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extern/opennurbs/opennurbs_quaternion.h

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/* $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>.
//
////////////////////////////////////////////////////////////////
*/
#if !defined(ON_QUATERNION_INC_)
#define ON_QUATERNION_INC_
class ON_CLASS ON_Quaternion
{
public:
// quaternion = a + bi + cj + dk
double a,b,c,d;
static const ON_Quaternion Zero; // 0 = (0,0,0,0
static const ON_Quaternion Identity; // 1 = (1,0,0,0)
static const ON_Quaternion I; // "i" = (0,1,0,0)
static const ON_Quaternion J; // "j" = (0,0,1,0)
static const ON_Quaternion K; // "k" = (0,0,0,1)
ON_Quaternion() {}
ON_Quaternion(double qa, double qb, double qc, double qd);
// (a,b,c,d) = (0,v.x,v.y,v.z)
ON_Quaternion(const ON_3dVector& v);
// (a,b,c,d) = (0,v.x,v.y,v.z)
ON_Quaternion& operator=(const ON_3dVector& v);
void Set(double qa, double qb, double qc, double qd);
// arithmetic operators
ON_Quaternion operator*(int) const;
ON_Quaternion operator/(int) const;
ON_Quaternion operator*(float) const;
ON_Quaternion operator/(float) const;
ON_Quaternion operator*(double) const;
ON_Quaternion operator/(double) const;
ON_Quaternion operator+(const ON_Quaternion&) const;
ON_Quaternion operator-(const ON_Quaternion&) const;
// quaternion multiplication is not commutative
ON_Quaternion operator*(const ON_Quaternion&) const;
/*
Returns:
True if a, b, c, and d are valid finite IEEE doubles.
*/
bool IsValid() const;
/*
Description:
Returns the conjugate of the quaternion = (a,-b,-c,-d).
*/
ON_Quaternion Conjugate() const;
/*
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.
*/
bool Invert();
/*
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.
*/
ON_Quaternion Inverse() const;
/*
Returns:
Returns the length or norm of the quaternion
sqrt(a*a + b*b + c*c + d*d).
*/
double Length() const;
/*
Returns:
Returns a*a + b*b + c*c + d*d.
*/
double LengthSquared() const;
/*
Returns:
The distance or norm of the difference between the two quaternions.
= ("this" - q).Length().
*/
double DistanceTo(const ON_Quaternion& q) const;
/*
Returns:
The distance or norm of the difference between the two quaternions.
= (p - q).Length().
*/
static double Distance(const ON_Quaternion& p, const ON_Quaternion& q);
/*
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.
*/
ON_Xform MatrixForm() const;
/*
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.
*/
bool Unitize();
/*
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:
*/
void SetRotation(double angle, const ON_3dVector& axis);
/*
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.
*/
static ON_Quaternion Rotation(double angle, const ON_3dVector& axis);
/*
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.
*/
void SetRotation(const ON_Plane& plane0, const ON_Plane& plane1);
/*
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.
*/
static ON_Quaternion Rotation(const ON_Plane& plane0, const ON_Plane& plane1);
/*
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.
*/
bool GetRotation(double& angle, ON_3dVector& axis) 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).
*/
bool GetRotation(ON_Xform& xform) 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).
*/
bool GetRotation(ON_Plane& plane) 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.
*/
ON_3dVector Rotate(ON_3dVector v) const;
/*
Returns:
The "vector" or "imaginary" part of the quaternion = (b,c,d)
*/
ON_3dVector Vector() const;
/*
Returns:
The "real" or "scalar" part of the quaternion = a.
*/
double Scalar() const;
/*
Returns:
True if a, b, c, and d are all zero.
*/
bool IsZero() const;
/*
Returns:
True if a, b, c, and d are all valid, finite and at least one is non-zero.
*/
bool IsNotZero() const;
/*
Returns:
True if b, c, and d are all zero.
*/
bool IsScalar() const;
/*
Returns:
True if a = 0 and at least one of b, c, or d is not zero.
*/
bool IsVector() const;
/*
Returns:
exp(q) = e^a*( cos(|V|) + V/|V|*sin(|V|) ), where V = b*i + c*j + d*k.
*/
static ON_Quaternion Exp(ON_Quaternion q);
/*
Returns:
log(q) = log(|q|) + V/|V|*acos(a/|q|), where V = b*i + c*j + d*k.
*/
static ON_Quaternion Log(ON_Quaternion q);
/*
Returns:
q^t = Exp(t*Log(q))
*/
static ON_Quaternion Pow(ON_Quaternion q, double t);
static ON_Quaternion Slerp(ON_Quaternion q0, ON_Quaternion q1, double t);
};
/*
Returns:
The quaternion product of p and q. This is the same value as p*q.
*/
ON_DECL
ON_Quaternion ON_QuaternionProduct( const ON_Quaternion& p, const ON_Quaternion& q);
/*
Returns:
The vector cross product of p and q = (0,x,y,z) where
(x,y,z) = ON_CrossProduct(p.Vector(),q.Vector())
This is NOT the same as the quaternion product p*q.
*/
ON_DECL
ON_Quaternion ON_CrossProduct( const ON_Quaternion& p, const ON_Quaternion& q);
ON_DECL
ON_Quaternion operator*(int, const ON_Quaternion&);
ON_DECL
ON_Quaternion operator*(float, const ON_Quaternion&);
ON_DECL
ON_Quaternion operator*(double, const ON_Quaternion&);
#endif