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Quaternion Class Reference

Implementation of a 3D quaternion (by Vitaliy). More...

#include <Quaternion.h>

Public Member Functions

 Quaternion ()
 Constructor; sets quaternion value to (1,0,0,0) More...
 
 Quaternion (Mdouble q0, Mdouble q1, Mdouble q2, Mdouble q3)
 Alternative constructor. Sets quaternion value to (q0,q1,q2,q3) More...
 
 Quaternion (Vec3D normal)
 
void setUnity ()
 Sets quaternion value to (1,0,0,0) More...
 
bool isUnity () const
 Checks if the quaternion value is (1,0,0,0) More...
 
Quaternion operator+ (const Quaternion &a) const
 Adds another quaternion and returns the result. More...
 
Quaternion operator- (const Quaternion &a) const
 Subtracts another quaternion and returns the result. More...
 
Quaternion operator* (Mdouble a) const
 Multiplies by a scalar. More...
 
Quaternion operator/ (Mdouble a) const
 Divides by a scalar. More...
 
Quaternion & operator+= (const Quaternion &a)
 Adds another quaternion. More...
 
Quaternion & operator-= (const Quaternion &a)
 Subtracts another quaternion. More...
 
Quaternion & operator*= (Mdouble a)
 Multiplies *this by a scalar. More...
 
Quaternion & operator/= (Mdouble a)
 Divides by a scalar. More...
 
void normalise ()
 Makes this Quaternion unit length |q|=1. More...
 
void setLength (Mdouble length)
 Make this Quaternion a certain length |q|=length. More...
 
Mdouble getLength () const
 Calculates the length of this Quaternion: \( \sqrt{a\cdot a} \). More...
 
Mdouble getLengthSquared () const
 Calculates the squared length of this Quaternion: \( a\cdot a \). More...
 
Mdouble getComponent (int index) const
 Returns the requested component of this Quaternion. More...
 
Quaternion angularVelocityBodyFixedFrameToAngularDisplacement (Vec3D v) const
 
Quaternion angularDisplacementTimeDerivative (Vec3D v) const
 Converts an angular momentum v=omega into a quaternion rate of change, q(t+dt)-q(t)/dt. More...
 
void updateAngularDisplacement (Vec3D angularVelocityDt)
 
Vec3D applyCInverse (Quaternion q) const
 Converts quaternion rate of change into an angular momentum omega. More...
 
void setComponent (int index, double val)
 Sets the requested component of this Quaternion to the requested value. More...
 
bool isEqualTo (const Quaternion &other, double tol) const
 Checks if the length this Quaternion is equal the length of other with a certain tolerance. More...
 
Vec3D getEuler () const
 Convert a quaternion to Euler angles. See Wikipedia for details. More...
 
void setEuler (const Vec3D &e)
 Convert Euler angles to a quaternion. See Wikipedia for details. More...
 
Mdouble getAngleZ () const
 Converts a quaternion to the rotation angle in the XY plane (for Mercury2D). See Wikipedia for details. More...
 
void setAngleZ (Mdouble psi)
 Converts the rotation angle in the XY plane into a quaternion (for Mercury2D). See Wikipedia for details. More...
 
MatrixSymmetric3D rotateInverseInertiaTensor (const MatrixSymmetric3D &invI) const
 Converts the inverse inertia tensor from the reference frame to the lab frame; see See QuaternionsWouter.pdf for details, where this operation is denoted by \(A*I^{-1}*A^T\). More...
 
void rotateTensor (SmallMatrix< 3, 3 > I) const
 
Vec3D getAxis () const
 Converts the quaternions into a normal vector by rotating the vector x=(1,0,0); see See Wiki for details. More...
 
void setOrientationViaNormal (Vec3D normal)
 Used to the the normal of an InfiniteWall that has a normal into the x-direction by default. More...
 
void getRotationMatrix (SmallMatrix< 3, 3 > &A) const
 Retrieves the rotation matrix. More...
 
void rotate (Vec3D &position) const
 Applies the rotation to a position. More...
 
void rotate (SmallVector< 3 > &position) const
 Applies the rotation to a position. More...
 
void rotateBack (Vec3D &position) const
 Applies the inverse rotation to a position. More...
 
Mdouble getDistance (Vec3D p, Vec3D p0) const
 Calculates the distance from a wall through p0 whose normal is the vector (1,0,0). More...
 

Static Public Member Functions

static Mdouble getDistance (const Quaternion &a, const Quaternion &b)
 Calculates the distance between two Quaternion: \( \sqrt{\left(a-b\right) \cdot \left(a-b\right)} \). More...
 
static Mdouble getDistanceSquared (const Quaternion &a, const Quaternion &b)
 Calculates the squared distance between two Quaternion: \( \left(a-b\right) \cdot \left(a-b\right) \). More...
 
static Mdouble getLength (const Quaternion &a)
 Calculates the length of a Quaternion: \( \sqrt{a\cdot a} \). More...
 
static Mdouble getLengthSquared (const Quaternion &a)
 Calculates the squared length of a Quaternion: \( a\cdot a \). More...
 
static Quaternion getUnitQuaternion (const Quaternion &a)
 Returns a unit Quaternion based on a. More...
 

Public Attributes

Mdouble q0
 the zeroth component of the quaternion q = (q0,q1,q2,q3) More...
 
Mdouble q1
 the first component of the quaternion q = (q0,q1,q2,q3) More...
 
Mdouble q2
 the second component of the quaternion q = (q0,q1,q2,q3) More...
 
Mdouble q3
 the third component of the quaternion q = (q0,q1,q2,q3) More...
 

Friends

std::ostream & operator<< (std::ostream &os, const Quaternion &a)
 Adds elements to an output stream. More...
 
std::istream & operator>> (std::istream &is, Quaternion &a)
 Adds elements to an input stream. More...
 
Quaternion operator+ (Mdouble a, const Quaternion &b)
 Adds a scalar to a quaternion. More...
 
Quaternion operator- (Mdouble a, const Quaternion &b)
 Subtracts the elements of a quaternion from a scalar. More...
 
Quaternion operator- (const Quaternion &a)
 Subtracts a quaternion. More...
 
Quaternion operator* (Mdouble a, const Quaternion &b)
 Multiplies all elements by a scalar. More...
 

Detailed Description

Implementation of a 3D quaternion (by Vitaliy).

Modifications 21:9:2009 - Added the inclusion guards and some include objects

Todo:
Need to generalize this to n-dimensional quaternions of any type

This class contains the 4 components of a quaternion and the standard operators and functions needed for quaternion arithmetic.

A quaternion is a four-dimensional vector q = (q0,q1,q2,q3) that satisfies |q|^2=q0^2+q1^2+q2^2+q3^2=1. It can be used to describe the orientation of an object in space.

The properties (e.g. inertia tensor) of any interactable (particle or wall) in MercuryDPM are described in its reference frame. The quaternion is used to rotate the object into the lab frame (the system geometry). A few examples to help visualising quaternions can be found here .

The unit quaternion, q=(1,0,0,0) denotes the state where the lab frame and the reference frame is identical.

To see how to convert a quaternion to Euler angles or to compare it to a rotation of an object around a axis, see Wikipedia for details.

Definition at line 62 of file Quaternion.h.

Constructor & Destructor Documentation

Quaternion::Quaternion ( )

Constructor; sets quaternion value to (1,0,0,0)

Default constructor

Definition at line 30 of file Quaternion.cc.

References setUnity().

Referenced by angularDisplacementTimeDerivative(), angularVelocityBodyFixedFrameToAngularDisplacement(), getUnitQuaternion(), operator*(), operator+(), operator-(), operator/(), and setOrientationViaNormal().

31 {
32  setUnity();
33 }
Quaternion::setUnity
void setUnity()
Sets quaternion value to (1,0,0,0)
Definition: Quaternion.cc:53
Quaternion::Quaternion ( Mdouble  q0,
Mdouble  q1,
Mdouble  q2,
Mdouble  q3 
)

Alternative constructor. Sets quaternion value to (q0,q1,q2,q3)

Alternative constructor, lets you define all four elements.

Parameters
[in]q0the q0-component
[in]q1the q1-component
[in]q2the q2-component
[in]q3the q3-component

Definition at line 42 of file Quaternion.cc.

References q0, q1, q2, and q3.

43 {
44  this->q0 = q0;
45  this->q1 = q1;
46  this->q2 = q2;
47  this->q3 = q3;
48 }
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Quaternion::Quaternion ( Vec3D  normal)
inline
Todo:
should be explicit as teh conversion is not unique
Parameters
normal

Definition at line 97 of file Quaternion.h.

References setOrientationViaNormal().

98  {
99  setOrientationViaNormal(normal);
100  }
Quaternion::setOrientationViaNormal
void setOrientationViaNormal(Vec3D normal)
Used to the the normal of an InfiniteWall that has a normal into the x-direction by default...
Definition: Quaternion.cc:536

Member Function Documentation

Quaternion Quaternion::angularDisplacementTimeDerivative ( Vec3D  v) const

Converts an angular momentum v=omega into a quaternion rate of change, q(t+dt)-q(t)/dt.

Given v = * dt, with omega the angular velocity, this computes the change in angular displacement to be added in the time integration.

This is equivalent to applying the matrix {C}

Definition at line 422 of file Quaternion.cc.

References q0, q1, q2, q3, Quaternion(), Vec3D::X, Vec3D::Y, and Vec3D::Z.

Referenced by updateAngularDisplacement().

423 {
424  return 0.5 * Quaternion(
425  -q1 * v.X - q2 * v.Y - q3 * v.Z,
426  q0 * v.X + q3 * v.Y - q2 * v.Z,
427  -q3 * v.X + q0 * v.Y + q1 * v.Z,
428  q2 * v.X - q1 * v.Y + q0 * v.Z);
429 }
Vec3D::X
Mdouble X
the vector components
Definition: Vector.h:65
Quaternion::Quaternion
Quaternion()
Constructor; sets quaternion value to (1,0,0,0)
Definition: Quaternion.cc:30
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Vec3D::Y
Mdouble Y
Definition: Vector.h:65
Vec3D::Z
Mdouble Z
Definition: Vector.h:65
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Quaternion Quaternion::angularVelocityBodyFixedFrameToAngularDisplacement ( Vec3D  v) const
Todo:
should the arguments be passed by reference?
Todo:
rename to angularVelocityBodyFixedFrameToAngularDisplacement?

Definition at line 411 of file Quaternion.cc.

References q0, q1, q2, q3, Quaternion(), Vec3D::X, Vec3D::Y, and Vec3D::Z.

412 {
413  return Quaternion(
414  -q1 * v.X - q2 * v.Y - q3 * v.Z,
415  q0 * v.X - q3 * v.Y + q2 * v.Z,
416  q3 * v.X + q0 * v.Y - q1 * v.Z,
417  -q2 * v.X + q1 * v.Y + q0 * v.Z);
418 }
Vec3D::X
Mdouble X
the vector components
Definition: Vector.h:65
Quaternion::Quaternion
Quaternion()
Constructor; sets quaternion value to (1,0,0,0)
Definition: Quaternion.cc:30
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Vec3D::Y
Mdouble Y
Definition: Vector.h:65
Vec3D::Z
Mdouble Z
Definition: Vector.h:65
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Vec3D Quaternion::applyCInverse ( Quaternion  q) const

Converts quaternion rate of change into an angular momentum omega.

Todo:
rename to angularDisplacementToAngularVelocity?

Definition at line 441 of file Quaternion.cc.

References q0, q1, q2, and q3.

442 {
443  return 2.0 * Vec3D(
444  -q1 * q.q0 + q0 * q.q1 - q3 * q.q2 + q2 * q.q3,
445  -q2 * q.q0 + q3 * q.q1 + q0 * q.q2 - q1 * q.q3,
446  -q3 * q.q0 - q2 * q.q1 + q1 * q.q2 + q0 * q.q3);
447 }
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Vec3D
Definition: Vector.h:49
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Mdouble Quaternion::getAngleZ ( ) const

Converts a quaternion to the rotation angle in the XY plane (for Mercury2D). See Wikipedia for details.

Definition at line 487 of file Quaternion.cc.

References q0, q1, q2, and q3.

488 {
489  return -std::atan2(2 * (q0 * q3 + q1 * q2), 1 - 2 * (q2 * q2 + q3 * q3));
490 }
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Vec3D Quaternion::getAxis ( ) const

Converts the quaternions into a normal vector by rotating the vector x=(1,0,0); see See Wiki for details.

Definition at line 501 of file Quaternion.cc.

References q0, q1, q2, and q3.

Referenced by HorizontalBaseScrew::convertLimits(), InfiniteWall::createVTK(), HorizontalBaseScrew::getDistanceAndNormal(), InfiniteWall::getDistanceAndNormal(), AxisymmetricIntersectionOfWalls::getDistanceAndNormal(), InfiniteWall::getDistanceNormalOverlapSuperquadric(), InfiniteWall::getNormal(), CGFields::OrientationField::setFields(), AngledPeriodicBoundary::shiftPosition(), and HorizontalBaseScrew::writeVTK().

502 {
503  //logger(ERROR,"o % d % d %",*this,Vec3D(1-2.0*q2*q2-2.0*q3*q3, 2.0*(q1*q2+q3*q0), 2.0*(q1*q3-q2*q0)),Vec3D(q0*q0+q1*q1-q2*q2-q3*q3, 2.0*(q1*q2+q3*q0), 2.0*(q1*q3-q2*q0)));
504  return Vec3D(q0 * q0 - q3 * q3 + q1 * q1 - q2 * q2, 2.0 * (q1 * q2 + q3 * q0), 2.0 * (q1 * q3 - q2 * q0));
505 }
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Vec3D
Definition: Vector.h:49
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Mdouble Quaternion::getComponent ( int  index) const

Returns the requested component of this Quaternion.

returns the quaternion element belonging to the given index.

Parameters
[in]indexthe index of interest (should be 0, 1 or 2)
Returns
the value of the quaternion element belonging to the given index

Definition at line 232 of file Quaternion.cc.

References ERROR, logger, q0, q1, q2, and q3.

Referenced by mathsFunc::isEqual().

233 {
234  switch (index)
235  {
236  case 0:
237  return q0;
238  case 1:
239  return q1;
240  case 2:
241  return q2;
242  case 3:
243  return q3;
244  default:
245  logger(ERROR,
246  "[Quaternion::getComponent] Index = %, which is too high for a 3D quaternion (should be 0-2).",
247  index);
248  return 0;
249  }
250 }
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Mdouble Quaternion::getDistance ( const Quaternion &  a,
const Quaternion &  b 
)
static

Calculates the distance between two Quaternion: \( \sqrt{\left(a-b\right) \cdot \left(a-b\right)} \).

Calculates the distance (i.e. the length of the difference) between two quaternions NB: this is a STATIC function!

Parameters
[in]athe first quaternion
[in]bthe second quaternion
Returns
the distance between the two arguments.

Definition at line 188 of file Quaternion.cc.

References getDistanceSquared().

Referenced by InfiniteWall::getDistance(), and isEqualTo().

189 {
190  return std::sqrt(getDistanceSquared(a, b));
191 }
Quaternion::getDistanceSquared
static Mdouble getDistanceSquared(const Quaternion &a, const Quaternion &b)
Calculates the squared distance between two Quaternion: .
Definition: Quaternion.cc:201
Mdouble Quaternion::getDistance ( Vec3D  p,
Vec3D  p0 
) const

Calculates the distance from a wall through p0 whose normal is the vector (1,0,0).

Used for the calculation of the distance in InfiniteWalls

Definition at line 615 of file Quaternion.cc.

References q0, q1, q2, q3, Vec3D::X, Vec3D::Y, and Vec3D::Z.

616 {
617  return (q0 * q0 + q1 * q1 - q2 * q2 - q3 * q3) * (p0.X - p.X) +
618  2.0 * ((q1 * q2 + q0 * q3) * (p0.Y - p.Y) + (q1 * q3 - q0 * q2) * (p0.Z - p.Z));
619 }
Vec3D::X
Mdouble X
the vector components
Definition: Vector.h:65
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Vec3D::Y
Mdouble Y
Definition: Vector.h:65
Vec3D::Z
Mdouble Z
Definition: Vector.h:65
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Mdouble Quaternion::getDistanceSquared ( const Quaternion &  a,
const Quaternion &  b 
)
static

Calculates the squared distance between two Quaternion: \( \left(a-b\right) \cdot \left(a-b\right) \).

Calculates the square of the distance (i.e. the length of the difference) between two quaternions. NB: this is a STATIC function!

Parameters
[in]athe first quaternion
[in]bthe second quaternion
Returns
the square of the distance between the two arguments.

Definition at line 201 of file Quaternion.cc.

References q0, q1, q2, and q3.

Referenced by getDistance().

202 {
203  return ((a.q0 - b.q0) * (a.q0 - b.q0) + (a.q1 - b.q1) * (a.q1 - b.q1) + (a.q2 - b.q2) * (a.q2 - b.q2) +
204  (a.q3 - b.q3) * (a.q3 - b.q3));
205 }
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Vec3D Quaternion::getEuler ( ) const

Convert a quaternion to Euler angles. See Wikipedia for details.

Get the Euler angles of this quaternion. Example of visualising Euler angles can be found here

Definition at line 452 of file Quaternion.cc.

References constants::pi, q0, q1, q2, and q3.

453 {
454  Mdouble sinp = 2 * (q0 * q2 - q3 * q1);
455  Mdouble pitch;
456  const Mdouble pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068;
457 
458  if ((std::abs(sinp) < 1))
459  {
460  pitch = std::asin(sinp);
461  }
462  else
463  {
464  pitch = copysign(pi/2., sinp);
465  }
466 
467  return Vec3D(
468  std::atan2(2 * (q0 * q1 + q2 * q3), 1 - 2 * (q1 * q1 + q2 * q2)),
469  pitch,
470  std::atan2(2 * (q0 * q3 + q1 * q2), 1 - 2 * (q2 * q2 + q3 * q3)));
471 }
Mdouble
double Mdouble
Definition: GeneralDefine.h:34
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
constants::pi
const Mdouble pi
Definition: ExtendedMath.h:45
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Vec3D
Definition: Vector.h:49
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Mdouble Quaternion::getLength ( const Quaternion &  a)
static

Calculates the length of a Quaternion: \( \sqrt{a\cdot a} \).

Calculates the length of a given quaternion NB: this is a STATIC function!

Parameters
[in]aquaternion to be measured.
Returns
length of the argument.

Definition at line 310 of file Quaternion.cc.

References getLength().

Referenced by getLength().

311 {
312  return a.getLength();
313 }
Quaternion::getLength
static Mdouble getLength(const Quaternion &a)
Calculates the length of a Quaternion: .
Definition: Quaternion.cc:310
Mdouble Quaternion::getLength ( ) const

Calculates the length of this Quaternion: \( \sqrt{a\cdot a} \).

Calculates the length of this quaternion

Returns
the (scalar) length of this quaternion

Definition at line 299 of file Quaternion.cc.

References getLengthSquared().

Referenced by setLength().

300 {
301  return std::sqrt(getLengthSquared());
302 }
Quaternion::getLengthSquared
Mdouble getLengthSquared() const
Calculates the squared length of this Quaternion: .
Definition: Quaternion.cc:222
Mdouble Quaternion::getLengthSquared ( const Quaternion &  a)
static

Calculates the squared length of a Quaternion: \( a\cdot a \).

Calculates the square of the length of a given quaternion. NB: this is a STATIC function!

Parameters
[in]athe quaternion.
Returns
the square of the length of the argument.

Definition at line 213 of file Quaternion.cc.

References q0, q1, q2, and q3.

Referenced by getUnitQuaternion().

214 {
215  return (a.q0 * a.q0 + a.q1 * a.q1 + a.q2 * a.q2 + a.q3 * a.q3);
216 }
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Mdouble Quaternion::getLengthSquared ( ) const

Calculates the squared length of this Quaternion: \( a\cdot a \).

Calculates the square of the length of itself

Returns
the square of the length of this quaternion

Definition at line 222 of file Quaternion.cc.

References q0, q1, q2, and q3.

Referenced by getLength(), and normalise().

223 {
224  return (q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
225 }
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
void Quaternion::getRotationMatrix ( SmallMatrix< 3, 3 > &  A) const

Retrieves the rotation matrix.

Parameters
[out]AThe rotation matrix

Definition at line 508 of file Quaternion.cc.

References A, q0, q1, q2, and q3.

Referenced by SuperQuadricParticle::computeHessianLabFixed(), rotate(), and rotateTensor().

509 {
510 
511  Mdouble q00 = q0 * q0;
512  Mdouble q01 = 2 * q0 * q1;
513  Mdouble q02 = 2 * q0 * q2;
514  Mdouble q03 = 2 * q0 * q3;
515  Mdouble q11 = q1 * q1;
516  Mdouble q12 = 2 * q1 * q2;
517  Mdouble q13 = 2 * q1 * q3;
518  Mdouble q22 = q2 * q2;
519  Mdouble q23 = 2 * q2 * q3;
520  Mdouble q33 = q3 * q3;
521  A(0, 0) = q00 + q11 - q22 - q33;
522  A(1, 0) = q12 + q03;
523  A(2, 0) = q13 - q02;
524  A(0, 1) = q12 - q03;
525  A(1, 1) = q00 - q11 + q22 - q33;
526  A(2, 1) = q23 + q01;
527  A(0, 2) = q13 + q02;
528  A(1, 2) = q23 - q01;
529  A(2, 2) = q00 - q11 - q22 + q33;
530 }
Mdouble
double Mdouble
Definition: GeneralDefine.h:34
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Quaternion Quaternion::getUnitQuaternion ( const Quaternion &  a)
static

Returns a unit Quaternion based on a.

Calculates the unit quaternion of a given quaternion (unless it is a quaternion with zero length; in that case it returns a 3D quaternion with each element equal to zero). NB: this is a STATIC function!

Parameters
[in]athe quaternion of interest
Returns
unit quaternion in the direction of the argument (unless the argument has length zero; in that case a zero-quaternion).

Definition at line 324 of file Quaternion.cc.

References getLengthSquared(), and Quaternion().

325 {
326  Mdouble Length2 = a.getLengthSquared();
327  if (Length2 != 0.0)
328  return a / std::sqrt(Length2);
329  else
330  return Quaternion(1, 0, 0, 0);
331 }
Mdouble
double Mdouble
Definition: GeneralDefine.h:34
Quaternion::Quaternion
Quaternion()
Constructor; sets quaternion value to (1,0,0,0)
Definition: Quaternion.cc:30
Quaternion::getLengthSquared
static Mdouble getLengthSquared(const Quaternion &a)
Calculates the squared length of a Quaternion: .
Definition: Quaternion.cc:213
bool Quaternion::isEqualTo ( const Quaternion &  other,
double  tol 
) const

Checks if the length this Quaternion is equal the length of other with a certain tolerance.

Checks if the length of the quaternion is equal to the one given in the first argument (other), with a tolerance given in the second argument (tol).

Parameters
[in]otherthe 3D quaternion to check against
[in]tolthe tolerance
Returns
returns TRUE if the difference between the lengths of this quaternion and that given in the first argument (other) is smaller than the given tolerance.

Definition at line 290 of file Quaternion.cc.

References getDistance().

291 {
292  return (getDistance(*this, other) <= tol * tol);
293 }
Quaternion::getDistance
static Mdouble getDistance(const Quaternion &a, const Quaternion &b)
Calculates the distance between two Quaternion: .
Definition: Quaternion.cc:188
bool Quaternion::isUnity ( ) const
inline

Checks if the quaternion value is (1,0,0,0)

Checks if ALL elements are zero

Returns
TRUE if q0 equals one and ALL other elements are zero
Bug:
use isEqual instead of ==

Definition at line 113 of file Quaternion.h.

References q0, q1, q2, and q3.

114  {
115  return q0 == 1.0 && q1 == 0.0 && q2 == 0.0 && q3 == 0.0;
116  };
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
void Quaternion::normalise ( )

Makes this Quaternion unit length |q|=1.

Normalises the quaternion, i.e. divides all elements by the quaternions length (resulting in a quaternion in the same direction, but with unit length).

Definition at line 161 of file Quaternion.cc.

References ERROR, getLengthSquared(), and logger.

Referenced by setOrientationViaNormal(), and updateAngularDisplacement().

162 {
163  const Mdouble length2 = getLengthSquared();
164  if (length2 == 0)
165  {
166  logger(ERROR, "Normalizing a quaternion of length 0");
167  }
168  *this /= sqrt(length2);
169 }
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
Mdouble
double Mdouble
Definition: GeneralDefine.h:34
Quaternion::getLengthSquared
Mdouble getLengthSquared() const
Calculates the squared length of this Quaternion: .
Definition: Quaternion.cc:222
Quaternion Quaternion::operator* ( Mdouble  a) const

Multiplies by a scalar.

Multiplies each element with a scalar

Parameters
[in]athe scalar to be multiplied with
Returns
the resulting quaternion

Definition at line 86 of file Quaternion.cc.

References q0, q1, q2, q3, and Quaternion().

87 {
88  return Quaternion(q0 * a, q1 * a, q2 * a, q3 * a);
89 }
Quaternion::Quaternion
Quaternion()
Constructor; sets quaternion value to (1,0,0,0)
Definition: Quaternion.cc:30
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Quaternion & Quaternion::operator*= ( Mdouble  a)

Multiplies *this by a scalar.

Multiplies each element by a scalar

Parameters
[in]ascalar to be multiplied by
Returns
(reference to) itself, i.e. resulting quaternion

Definition at line 134 of file Quaternion.cc.

References q0, q1, q2, and q3.

135 {
136  q0 *= a;
137  q1 *= a;
138  q2 *= a;
139  q3 *= a;
140  return *this;
141 }
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Quaternion Quaternion::operator+ ( const Quaternion &  a) const

Adds another quaternion and returns the result.

Adds quaternion to itself

Parameters
[in]aquaternion to be added
Returns
resulting 3D quaternion

Definition at line 66 of file Quaternion.cc.

References q0, q1, q2, q3, and Quaternion().

67 {
68  return Quaternion(q0 + a.q0, q1 + a.q1, q2 + a.q2, q3 + a.q3);
69 }
Quaternion::Quaternion
Quaternion()
Constructor; sets quaternion value to (1,0,0,0)
Definition: Quaternion.cc:30
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Quaternion & Quaternion::operator+= ( const Quaternion &  a)

Adds another quaternion.

Adds a quaternion to itself

Parameters
[in]aquaternion to be added
Returns
(reference to) itself, i.e. resulting quaternion

Definition at line 106 of file Quaternion.cc.

References q0, q1, q2, and q3.

107 {
108  q0 += a.q0;
109  q1 += a.q1;
110  q2 += a.q2;
111  q3 += a.q3;
112  return *this;
113 }
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Quaternion Quaternion::operator- ( const Quaternion &  a) const

Subtracts another quaternion and returns the result.

Subtracts quaternion from itself

Parameters
[in]aquaternion to be subtracted
Returns
resulting quaternion

Definition at line 76 of file Quaternion.cc.

References q0, q1, q2, q3, and Quaternion().

77 {
78  return Quaternion(q0 - a.q0, q1 - a.q1, q2 - a.q2, q3 - a.q3);
79 }
Quaternion::Quaternion
Quaternion()
Constructor; sets quaternion value to (1,0,0,0)
Definition: Quaternion.cc:30
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Quaternion & Quaternion::operator-= ( const Quaternion &  a)

Subtracts another quaternion.

Subtracts a quaternion from itself

Parameters
[in]aquaternion to be subtracted
Returns
(reference to) itself, i.e. resulting quaternion

Definition at line 120 of file Quaternion.cc.

References q0, q1, q2, and q3.

121 {
122  q0 -= a.q0;
123  q1 -= a.q1;
124  q2 -= a.q2;
125  q3 -= a.q3;
126  return *this;
127 }
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Quaternion Quaternion::operator/ ( Mdouble  a) const

Divides by a scalar.

Divides each element by a scalar

Parameters
[in]athe scalar to be divided by
Returns
resulting quaternion

Definition at line 96 of file Quaternion.cc.

References q0, q1, q2, q3, and Quaternion().

97 {
98  return Quaternion(q0 / a, q1 / a, q2 / a, q3 / a);
99 }
Quaternion::Quaternion
Quaternion()
Constructor; sets quaternion value to (1,0,0,0)
Definition: Quaternion.cc:30
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Quaternion & Quaternion::operator/= ( Mdouble  a)

Divides by a scalar.

Divides each element by a scalar

Parameters
[in]ascalar to be divided by
Returns
(reference to) itself, i.e. resulting quaternion

Definition at line 148 of file Quaternion.cc.

References q0, q1, q2, and q3.

149 {
150  q0 /= a;
151  q1 /= a;
152  q2 /= a;
153  q3 /= a;
154  return *this;
155 }
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
void Quaternion::rotate ( Vec3D &  position) const

Applies the rotation to a position.

Definition at line 563 of file Quaternion.cc.

References q0, q1, q2, and q3.

Referenced by SuperQuadricParticle::computeShapeGradientLabFixed(), HorizontalBaseScrew::convertLimits(), NurbsWall::getDistanceAndNormal(), Screw::getDistanceAndNormal(), BasicIntersectionOfWalls::getDistanceAndNormal(), BasicUnionOfWalls::getDistanceAndNormal(), LevelSetWall::getDistanceAndNormal(), IntersectionOfWalls::getDistanceAndNormal(), InfiniteWall::getDistanceNormalOverlapSuperquadric(), BaseWall::getInteractionWith(), BasicIntersectionOfWalls::getVTK(), BasicUnionOfWalls::getVTK(), TriangleWall::updateVertexAndNormal(), NurbsWall::writeVTK(), LevelSetWall::writeVTK(), Screw::writeVTK(), AxisymmetricIntersectionOfWalls::writeVTK(), ScrewsymmetricIntersectionOfWalls::writeVTK(), and IntersectionOfWalls::writeVTK().

564 {
565  Mdouble q00 = q0 * q0;
566  Mdouble q01 = 2 * q0 * q1;
567  Mdouble q02 = 2 * q0 * q2;
568  Mdouble q03 = 2 * q0 * q3;
569  Mdouble q11 = q1 * q1;
570  Mdouble q12 = 2 * q1 * q2;
571  Mdouble q13 = 2 * q1 * q3;
572  Mdouble q22 = q2 * q2;
573  Mdouble q23 = 2 * q2 * q3;
574  Mdouble q33 = q3 * q3;
575  position = Matrix3D(
576  q00 + q11 - q22 - q33, q12 - q03, q13 + q02,
577  q12 + q03, q00 - q11 + q22 - q33, q23 - q01,
578  q13 - q02, q23 + q01, q00 - q11 - q22 + q33) * position;
579 }
Mdouble
double Mdouble
Definition: GeneralDefine.h:34
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Matrix3D
Implementation of a 3D matrix.
Definition: Matrix.h:37
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
void Quaternion::rotate ( SmallVector< 3 > &  position) const

Applies the rotation to a position.

Rotate the given vector from the body-fixed angles to the lab-fixed angles.

This is the same as multiplying with the rotation matrix, A.

Definition at line 583 of file Quaternion.cc.

References A, and getRotationMatrix().

584 {
585  SmallMatrix<3, 3> A;
586  getRotationMatrix(A);
587  position = A * position;
588 }
Quaternion::getRotationMatrix
void getRotationMatrix(SmallMatrix< 3, 3 > &A) const
Retrieves the rotation matrix.
Definition: Quaternion.cc:508
SmallMatrix
Data type for small dense matrix.
Definition: SmallMatrix.h:67
void Quaternion::rotateBack ( Vec3D &  position) const

Applies the inverse rotation to a position.

Rotate the given vector from the lab-fixed angles to the body-fixed angles.

This is the same as multiplying with the inverse/transpose of the rotation matrix, A^T = A^{-1}.

Definition at line 592 of file Quaternion.cc.

References q0, q1, q2, and q3.

Referenced by SuperQuadricParticle::computeHessianLabFixed(), SuperQuadricParticle::computeShape(), SuperQuadricParticle::computeShapeGradientLabFixed(), AxisymmetricIntersectionOfWalls::convertLimits(), ScrewsymmetricIntersectionOfWalls::convertLimits(), NurbsWall::getDistanceAndNormal(), Screw::getDistanceAndNormal(), BasicIntersectionOfWalls::getDistanceAndNormal(), BasicUnionOfWalls::getDistanceAndNormal(), LevelSetWall::getDistanceAndNormal(), IntersectionOfWalls::getDistanceAndNormal(), InfiniteWall::getDistanceNormalOverlapSuperquadric(), and BaseWall::getInteractionWith().

593 {
594  Mdouble q00 = q0 * q0;
595  Mdouble q01 = 2 * q0 * q1;
596  Mdouble q02 = 2 * q0 * q2;
597  Mdouble q03 = 2 * q0 * q3;
598  Mdouble q11 = q1 * q1;
599  Mdouble q12 = 2 * q1 * q2;
600  Mdouble q13 = 2 * q1 * q3;
601  Mdouble q22 = q2 * q2;
602  Mdouble q23 = 2 * q2 * q3;
603  Mdouble q33 = q3 * q3;
604  position = Matrix3D(
605  q00 + q11 - q22 - q33, q12 + q03, q13 - q02,
606  q12 - q03, q00 - q11 + q22 - q33, q23 + q01,
607  q13 + q02, q23 - q01, q00 - q11 - q22 + q33) * position;
608 }
Mdouble
double Mdouble
Definition: GeneralDefine.h:34
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Matrix3D
Implementation of a 3D matrix.
Definition: Matrix.h:37
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
MatrixSymmetric3D Quaternion::rotateInverseInertiaTensor ( const MatrixSymmetric3D &  invI) const

Converts the inverse inertia tensor from the reference frame to the lab frame; see See QuaternionsWouter.pdf for details, where this operation is denoted by \(A*I^{-1}*A^T\).

Todo:
move link to where it belongs http://stackoverflow.com/questions/1171849/finding-quaternion-representing-the-rotation-from-one-vector-to-another This is the same as rotateTensor, but than for MatrixSymmetric3D instead of SmallMatrix<3,3>.

Definition at line 626 of file Quaternion.cc.

References constants::i, q0, q1, q2, q3, MatrixSymmetric3D::XX, MatrixSymmetric3D::XY, MatrixSymmetric3D::XZ, MatrixSymmetric3D::YY, MatrixSymmetric3D::YZ, and MatrixSymmetric3D::ZZ.

627 {
628  Mdouble a = 1 - 2 * q2 * q2 - 2 * q3 * q3;
629  Mdouble b = 2 * q1 * q2 - 2 * q0 * q3;
630  Mdouble c = 2 * q1 * q3 + 2 * q0 * q2;
631  Mdouble d = 2 * q1 * q2 + 2 * q0 * q3;
632  Mdouble e = 1 - 2 * q1 * q1 - 2 * q3 * q3;
633  Mdouble f = 2 * q2 * q3 - 2 * q0 * q1;
634  Mdouble g = 2 * q1 * q3 - 2 * q0 * q2;
635  Mdouble h = 2 * q2 * q3 + 2 * q0 * q1;
636  Mdouble i = 1 - 2 * q1 * q1 - 2 * q2 * q2;
637  MatrixSymmetric3D ans = MatrixSymmetric3D(
638  invI.XX * a * a + 2 * invI.XY * a * b + 2 * invI.XZ * a * c + invI.YY * b * b + 2 * invI.YZ * b * c +
639  invI.ZZ * c * c,
640  d * (invI.XX * a + invI.XY * b + invI.XZ * c) + e * (invI.XY * a + invI.YY * b + invI.YZ * c) +
641  f * (invI.XZ * a + invI.YZ * b + invI.ZZ * c),
642  g * (invI.XX * a + invI.XY * b + invI.XZ * c) + h * (invI.XY * a + invI.YY * b + invI.YZ * c) +
643  i * (invI.XZ * a + invI.YZ * b + invI.ZZ * c),
644  invI.XX * d * d + 2 * invI.XY * d * e + 2 * invI.XZ * d * f + invI.YY * e * e + 2 * invI.YZ * e * f +
645  invI.ZZ * f * f,
646  g * (invI.XX * d + invI.XY * e + invI.XZ * f) + h * (invI.XY * d + invI.YY * e + invI.YZ * f) +
647  i * (invI.XZ * d + invI.YZ * e + invI.ZZ * f),
648  invI.XX * g * g + 2 * invI.XY * g * h + 2 * invI.XZ * g * i + invI.YY * h * h + 2 * invI.YZ * h * i +
649  invI.ZZ * i * i
650  );
651  return ans;
652 }
Mdouble
double Mdouble
Definition: GeneralDefine.h:34
constants::i
const std::complex< Mdouble > i
Definition: ExtendedMath.h:50
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
MatrixSymmetric3D
Implementation of a 3D symmetric matrix.
Definition: MatrixSymmetric.h:36
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
MatrixSymmetric3D::XX
Mdouble XX
The six distinctive matrix elements.
Definition: MatrixSymmetric.h:42
void Quaternion::rotateTensor ( SmallMatrix< 3, 3 >  I) const

Definition at line 654 of file Quaternion.cc.

References A, getRotationMatrix(), and SmallMatrix< numberOfRows, numberOfColumns >::transpose().

655 {
656  SmallMatrix<3, 3> A;
657  getRotationMatrix(A);
658  I = A * I * A.transpose();
659 }
SmallMatrix::transpose
SmallMatrix< numberOfColumns, numberOfRows > transpose() const
Definition: SmallMatrix.h:330
Quaternion::getRotationMatrix
void getRotationMatrix(SmallMatrix< 3, 3 > &A) const
Retrieves the rotation matrix.
Definition: Quaternion.cc:508
SmallMatrix
Data type for small dense matrix.
Definition: SmallMatrix.h:67
void Quaternion::setAngleZ ( Mdouble  psi)

Converts the rotation angle in the XY plane into a quaternion (for Mercury2D). See Wikipedia for details.

Definition at line 492 of file Quaternion.cc.

References mathsFunc::cos(), q0, q1, q2, q3, and mathsFunc::sin().

Referenced by DPMBase::readNextDataFile().

493 {
494  //assuming theta=phi=0
495  q0 = std::cos(-0.5 * psi);
496  q1 = 0;
497  q2 = 0;
498  q3 = std::sin(-0.5 * psi);
499 }
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
mathsFunc::cos
Mdouble cos(Mdouble x)
Definition: ExtendedMath.cc:64
mathsFunc::sin
Mdouble sin(Mdouble x)
Definition: ExtendedMath.cc:44
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
void Quaternion::setComponent ( int  index,
double  val 
)

Sets the requested component of this Quaternion to the requested value.

Sets the element of the quaternion belonging to the first argument (index) to the value given in the second argument (val).

Parameters
[in]indexindex of element of interest,
[in]valvalue to be set

Definition at line 258 of file Quaternion.cc.

References ERROR, logger, q0, q1, q2, and q3.

259 {
260  switch (index)
261  {
262  case 0:
263  q0 = val;
264  break;
265  case 1:
266  q1 = val;
267  break;
268  case 2:
269  q2 = val;
270  break;
271  case 3:
272  q3 = val;
273  break;
274  default:
275  logger(ERROR,
276  "[Quaternion::setComponent] Index = %, which is too high for a 3D quaternion (should be 0-2).",
277  index);
278  }
279 }
logger
Logger< MERCURY_LOGLEVEL > logger("MercuryKernel")
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
void Quaternion::setEuler ( const Vec3D &  e)

Convert Euler angles to a quaternion. See Wikipedia for details.

Definition at line 473 of file Quaternion.cc.

References mathsFunc::cos(), q0, q1, q2, q3, mathsFunc::sin(), Vec3D::X, Vec3D::Y, and Vec3D::Z.

Referenced by BaseParticle::oldRead(), DPMBase::readNextDataFile(), and BaseInteractable::setOrientationViaEuler().

474 {
475  Mdouble cp = std::cos(0.5 * e.Y);
476  Mdouble sp = std::sin(0.5 * e.Y);
477  Mdouble cr = std::cos(0.5 * e.X);
478  Mdouble sr = std::sin(0.5 * e.X);
479  Mdouble cy = std::cos(0.5 * e.Z);
480  Mdouble sy = std::sin(0.5 * e.Z);
481  q0 = cr * cp * cy + sr * sp * sy;
482  q1 = sr * cp * cy - cr * sp * sy;
483  q2 = cr * sp * cy + sr * cp * sy;
484  q3 = cr * cp * sy - sr * sp * cy;
485 }
Vec3D::X
Mdouble X
the vector components
Definition: Vector.h:65
Mdouble
double Mdouble
Definition: GeneralDefine.h:34
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
mathsFunc::cos
Mdouble cos(Mdouble x)
Definition: ExtendedMath.cc:64
mathsFunc::sin
Mdouble sin(Mdouble x)
Definition: ExtendedMath.cc:44
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Vec3D::Y
Mdouble Y
Definition: Vector.h:65
Vec3D::Z
Mdouble Z
Definition: Vector.h:65
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
void Quaternion::setLength ( Mdouble  length)

Make this Quaternion a certain length |q|=length.

Sets the length of the quaternion to a given scalar (while maintaining the direction).

Parameters
[in]lengththe length to be set

Definition at line 176 of file Quaternion.cc.

References getLength().

177 {
178  *this /= this->getLength() * length;
179 }
Quaternion::getLength
Mdouble getLength() const
Calculates the length of this Quaternion: .
Definition: Quaternion.cc:299
void Quaternion::setOrientationViaNormal ( Vec3D  normal)

Used to the the normal of an InfiniteWall that has a normal into the x-direction by default.

Defines one possible orientation that rotates the x-axis into the direction given by normal.

This can be changed by resetting the wall orientation; thus the normal is the vector (1,0,0) rotated by this quaternion.

Parameters
[in]normalthe vector that the x-axis is rotated into.

Definition at line 536 of file Quaternion.cc.

References normalise(), Vec3D::normalise(), q0, q1, q2, q3, Quaternion(), Vec3D::X, Vec3D::Y, and Vec3D::Z.

Referenced by Quaternion(), and BaseInteractable::setOrientationViaNormal().

537 {
538  //if the normal vector cannot be read properly
539 // if (normal.getLengthSquared() < 1e-20)
540 // {
541 // setUnity();
542 // return;
543 // }
544 
545  normal.normalise();
546 
547  if (normal.X <= -1 + 1e-14)
548  {
549  *this = Quaternion(0, 0, 1, 0);
550  return;
551  }
552 
553  Vec3D half = Vec3D(1, 0, 0) + normal;
554  q0 = half.X;
555  q1 = 0;
556  q2 = -half.Z;
557  q3 = half.Y;
558  normalise();
559  //note, it can technically happen that normalising a normalised vector slightly changes the result.
560 }
Vec3D::X
Mdouble X
the vector components
Definition: Vector.h:65
Vec3D::normalise
void normalise()
Makes this Vec3D unit length.
Definition: Vector.cc:123
Quaternion::Quaternion
Quaternion()
Constructor; sets quaternion value to (1,0,0,0)
Definition: Quaternion.cc:30
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Vec3D::Y
Mdouble Y
Definition: Vector.h:65
Vec3D
Definition: Vector.h:49
Vec3D::Z
Mdouble Z
Definition: Vector.h:65
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Quaternion::normalise
void normalise()
Makes this Quaternion unit length |q|=1.
Definition: Quaternion.cc:161
void Quaternion::setUnity ( )

Sets quaternion value to (1,0,0,0)

Sets q0 to 1, and all other elements to zero.

Definition at line 53 of file Quaternion.cc.

References q0, q1, q2, and q3.

Referenced by BaseInteractable::BaseInteractable(), and Quaternion().

54 {
55  q0 = 1.0;
56  q1 = 0.0;
57  q2 = 0.0;
58  q3 = 0.0;
59 }
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
void Quaternion::updateAngularDisplacement ( Vec3D  angularVelocityDt)

Definition at line 431 of file Quaternion.cc.

References angularDisplacementTimeDerivative(), and normalise().

Referenced by BaseInteractable::rotate().

432 {
433  *this += angularDisplacementTimeDerivative(angularVelocityDt);
434  //const Quaternion q = *this;
435  normalise();
436  //logger(INFO,"%|%",q,*this);
437 }
Quaternion::angularDisplacementTimeDerivative
Quaternion angularDisplacementTimeDerivative(Vec3D v) const
Converts an angular momentum v=omega into a quaternion rate of change, q(t+dt)-q(t)/dt.
Definition: Quaternion.cc:422
Quaternion::normalise
void normalise()
Makes this Quaternion unit length |q|=1.
Definition: Quaternion.cc:161

Friends And Related Function Documentation

Quaternion operator* ( Mdouble  a,
const Quaternion &  b 
)
friend

Multiplies all elements by a scalar.

Multiplies each element of a given quaternion (b) by a given scalar (a). NB: this is a global function and a friend of the Quaternion class. Gets called when a scalar multiplication of the form (Mdouble) * (Quaternion) is performed.

Parameters
[in]athe scalar
[in]bthe quaternion
Returns
the resulting quaternion

Definition at line 405 of file Quaternion.cc.

406 {
407  return Quaternion(b.q0 * a, b.q1 * a, b.q2 * a, b.q3 * a);
408 }
Quaternion::Quaternion
Quaternion()
Constructor; sets quaternion value to (1,0,0,0)
Definition: Quaternion.cc:30
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Quaternion operator+ ( Mdouble  a,
const Quaternion &  b 
)
friend

Adds a scalar to a quaternion.

Adds a scalar to the elements of given quaternion NB this is a global function and a friend of the Quaternion class. Gets called when addition operation of the form (Mdouble) + (Quaternion) is performed.

Parameters
[in]athe scalar to be added
[in]bthe quaternion the scalar gets added to.
Returns
the resulting quaternion.

Definition at line 367 of file Quaternion.cc.

368 {
369  return Quaternion(b.q0 + a, b.q1 + a, b.q2 + a, b.q3 + a);
370 }
Quaternion::Quaternion
Quaternion()
Constructor; sets quaternion value to (1,0,0,0)
Definition: Quaternion.cc:30
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Quaternion operator- ( Mdouble  a,
const Quaternion &  b 
)
friend

Subtracts the elements of a quaternion from a scalar.

Subtracts each element of a given quaternion from a scalar NB this is a global function and a friend of the Quaternion class. Gets called when subtraction operation of the form (Mdouble) - (Quaternion) is performed.

Parameters
[in]athe scalar
[in]bthe quaternion to be subtracted the scalar gets subtracted from.
Returns
the resulting quaternion.

Definition at line 380 of file Quaternion.cc.

381 {
382  return Quaternion(a - b.q0, a - b.q1, a - b.q2, a - b.q3);
383 }
Quaternion::Quaternion
Quaternion()
Constructor; sets quaternion value to (1,0,0,0)
Definition: Quaternion.cc:30
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
Quaternion operator- ( const Quaternion &  a)
friend

Subtracts a quaternion.

Returns the negative of a given quaternion. NB: this is a global function and a friend of the Quaternion class. Gets called when a negation operation of the form - (Quaternion) is performed.

Parameters
[in]athe quaternion to be negated
Returns
the negated quaternion

Definition at line 392 of file Quaternion.cc.

393 {
394  return Quaternion(-a.q0, -a.q1, -a.q2, -a.q3);
395 }
Quaternion::Quaternion
Quaternion()
Constructor; sets quaternion value to (1,0,0,0)
Definition: Quaternion.cc:30
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
std::ostream& operator<< ( std::ostream &  os,
const Quaternion &  a 
)
friend

Adds elements to an output stream.

Adds all elements of the quaternion to an output stream. NB: this is a global function and a friend of the Quaternion class!

Parameters
[in]osthe output stream,
[in]aThe quaternion of interest
Returns
the output stream with quaternion elements added

Definition at line 340 of file Quaternion.cc.

341 {
342  os << a.q0 << ' ' << a.q1 << ' ' << a.q2 << ' ' << a.q3;
343  return os;
344 }
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73
std::istream& operator>> ( std::istream &  is,
Quaternion &  a 
)
friend

Adds elements to an input stream.

Reads all elements of a given quaternion from an input stream. NB: this is a global function and a friend of the Quaternion class!

Parameters
[in,out]isthe input stream
[in,out]athe quaternion to be read in
Returns
the input stream from which the quaternion elements were read

Definition at line 353 of file Quaternion.cc.

354 {
355  is >> a.q0 >> a.q1 >> a.q2 >> a.q3;
356  return is;
357 }
Quaternion::q2
Mdouble q2
the second component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:77
Quaternion::q3
Mdouble q3
the third component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:81
Quaternion::q0
Mdouble q0
the zeroth component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:69
Quaternion::q1
Mdouble q1
the first component of the quaternion q = (q0,q1,q2,q3)
Definition: Quaternion.h:73

Member Data Documentation

Mdouble Quaternion::q0

the zeroth component of the quaternion q = (q0,q1,q2,q3)

Definition at line 69 of file Quaternion.h.

Referenced by angularDisplacementTimeDerivative(), angularVelocityBodyFixedFrameToAngularDisplacement(), applyCInverse(), getAngleZ(), getAxis(), getComponent(), getDistance(), getDistanceSquared(), getEuler(), getLengthSquared(), getRotationMatrix(), isUnity(), operator*(), operator*(), operator*=(), operator+(), operator+(), operator+=(), operator-(), operator-(), operator-=(), operator/(), operator/=(), operator<<(), operator>>(), Quaternion(), rotate(), rotateBack(), rotateInverseInertiaTensor(), setAngleZ(), setComponent(), setEuler(), setOrientationViaNormal(), and setUnity().

Mdouble Quaternion::q1

the first component of the quaternion q = (q0,q1,q2,q3)

Definition at line 73 of file Quaternion.h.

Referenced by angularDisplacementTimeDerivative(), angularVelocityBodyFixedFrameToAngularDisplacement(), applyCInverse(), getAngleZ(), BaseWall::getAxis(), getAxis(), getComponent(), getDistance(), getDistanceSquared(), getEuler(), getLengthSquared(), getRotationMatrix(), isUnity(), operator*(), operator*(), operator*=(), operator+(), operator+(), operator+=(), operator-(), operator-(), operator-=(), operator/(), operator/=(), operator<<(), operator>>(), Quaternion(), rotate(), rotateBack(), rotateInverseInertiaTensor(), setAngleZ(), setComponent(), setEuler(), setOrientationViaNormal(), and setUnity().

Mdouble Quaternion::q2

the second component of the quaternion q = (q0,q1,q2,q3)

Definition at line 77 of file Quaternion.h.

Referenced by angularDisplacementTimeDerivative(), angularVelocityBodyFixedFrameToAngularDisplacement(), applyCInverse(), getAngleZ(), BaseWall::getAxis(), getAxis(), getComponent(), getDistance(), getDistanceSquared(), getEuler(), getLengthSquared(), getRotationMatrix(), isUnity(), operator*(), operator*(), operator*=(), operator+(), operator+(), operator+=(), operator-(), operator-(), operator-=(), operator/(), operator/=(), operator<<(), operator>>(), Quaternion(), rotate(), rotateBack(), rotateInverseInertiaTensor(), setAngleZ(), setComponent(), setEuler(), setOrientationViaNormal(), and setUnity().

Mdouble Quaternion::q3

the third component of the quaternion q = (q0,q1,q2,q3)

Definition at line 81 of file Quaternion.h.

Referenced by angularDisplacementTimeDerivative(), angularVelocityBodyFixedFrameToAngularDisplacement(), applyCInverse(), getAngleZ(), BaseWall::getAxis(), getAxis(), getComponent(), getDistance(), getDistanceSquared(), getEuler(), getLengthSquared(), getRotationMatrix(), isUnity(), operator*(), operator*(), operator*=(), operator+(), operator+(), operator+=(), operator-(), operator-(), operator-=(), operator/(), operator/=(), operator<<(), operator>>(), Quaternion(), rotate(), rotateBack(), rotateInverseInertiaTensor(), setAngleZ(), setComponent(), setEuler(), setOrientationViaNormal(), and setUnity().

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