quat4::rotatePoint().

void base::Orient::serialize (  Serializer &  s  )

read or write object state to Serializer Referenced by base::Serializer::operator()().

void base::Orient::setFromRotationComponent (  const Matrix4 &  mt  )

Referenced by base::Transform::getRotation().

void base::Orient::setIdentity (  Representation  representation = Quat  )

Referenced by base::Transform::getRotation().

Int base::Orient::size (   )  const [inline]

Definition at line 188 of file Orient. References base::Int, and rep.

Int base::Orient::size (  Representation  rep  )  [inline, static]

Definition at line 181 of file Orient. References base::Int, Mat, Quat, and Representation.

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Friends And Related Function Documentation

std::ostream& operator<< (  std::ostream &  out, const Orient &  o )  [friend]

Definition at line 358 of file Orient.

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Member Data Documentation

const Representation base::Orient::EulerRPY [static]

Definition at line 140 of file Orient.

const Representation base::Orient::EulerXYXr [static]

Definition at line 126 of file Orient.

const Representation base::Orient::EulerXYXs [static]

Definition at line 113 of file Orient.

const Representation base::Orient::EulerXYZr [static]

Definition at line 135 of file Orient.

const Representation base::Orient::EulerXYZs [static]

Definition at line 112 of file Orient.

const Representation base::Orient::EulerXZXr [static]

Definition at line 128 of file Orient.

const Representation base::Orient::EulerXZXs [static]

Definition at line 115 of file Orient.

const Representation base::Orient::EulerXZYr [static]

Definition at line 129 of file Orient.

const Representation base::Orient::EulerXZYs [static]

Definition at line 114 of file Orient.

const Representation base::Orient::EulerYXYr [static]

Definition at line 132 of file Orient.

const Representation base::Orient::EulerYXYs [static]

Definition at line 119 of file Orient.

const Representation base::Orient::EulerYXZr [static]

Definition at line 133 of file Orient.

const Representation base::Orient::EulerYXZs [static]

Definition at line 118 of file Orient.

const Representation base::Orient::EulerYZXr [static]

Definition at line 127 of file Orient.

const Representation base::Orient::EulerYZXs [static]

Definition at line 116 of file Orient.

const Representation base::Orient::EulerYZYr [static]

Definition at line 130 of file Orient.

const Representation base::Orient::EulerYZYs [static]

Definition at line 117 of file Orient.

const Representation base::Orient::EulerZXYr [static]

Definition at line 131 of file Orient.

const Representation base::Orient::EulerZXYs [static]

Definition at line 120 of file Orient.

const Representation base::Orient::EulerZXZr [static]

Definition at line 134 of file Orient.

const Representation base::Orient::EulerZXZs [static]

Definition at line 121 of file Orient.

const Representation base::Orient::EulerZYXr [static]

Definition at line 125 of file Orient.

const Representation base::Orient::EulerZYXs [static]

Definition at line 122 of file Orient.

const Representation base::Orient::EulerZYZr [static]

Definition at line 136 of file Orient.

const Representation base::Orient::EulerZYZs [static]

Definition at line 123 of file Orient.

Byte base::Orient::EulNext[4] [static, protected]

Definition at line 345 of file Orient. Referenced by axisJ(), axisK(), and getRep().

Byte base::Orient::EulSafe[4] [static, protected]

Definition at line 344 of file Orient. Referenced by axisI(), and getRep().

const Representation base::Orient::LastEuler = 23 [static]

Definition at line 138 of file Orient. Referenced by isEuler().

MatrixRef base::Orient::m [mutable, protected]

Matrix(3,3) ref if rep==Mat. Definition at line 312 of file Orient. Referenced by base::operator<<().

const Representation base::Orient::Mat = 25 [static]

Definition at line 143 of file Orient. Referenced by operator Vector(), operator=(), operator[](), and size().

const Representation base::Orient::Quat = 24 [static]

Definition at line 142 of file Orient. Referenced by operator=(), and size().

Representation base::Orient::rep [mutable, protected]

Definition at line 309 of file Orient. Referenced by isEuler(), operator Vector(), base::operator<<(), operator=(), operator[](), representation(), and size().

const Representation base::Orient::RepEnd = 27 [static]

Definition at line 145 of file Orient.

const Representation base::Orient::Rodriguez = 26 [static]

Definition at line 144 of file Orient.

Vector base::Orient::v [mutable, protected]

component of vector-based representations (Quat, Euler, etc.) Definition at line 310 of file Orient. Referenced by base::operator<<().

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The documentation for this class was generated from the following file:

• base/Orient

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