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-/****************************************************************************
-**
-** Copyright (C) 2008-2012 NVIDIA Corporation.
-** Copyright (C) 2017 The Qt Company Ltd.
-** Contact: https://www.qt.io/licensing/
-**
-** This file is part of Qt 3D Studio.
-**
-** $QT_BEGIN_LICENSE:GPL$
-** Commercial License Usage
-** Licensees holding valid commercial Qt licenses may use this file in
-** accordance with the commercial license agreement provided with the
-** Software or, alternatively, in accordance with the terms contained in
-** a written agreement between you and The Qt Company. For licensing terms
-** and conditions see https://www.qt.io/terms-conditions. For further
-** information use the contact form at https://www.qt.io/contact-us.
-**
-** GNU General Public License Usage
-** Alternatively, this file may be used under the terms of the GNU
-** General Public License version 3 or (at your option) any later version
-** approved by the KDE Free Qt Foundation. The licenses are as published by
-** the Free Software Foundation and appearing in the file LICENSE.GPL3
-** included in the packaging of this file. Please review the following
-** information to ensure the GNU General Public License requirements will
-** be met: https://www.gnu.org/licenses/gpl-3.0.html.
-**
-** $QT_END_LICENSE$
-**
-****************************************************************************/
-
-#ifndef QT3DS_FOUNDATION_QT3DS_QUAT_H
-#define QT3DS_FOUNDATION_QT3DS_QUAT_H
-
-/** \addtogroup foundation
-@{
-*/
-
-#include "foundation/Qt3DSVec3.h"
-
-#ifndef QT3DS_DOXYGEN
-namespace qt3ds {
-#endif
-
-/**
-\brief This is a quaternion class. For more information on quaternion mathematics
-consult a mathematics source on complex numbers.
-
-*/
-
-class QT3DSQuat
-{
-public:
- /**
- \brief Default constructor, does not do any initialization.
- */
- QT3DS_CUDA_CALLABLE QT3DS_FORCE_INLINE QT3DSQuat() {}
-
- /**
- \brief Constructor. Take note of the order of the elements!
- */
- QT3DS_CUDA_CALLABLE QT3DS_FORCE_INLINE QT3DSQuat(NVReal nx, NVReal ny, NVReal nz, NVReal nw)
- : x(nx)
- , y(ny)
- , z(nz)
- , w(nw)
- {
- }
-
- /**
- \brief Creates from angle-axis representation.
-
- Axis must be normalized!
-
- Angle is in radians!
-
- <b>Unit:</b> Radians
- */
- QT3DS_CUDA_CALLABLE QT3DS_INLINE QT3DSQuat(NVReal angleRadians, const QT3DSVec3 &unitAxis)
- {
- QT3DS_ASSERT(NVAbs(1.0f - unitAxis.magnitude()) < 1e-3f);
- const NVReal a = angleRadians * 0.5f;
- const NVReal s = NVSin(a);
- w = NVCos(a);
- x = unitAxis.x * s;
- y = unitAxis.y * s;
- z = unitAxis.z * s;
- }
-
- /**
- \brief Copy ctor.
- */
- QT3DS_CUDA_CALLABLE QT3DS_FORCE_INLINE QT3DSQuat(const QT3DSQuat &v)
- : x(v.x)
- , y(v.y)
- , z(v.z)
- , w(v.w)
- {
- }
-
- /**
- \brief Creates from orientation matrix.
-
- \param[in] m Rotation matrix to extract quaternion from.
- */
- QT3DS_CUDA_CALLABLE QT3DS_INLINE explicit QT3DSQuat(const QT3DSMat33 &m); /* defined in Qt3DSMat33.h */
-
- /**
- \brief returns true if all elements are finite (not NAN or INF, etc.)
- */
- QT3DS_CUDA_CALLABLE bool isFinite() const
- {
- return NVIsFinite(x) && NVIsFinite(y) && NVIsFinite(z) && NVIsFinite(w);
- }
-
- /**
- \brief returns true if finite and magnitude is close to unit
- */
-
- QT3DS_CUDA_CALLABLE bool isUnit() const
- {
- const NVReal unitTolerance = NVReal(1e-4);
- return isFinite() && NVAbs(magnitude() - 1) < unitTolerance;
- }
-
- /**
- \brief returns true if finite and magnitude is reasonably close to unit to allow for some
- accumulation of error vs isValid
- */
-
- QT3DS_CUDA_CALLABLE bool isSane() const
- {
- const NVReal unitTolerance = NVReal(1e-2);
- return isFinite() && NVAbs(magnitude() - 1) < unitTolerance;
- }
-
- /**
- \brief converts this quaternion to angle-axis representation
- */
-
- QT3DS_CUDA_CALLABLE QT3DS_INLINE void toRadiansAndUnitAxis(NVReal &angle, QT3DSVec3 &axis) const
- {
- const NVReal quatEpsilon = (NVReal(1.0e-8f));
- const NVReal s2 = x * x + y * y + z * z;
- if (s2 < quatEpsilon * quatEpsilon) // can't extract a sensible axis
- {
- angle = 0;
- axis = QT3DSVec3(1, 0, 0);
- } else {
- const NVReal s = NVRecipSqrt(s2);
- axis = QT3DSVec3(x, y, z) * s;
- angle = w < quatEpsilon ? NVPi : NVAtan2(s2 * s, w) * 2;
- }
- }
-
- /**
- \brief Gets the angle between this quat and the identity quaternion.
-
- <b>Unit:</b> Radians
- */
- QT3DS_CUDA_CALLABLE QT3DS_INLINE NVReal getAngle() const { return NVAcos(w) * NVReal(2); }
-
- /**
- \brief Gets the angle between this quat and the argument
-
- <b>Unit:</b> Radians
- */
- QT3DS_CUDA_CALLABLE QT3DS_INLINE NVReal getAngle(const QT3DSQuat &q) const
- {
- return NVAcos(dot(q)) * NVReal(2);
- }
-
- /**
- \brief This is the squared 4D vector length, should be 1 for unit quaternions.
- */
- QT3DS_CUDA_CALLABLE QT3DS_FORCE_INLINE NVReal magnitudeSquared() const
- {
- return x * x + y * y + z * z + w * w;
- }
-
- /**
- \brief returns the scalar product of this and other.
- */
- QT3DS_CUDA_CALLABLE QT3DS_FORCE_INLINE NVReal dot(const QT3DSQuat &v) const
- {
- return x * v.x + y * v.y + z * v.z + w * v.w;
- }
-
- QT3DS_CUDA_CALLABLE QT3DS_INLINE QT3DSQuat getNormalized() const
- {
- const NVReal s = 1.0f / magnitude();
- return QT3DSQuat(x * s, y * s, z * s, w * s);
- }
-
- QT3DS_CUDA_CALLABLE QT3DS_INLINE float magnitude() const { return NVSqrt(magnitudeSquared()); }
-
- // modifiers:
- /**
- \brief maps to the closest unit quaternion.
- */
- QT3DS_CUDA_CALLABLE QT3DS_INLINE NVReal normalize() // convert this QT3DSQuat to a unit quaternion
- {
- const NVReal mag = magnitude();
- if (mag) {
- const NVReal imag = NVReal(1) / mag;
-
- x *= imag;
- y *= imag;
- z *= imag;
- w *= imag;
- }
- return mag;
- }
-
- /*
- \brief returns the conjugate.
-
- \note for unit quaternions, this is the inverse.
- */
- QT3DS_CUDA_CALLABLE QT3DS_INLINE QT3DSQuat getConjugate() const { return QT3DSQuat(-x, -y, -z, w); }
-
- /*
- \brief returns imaginary part.
- */
- QT3DS_CUDA_CALLABLE QT3DS_INLINE QT3DSVec3 getImaginaryPart() const { return QT3DSVec3(x, y, z); }
-
- /** brief computes rotation of x-axis */
- QT3DS_CUDA_CALLABLE QT3DS_FORCE_INLINE QT3DSVec3 getBasisVector0() const
- {
- // return rotate(QT3DSVec3(1,0,0));
- const QT3DSF32 x2 = x * 2.0f;
- const QT3DSF32 w2 = w * 2.0f;
- return QT3DSVec3((w * w2) - 1.0f + x * x2, (z * w2) + y * x2, (-y * w2) + z * x2);
- }
-
- /** brief computes rotation of y-axis */
- QT3DS_CUDA_CALLABLE QT3DS_FORCE_INLINE QT3DSVec3 getBasisVector1() const
- {
- // return rotate(QT3DSVec3(0,1,0));
- const QT3DSF32 y2 = y * 2.0f;
- const QT3DSF32 w2 = w * 2.0f;
- return QT3DSVec3((-z * w2) + x * y2, (w * w2) - 1.0f + y * y2, (x * w2) + z * y2);
- }
-
- /** brief computes rotation of z-axis */
- QT3DS_CUDA_CALLABLE QT3DS_FORCE_INLINE QT3DSVec3 getBasisVector2() const
- {
- // return rotate(QT3DSVec3(0,0,1));
- const QT3DSF32 z2 = z * 2.0f;
- const QT3DSF32 w2 = w * 2.0f;
- return QT3DSVec3((y * w2) + x * z2, (-x * w2) + y * z2, (w * w2) - 1.0f + z * z2);
- }
-
- /**
- rotates passed vec by this (assumed unitary)
- */
- QT3DS_CUDA_CALLABLE QT3DS_FORCE_INLINE const QT3DSVec3 rotate(const QT3DSVec3 &v) const
- // QT3DS_CUDA_CALLABLE QT3DS_INLINE const QT3DSVec3 rotate(const QT3DSVec3& v) const
- {
- const QT3DSF32 vx = 2.0f * v.x;
- const QT3DSF32 vy = 2.0f * v.y;
- const QT3DSF32 vz = 2.0f * v.z;
- const QT3DSF32 w2 = w * w - 0.5f;
- const QT3DSF32 dot2 = (x * vx + y * vy + z * vz);
- return QT3DSVec3((vx * w2 + (y * vz - z * vy) * w + x * dot2),
- (vy * w2 + (z * vx - x * vz) * w + y * dot2),
- (vz * w2 + (x * vy - y * vx) * w + z * dot2));
- /*
- const QT3DSVec3 qv(x,y,z);
- return (v*(w*w-0.5f) + (qv.cross(v))*w + qv*(qv.dot(v)))*2;
- */
- }
-
- /**
- inverse rotates passed vec by this (assumed unitary)
- */
- QT3DS_CUDA_CALLABLE QT3DS_FORCE_INLINE const QT3DSVec3 rotateInv(const QT3DSVec3 &v) const
- // QT3DS_CUDA_CALLABLE QT3DS_INLINE const QT3DSVec3 rotateInv(const QT3DSVec3& v) const
- {
- const QT3DSF32 vx = 2.0f * v.x;
- const QT3DSF32 vy = 2.0f * v.y;
- const QT3DSF32 vz = 2.0f * v.z;
- const QT3DSF32 w2 = w * w - 0.5f;
- const QT3DSF32 dot2 = (x * vx + y * vy + z * vz);
- return QT3DSVec3((vx * w2 - (y * vz - z * vy) * w + x * dot2),
- (vy * w2 - (z * vx - x * vz) * w + y * dot2),
- (vz * w2 - (x * vy - y * vx) * w + z * dot2));
- // const QT3DSVec3 qv(x,y,z);
- // return (v*(w*w-0.5f) - (qv.cross(v))*w + qv*(qv.dot(v)))*2;
- }
-
- /**
- \brief Assignment operator
- */
- QT3DS_CUDA_CALLABLE QT3DS_FORCE_INLINE QT3DSQuat &operator=(const QT3DSQuat &p)
- {
- x = p.x;
- y = p.y;
- z = p.z;
- w = p.w;
- return *this;
- }
-
- QT3DS_CUDA_CALLABLE QT3DS_FORCE_INLINE QT3DSQuat &operator*=(const QT3DSQuat &q)
- {
- const NVReal tx = w * q.x + q.w * x + y * q.z - q.y * z;
- const NVReal ty = w * q.y + q.w * y + z * q.x - q.z * x;
- const NVReal tz = w * q.z + q.w * z + x * q.y - q.x * y;
-
- w = w * q.w - q.x * x - y * q.y - q.z * z;
- x = tx;
- y = ty;
- z = tz;
-
- return *this;
- }
-
- QT3DS_CUDA_CALLABLE QT3DS_FORCE_INLINE QT3DSQuat &operator+=(const QT3DSQuat &q)
- {
- x += q.x;
- y += q.y;
- z += q.z;
- w += q.w;
- return *this;
- }
-
- QT3DS_CUDA_CALLABLE QT3DS_FORCE_INLINE QT3DSQuat &operator-=(const QT3DSQuat &q)
- {
- x -= q.x;
- y -= q.y;
- z -= q.z;
- w -= q.w;
- return *this;
- }
-
- QT3DS_CUDA_CALLABLE QT3DS_FORCE_INLINE QT3DSQuat &operator*=(const NVReal s)
- {
- x *= s;
- y *= s;
- z *= s;
- w *= s;
- return *this;
- }
-
- /** quaternion multiplication */
- QT3DS_CUDA_CALLABLE QT3DS_INLINE QT3DSQuat operator*(const QT3DSQuat &q) const
- {
- return QT3DSQuat(w * q.x + q.w * x + y * q.z - q.y * z, w * q.y + q.w * y + z * q.x - q.z * x,
- w * q.z + q.w * z + x * q.y - q.x * y, w * q.w - x * q.x - y * q.y - z * q.z);
- }
-
- /** quaternion addition */
- QT3DS_CUDA_CALLABLE QT3DS_FORCE_INLINE QT3DSQuat operator+(const QT3DSQuat &q) const
- {
- return QT3DSQuat(x + q.x, y + q.y, z + q.z, w + q.w);
- }
-
- /** quaternion subtraction */
- QT3DS_CUDA_CALLABLE QT3DS_FORCE_INLINE QT3DSQuat operator-() const { return QT3DSQuat(-x, -y, -z, -w); }
-
- QT3DS_CUDA_CALLABLE QT3DS_FORCE_INLINE QT3DSQuat operator-(const QT3DSQuat &q) const
- {
- return QT3DSQuat(x - q.x, y - q.y, z - q.z, w - q.w);
- }
-
- QT3DS_CUDA_CALLABLE QT3DS_FORCE_INLINE QT3DSQuat operator*(NVReal r) const
- {
- return QT3DSQuat(x * r, y * r, z * r, w * r);
- }
-
- static QT3DS_CUDA_CALLABLE QT3DS_INLINE QT3DSQuat createIdentity() { return QT3DSQuat(0, 0, 0, 1); }
-
- /** the quaternion elements */
- NVReal x, y, z, w;
-};
-
-#ifndef QT3DS_DOXYGEN
-} // namespace qt3ds
-#endif
-
-/** @} */
-#endif // QT3DS_FOUNDATION_QT3DS_QUAT_H