Rhino C++ API  7.24
Public Member Functions | Static Public Member Functions | Public Attributes | Static Public Attributes | List of all members
ON_Quaternion Class Reference

#include <opennurbs_quaternion.h>

Public Member Functions

 ON_Quaternion ()
 
 ON_Quaternion (const ON_3dVector &v)
 (a,b,c,d) = (0,v.x,v.y,v.z) More...
 
 ON_Quaternion (double qa, double qb, double qc, double qd)
 
ON_Quaternion Conjugate () const
 
double DistanceTo (const ON_Quaternion &q) const
 
bool GetRotation (double &angle, ON_3dVector &axis) const
 
bool GetRotation (ON_Plane &plane) const
 
bool GetRotation (ON_Xform &xform) const
 
ON_Quaternion Inverse () const
 
bool Invert ()
 
bool IsNotZero () const
 
bool IsScalar () const
 
bool IsValid () const
 
bool IsVector () const
 
bool IsZero () const
 
double Length () const
 
double LengthSquared () const
 
ON_Xform MatrixForm () const
 
ON_Quaternion operator* (const ON_Quaternion &) const
 quaternion multiplication is not commutative More...
 
ON_Quaternion operator* (double) const
 
ON_Quaternion operator* (float) const
 
ON_Quaternion operator* (int) const
 arithmetic operators More...
 
ON_Quaternion operator+ (const ON_Quaternion &) const
 
ON_Quaternion operator- (const ON_Quaternion &) const
 
ON_Quaternion operator/ (double) const
 
ON_Quaternion operator/ (float) const
 
ON_Quaternion operator/ (int) const
 
ON_Quaternionoperator= (const ON_3dVector &v)
 (a,b,c,d) = (0,v.x,v.y,v.z) More...
 
ON_3dVector Rotate (ON_3dVector v) const
 
double Scalar () const
 
void Set (double qa, double qb, double qc, double qd)
 
void SetRotation (const ON_Plane &plane0, const ON_Plane &plane1)
 
void SetRotation (double angle, const ON_3dVector &axis)
 
bool Unitize ()
 
ON_3dVector Vector () const
 

Static Public Member Functions

static double Distance (const ON_Quaternion &p, const ON_Quaternion &q)
 
static ON_Quaternion Exp (ON_Quaternion q)
 
static ON_Quaternion Log (ON_Quaternion q)
 
static ON_Quaternion Pow (ON_Quaternion q, double t)
 
static ON_Quaternion Rotation (const ON_Plane &plane0, const ON_Plane &plane1)
 
static ON_Quaternion Rotation (double angle, const ON_3dVector &axis)
 
static ON_Quaternion Slerp (ON_Quaternion q0, ON_Quaternion q1, double t)
 

Public Attributes

double a
 quaternion = a + bi + cj + dk More...
 
double b
 
double c
 
double d
 

Static Public Attributes

static const ON_Quaternion I
 "i" = (0,1,0,0) More...
 
static const ON_Quaternion Identity
 1 = (1,0,0,0) More...
 
static const ON_Quaternion J
 "j" = (0,0,1,0) More...
 
static const ON_Quaternion K
 "k" = (0,0,0,1) More...
 
static const ON_Quaternion Zero
 0 = (0,0,0,0 More...
 

Detailed Description

NoKeywords

/ / Copyright (c) 1993-2012 Robert McNeel & Associates. All rights reserved. / OpenNURBS, Rhinoceros, and Rhino3D are registered trademarks of Robert / McNeel & Associates. / / THIS SOFTWARE IS PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY. / ALL IMPLIED WARRANTIES OF FITNESS FOR ANY PARTICULAR PURPOSE AND OF / MERCHANTABILITY ARE HEREBY DISCLAIMED. /
/ For complete openNURBS copyright information see http://www.opennurbs.org. / //////////////////////////////////////////////////////////////

Constructor & Destructor Documentation

◆ ON_Quaternion() [1/3]

ON_Quaternion::ON_Quaternion ( )
inline

◆ ON_Quaternion() [2/3]

ON_Quaternion::ON_Quaternion ( double  qa,
double  qb,
double  qc,
double  qd 
)

◆ ON_Quaternion() [3/3]

ON_Quaternion::ON_Quaternion ( const ON_3dVector v)

(a,b,c,d) = (0,v.x,v.y,v.z)

Member Function Documentation

◆ Conjugate()

ON_Quaternion ON_Quaternion::Conjugate ( ) const

Description: Returns the conjugate of the quaternion = (a,-b,-c,-d).

◆ Distance()

static double ON_Quaternion::Distance ( const ON_Quaternion p,
const ON_Quaternion q 
)
static

Returns: The distance or norm of the difference between the two quaternions. = (p - q).Length().

◆ DistanceTo()

double ON_Quaternion::DistanceTo ( const ON_Quaternion q) const

Returns: The distance or norm of the difference between the two quaternions. = ("this" - q).Length().

◆ Exp()

static ON_Quaternion ON_Quaternion::Exp ( ON_Quaternion  q)
static

Returns: exp(q) = e^a*( cos(|V|) + V/|V|*sin(|V|) ), where V = b*i + c*j + d*k.

◆ GetRotation() [1/3]

bool ON_Quaternion::GetRotation ( double &  angle,
ON_3dVector axis 
) const

Parameters: angle - [out] in radians axis - [out] unit axis of rotation of 0 if (b,c,d) is the zero vector. Returns: The rotation defined by the quaternion. Remarks: If the quaternion is not unitized, the rotation of its unitized form is returned.

◆ GetRotation() [2/3]

bool ON_Quaternion::GetRotation ( ON_Plane plane) const

Parameters: plane - [out] Returns: The frame created by applying the quaternion's rotation to the canonical world frame (1,0,0),(0,1,0),(0,0,1).

◆ GetRotation() [3/3]

bool ON_Quaternion::GetRotation ( ON_Xform xform) const

Description: The transformation returned by this function has the property that xform*V = q.Rotate(V). Parameters: xform - [out] Returns: A transformation matrix that performs the rotation defined by the quaternion. Remarks: If the quaternion is not unitized, the rotation of its unitized form is returned. Do not confuse the result of this function the matrix returned by ON_Quaternion::MatrixForm(). The transformation returned by this function has the property that xform*V = q.Rotate(V).

◆ Inverse()

ON_Quaternion ON_Quaternion::Inverse ( ) const

Returns: Sets the quaternion to a/L2, -b/L2, -c/L2, -d/L2, where L2 = length squared = (a*a + b*b + c*c + d*d). This is the multiplicative inverse, i.e., (a,b,c,d)*(a/L2, -b/L2, -c/L2, -d/L2) = (1,0,0,0). If "this" is the zero quaternion, then the zero quaternion is returned.

◆ Invert()

bool ON_Quaternion::Invert ( )

Description: Sets the quaternion to a/L2, -b/L2, -c/L2, -d/L2, where L2 = length squared = (a*a + b*b + c*c + d*d). This is the multiplicative inverse, i.e., (a,b,c,d)*(a/L2, -b/L2, -c/L2, -d/L2) = (1,0,0,0). Returns: True if successful. False if the quaternion is zero and cannot be inverted.

◆ IsNotZero()

bool ON_Quaternion::IsNotZero ( ) const

Returns: True if a, b, c, and d are all valid, finite and at least one is non-zero.

◆ IsScalar()

bool ON_Quaternion::IsScalar ( ) const

Returns: True if b, c, and d are all zero.

◆ IsValid()

bool ON_Quaternion::IsValid ( ) const

Returns: True if a, b, c, and d are valid finite IEEE doubles.

◆ IsVector()

bool ON_Quaternion::IsVector ( ) const

Returns: True if a = 0 and at least one of b, c, or d is not zero.

◆ IsZero()

bool ON_Quaternion::IsZero ( ) const

Returns: True if a, b, c, and d are all zero.

◆ Length()

double ON_Quaternion::Length ( ) const

Returns: Returns the length or norm of the quaternion sqrt(a*a + b*b + c*c + d*d).

◆ LengthSquared()

double ON_Quaternion::LengthSquared ( ) const

Returns: Returns a*a + b*b + c*c + d*d.

◆ Log()

static ON_Quaternion ON_Quaternion::Log ( ON_Quaternion  q)
static

Returns: log(q) = log(|q|) + V/|V|*acos(a/|q|), where V = b*i + c*j + d*k.

◆ MatrixForm()

ON_Xform ON_Quaternion::MatrixForm ( ) const

Returns: 4x4 real valued matrix form of the quaternion

    a  b  c  d
   -b  a -d  c
   -c  d  a -b
   -d -c  b  a

which has the same arithmetic properties in as the quaternion. Remarks: Do not confuse this with the rotation defined by the quaternion. This function will only be interesting to math nerds and is not useful in rendering or animation applications.

◆ operator*() [1/4]

ON_Quaternion ON_Quaternion::operator* ( const ON_Quaternion ) const

quaternion multiplication is not commutative

◆ operator*() [2/4]

ON_Quaternion ON_Quaternion::operator* ( double  ) const

◆ operator*() [3/4]

ON_Quaternion ON_Quaternion::operator* ( float  ) const

◆ operator*() [4/4]

ON_Quaternion ON_Quaternion::operator* ( int  ) const

arithmetic operators

◆ operator+()

ON_Quaternion ON_Quaternion::operator+ ( const ON_Quaternion ) const

◆ operator-()

ON_Quaternion ON_Quaternion::operator- ( const ON_Quaternion ) const

◆ operator/() [1/3]

ON_Quaternion ON_Quaternion::operator/ ( double  ) const

◆ operator/() [2/3]

ON_Quaternion ON_Quaternion::operator/ ( float  ) const

◆ operator/() [3/3]

ON_Quaternion ON_Quaternion::operator/ ( int  ) const

◆ operator=()

ON_Quaternion& ON_Quaternion::operator= ( const ON_3dVector v)

(a,b,c,d) = (0,v.x,v.y,v.z)

◆ Pow()

static ON_Quaternion ON_Quaternion::Pow ( ON_Quaternion  q,
double  t 
)
static

Returns: q^t = Exp(t*Log(q))

◆ Rotate()

ON_3dVector ON_Quaternion::Rotate ( ON_3dVector  v) const

Description Rotate a 3d vector. This operation is also called conjugation, because the result is the same as

(q.Conjugate()*(0,x,y,x)*q/q.LengthSquared()).Vector()

Parameters: v - [in] Returns: R*v, where R is the rotation defined by the unit quaternion. This is mathematically the same as the values (Inverse(q)*(0,x,y,z)*q).Vector() and (q.Conjugate()*(0,x,y,x)*q/q.LengthSquared()).Vector() Remarks: If you need to rotate more than a dozen or so vectors, it will be more efficient to call GetRotation(ON_Xform& xform) and multiply the vectors by xform.

◆ Rotation() [1/2]

static ON_Quaternion ON_Quaternion::Rotation ( const ON_Plane plane0,
const ON_Plane plane1 
)
static

Parameters: plane0 - [in] plane1 - [in] Returns: The unit quaternion that represents the the rotation that maps plane0.xaxis to plane1.xaxis, plane0.yaxis to plane1.yaxis, and plane0.zaxis to plane1.zaxis. Remarks: The plane origins are ignored.

◆ Rotation() [2/2]

static ON_Quaternion ON_Quaternion::Rotation ( double  angle,
const ON_3dVector axis 
)
static

Parameters: angle - [in] in radians axis - [in] axis of rotation Returns: The unit quaternion

cos(angle/2), sin(angle/2)*x, sin(angle/2)*y, sin(angle/2)*z

where (x,y,z) is the unit vector parallel to axis. This is the unit quaternion that represents the rotation of angle about axis.

◆ Scalar()

double ON_Quaternion::Scalar ( ) const

Returns: The "real" or "scalar" part of the quaternion = a.

◆ Set()

void ON_Quaternion::Set ( double  qa,
double  qb,
double  qc,
double  qd 
)

◆ SetRotation() [1/2]

void ON_Quaternion::SetRotation ( const ON_Plane plane0,
const ON_Plane plane1 
)

Descriptin: Sets the quaternion to the unit quaternion which rotates plane0.xaxis to plane1.xaxis, plane0.yaxis to plane1.yaxis, and plane0.zaxis to plane1.zaxis. Parameters: plane0 - [in] plane1 - [in] Remarks: The plane origins are ignored.

◆ SetRotation() [2/2]

void ON_Quaternion::SetRotation ( double  angle,
const ON_3dVector axis 
)

Description: Sets the quaternion to

cos(angle/2), sin(angle/2)*x, sin(angle/2)*y, sin(angle/2)*z

where (x,y,z) is the unit vector parallel to axis. This is the unit quaternion that represents the rotation of angle about axis. Parameters: angle - [in] in radians axis - [in] axis of rotation Returns:

◆ Slerp()

static ON_Quaternion ON_Quaternion::Slerp ( ON_Quaternion  q0,
ON_Quaternion  q1,
double  t 
)
static

◆ Unitize()

bool ON_Quaternion::Unitize ( )

Description: Scales the quaternion's coordinates so that a*a + b*b + c*c + d*d = 1. Returns: True if successful. False if the quaternion is zero and cannot be unitized.

◆ Vector()

ON_3dVector ON_Quaternion::Vector ( ) const

Returns: The "vector" or "imaginary" part of the quaternion = (b,c,d)

Member Data Documentation

◆ a

double ON_Quaternion::a

quaternion = a + bi + cj + dk

◆ b

double ON_Quaternion::b

◆ c

double ON_Quaternion::c

◆ d

double ON_Quaternion::d

◆ I

const ON_Quaternion ON_Quaternion::I
static

"i" = (0,1,0,0)

◆ Identity

const ON_Quaternion ON_Quaternion::Identity
static

1 = (1,0,0,0)

◆ J

const ON_Quaternion ON_Quaternion::J
static

"j" = (0,0,1,0)

◆ K

const ON_Quaternion ON_Quaternion::K
static

"k" = (0,0,0,1)

◆ Zero

const ON_Quaternion ON_Quaternion::Zero
static

0 = (0,0,0,0