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/*
* SOLID - Software Library for Interference Detection
*
* Copyright (C) 2001-2003 Dtecta. All rights reserved.
*
* This library may be distributed under the terms of the Q Public License
* (QPL) as defined by Trolltech AS of Norway and appearing in the file
* LICENSE.QPL included in the packaging of this file.
*
* This library may be distributed and/or modified under the terms of the
* GNU General Public License (GPL) version 2 as published by the Free Software
* Foundation and appearing in the file LICENSE.GPL included in the
* packaging of this file.
*
* This library is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
* WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
*
* Commercial use or any other use of this library not covered by either
* the QPL or the GPL requires an additional license from Dtecta.
* Please contact info@dtecta.com for enquiries about the terms of commercial
* use of this library.
*/
#ifndef QUATERNION_H
#define QUATERNION_H
#if defined (__sgi)
#include <assert.h>
#else
#include <cassert>
#endif
#include "Tuple4.h"
#include "Vector3.h"
namespace MT {
template <typename Scalar>
class Quaternion : public Tuple4<Scalar> {
public:
Quaternion() {}
template <typename Scalar2>
explicit Quaternion(const Scalar2 *v) : Tuple4<Scalar>(v) {}
template <typename Scalar2>
Quaternion(const Scalar2& x, const Scalar2& y, const Scalar2& z, const Scalar2& w)
: Tuple4<Scalar>(x, y, z, w)
{}
Quaternion(const Vector3<Scalar>& axis, const Scalar& angle)
{
setRotation(axis, angle);
}
template <typename Scalar2>
Quaternion(const Scalar2& yaw, const Scalar2& pitch, const Scalar2& roll)
{
setEuler(yaw, pitch, roll);
}
void setRotation(const Vector3<Scalar>& axis, const Scalar& angle)
{
Scalar d = axis.length();
assert(d != Scalar(0.0));
Scalar s = Scalar_traits<Scalar>::sin(angle * Scalar(0.5)) / d;
setValue(axis[0] * s, axis[1] * s, axis[2] * s,
Scalar_traits<Scalar>::cos(angle * Scalar(0.5)));
}
template <typename Scalar2>
void setEuler(const Scalar2& yaw, const Scalar2& pitch, const Scalar2& roll)
{
Scalar halfYaw = Scalar(yaw) * Scalar(0.5);
Scalar halfPitch = Scalar(pitch) * Scalar(0.5);
Scalar halfRoll = Scalar(roll) * Scalar(0.5);
Scalar cosYaw = Scalar_traits<Scalar>::cos(halfYaw);
Scalar sinYaw = Scalar_traits<Scalar>::sin(halfYaw);
Scalar cosPitch = Scalar_traits<Scalar>::cos(halfPitch);
Scalar sinPitch = Scalar_traits<Scalar>::sin(halfPitch);
Scalar cosRoll = Scalar_traits<Scalar>::cos(halfRoll);
Scalar sinRoll = Scalar_traits<Scalar>::sin(halfRoll);
setValue(cosRoll * sinPitch * cosYaw + sinRoll * cosPitch * sinYaw,
cosRoll * cosPitch * sinYaw - sinRoll * sinPitch * cosYaw,
sinRoll * cosPitch * cosYaw - cosRoll * sinPitch * sinYaw,
cosRoll * cosPitch * cosYaw + sinRoll * sinPitch * sinYaw);
}
Quaternion<Scalar>& operator+=(const Quaternion<Scalar>& q)
{
this->m_co[0] += q[0]; this->m_co[1] += q[1]; this->m_co[2] += q[2]; this->m_co[3] += q[3];
return *this;
}
Quaternion<Scalar>& operator-=(const Quaternion<Scalar>& q)
{
this->m_co[0] -= q[0]; this->m_co[1] -= q[1]; this->m_co[2] -= q[2]; this->m_co[3] -= q[3];
return *this;
}
Quaternion<Scalar>& operator*=(const Scalar& s)
{
this->m_co[0] *= s; this->m_co[1] *= s; this->m_co[2] *= s; this->m_co[3] *= s;
return *this;
}
Quaternion<Scalar>& operator/=(const Scalar& s)
{
assert(s != Scalar(0.0));
return *this *= Scalar(1.0) / s;
}
Quaternion<Scalar>& operator*=(const Quaternion<Scalar>& q)
{
setValue(this->m_co[3] * q[0] + this->m_co[0] * q[3] + this->m_co[1] * q[2] - this->m_co[2] * q[1],
this->m_co[3] * q[1] + this->m_co[1] * q[3] + this->m_co[2] * q[0] - this->m_co[0] * q[2],
this->m_co[3] * q[2] + this->m_co[2] * q[3] + this->m_co[0] * q[1] - this->m_co[1] * q[0],
this->m_co[3] * q[3] - this->m_co[0] * q[0] - this->m_co[1] * q[1] - this->m_co[2] * q[2]);
return *this;
}
Scalar dot(const Quaternion<Scalar>& q) const
{
return this->m_co[0] * q[0] + this->m_co[1] * q[1] + this->m_co[2] * q[2] + this->m_co[3] * q[3];
}
Scalar length2() const
{
return dot(*this);
}
Scalar length() const
{
return Scalar_traits<Scalar>::sqrt(length2());
}
Quaternion<Scalar>& normalize()
{
return *this /= length();
}
Quaternion<Scalar> normalized() const
{
return *this / length();
}
Scalar angle(const Quaternion<Scalar>& q) const
{
Scalar s = Scalar_traits<Scalar>::sqrt(length2() * q.length2());
assert(s != Scalar(0.0));
return Scalar_traits<Scalar>::acos(dot(q) / s);
}
Quaternion<Scalar> conjugate() const
{
return Quaternion<Scalar>(-this->m_co[0], -this->m_co[1], -this->m_co[2], this->m_co[3]);
}
Quaternion<Scalar> inverse() const
{
return conjugate / length2();
}
Quaternion<Scalar> slerp(const Quaternion<Scalar>& q, const Scalar& t) const
{
Scalar theta = angle(q);
if (theta != Scalar(0.0))
{
Scalar d = Scalar(1.0) / Scalar_traits<Scalar>::sin(theta);
Scalar s0 = Scalar_traits<Scalar>::sin((Scalar(1.0) - t) * theta);
Scalar s1 = Scalar_traits<Scalar>::sin(t * theta);
return Quaternion<Scalar>((this->m_co[0] * s0 + q[0] * s1) * d,
(this->m_co[1] * s0 + q[1] * s1) * d,
(this->m_co[2] * s0 + q[2] * s1) * d,
(this->m_co[3] * s0 + q[3] * s1) * d);
}
else
{
return *this;
}
}
static Quaternion<Scalar> random()
{
// From: "Uniform Random Rotations", Ken Shoemake, Graphics Gems III,
// pg. 124-132
Scalar x0 = Scalar_traits<Scalar>::random();
Scalar r1 = Scalar_traits<Scalar>::sqrt(Scalar(1.0) - x0);
Scalar r2 = Scalar_traits<Scalar>::sqrt(x0);
Scalar t1 = Scalar_traits<Scalar>::TwoTimesPi() * Scalar_traits<Scalar>::random();
Scalar t2 = Scalar_traits<Scalar>::TwoTimesPi() * Scalar_traits<Scalar>::random();
Scalar c1 = Scalar_traits<Scalar>::cos(t1);
Scalar s1 = Scalar_traits<Scalar>::sin(t1);
Scalar c2 = Scalar_traits<Scalar>::cos(t2);
Scalar s2 = Scalar_traits<Scalar>::sin(t2);
return Quaternion<Scalar>(s1 * r1, c1 * r1, s2 * r2, c2 * r2);
}
};
template <typename Scalar>
inline Quaternion<Scalar>
operator+(const Quaternion<Scalar>& q1, const Quaternion<Scalar>& q2)
{
return Quaternion<Scalar>(q1[0] + q2[0], q1[1] + q2[1], q1[2] + q2[2], q1[3] + q2[3]);
}
template <typename Scalar>
inline Quaternion<Scalar>
operator-(const Quaternion<Scalar>& q1, const Quaternion<Scalar>& q2)
{
return Quaternion<Scalar>(q1[0] - q2[0], q1[1] - q2[1], q1[2] - q2[2], q1[3] - q2[3]);
}
template <typename Scalar>
inline Quaternion<Scalar>
operator-(const Quaternion<Scalar>& q)
{
return Quaternion<Scalar>(-q[0], -q[1], -q[2], -q[3]);
}
template <typename Scalar>
inline Quaternion<Scalar>
operator*(const Quaternion<Scalar>& q, const Scalar& s)
{
return Quaternion<Scalar>(q[0] * s, q[1] * s, q[2] * s, q[3] * s);
}
template <typename Scalar>
inline Quaternion<Scalar>
operator*(const Scalar& s, const Quaternion<Scalar>& q)
{
return q * s;
}
template <typename Scalar>
inline Quaternion<Scalar>
operator*(const Quaternion<Scalar>& q1, const Quaternion<Scalar>& q2) {
return Quaternion<Scalar>(q1[3] * q2[0] + q1[0] * q2[3] + q1[1] * q2[2] - q1[2] * q2[1],
q1[3] * q2[1] + q1[1] * q2[3] + q1[2] * q2[0] - q1[0] * q2[2],
q1[3] * q2[2] + q1[2] * q2[3] + q1[0] * q2[1] - q1[1] * q2[0],
q1[3] * q2[3] - q1[0] * q2[0] - q1[1] * q2[1] - q1[2] * q2[2]);
}
template <typename Scalar>
inline Quaternion<Scalar>
operator*(const Quaternion<Scalar>& q, const Vector3<Scalar>& w)
{
return Quaternion<Scalar>( q[3] * w[0] + q[1] * w[2] - q[2] * w[1],
q[3] * w[1] + q[2] * w[0] - q[0] * w[2],
q[3] * w[2] + q[0] * w[1] - q[1] * w[0],
-q[0] * w[0] - q[1] * w[1] - q[2] * w[2]);
}
template <typename Scalar>
inline Quaternion<Scalar>
operator*(const Vector3<Scalar>& w, const Quaternion<Scalar>& q)
{
return Quaternion<Scalar>( w[0] * q[3] + w[1] * q[2] - w[2] * q[1],
w[1] * q[3] + w[2] * q[0] - w[0] * q[2],
w[2] * q[3] + w[0] * q[1] - w[1] * q[0],
-w[0] * q[0] - w[1] * q[1] - w[2] * q[2]);
}
template <typename Scalar>
inline Scalar
dot(const Quaternion<Scalar>& q1, const Quaternion<Scalar>& q2)
{
return q1.dot(q2);
}
template <typename Scalar>
inline Scalar
length2(const Quaternion<Scalar>& q)
{
return q.length2();
}
template <typename Scalar>
inline Scalar
length(const Quaternion<Scalar>& q)
{
return q.length();
}
template <typename Scalar>
inline Scalar
angle(const Quaternion<Scalar>& q1, const Quaternion<Scalar>& q2)
{
return q1.angle(q2);
}
template <typename Scalar>
inline Quaternion<Scalar>
conjugate(const Quaternion<Scalar>& q)
{
return q.conjugate();
}
template <typename Scalar>
inline Quaternion<Scalar>
inverse(const Quaternion<Scalar>& q)
{
return q.inverse();
}
template <typename Scalar>
inline Quaternion<Scalar>
slerp(const Quaternion<Scalar>& q1, const Quaternion<Scalar>& q2, const Scalar& t)
{
return q1.slerp(q2, t);
}
}
#endif
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