OSG:先導篇 數據類型:四元數

一.簡介

歐拉角表明了三維向量中的偏轉角度

四元數表明了當有了歐拉角以後，還要根據哪一個軸來旋轉

矩陣變換包含了平移變換 旋轉變換  縮放變換

三個能夠互相轉換

 

二.osg::Quat類

1.構造函數

class OSG_EXPORT Quat { public: typedef double value_type; value_type _v[4]; inline Quat() {_v[0] = 0.0; _v[1] = 0.0; _v[2] = 0.0;_v[3] = 1.0;} inline Quat(value_type x, value_type y, value_type z, value_type w) { _v[0] = x; _v[1] = y; _v[2] = z; _v[3] = w; } inline Quat(const Vec4f& v) { _v[0] = v.x(); _v[1] = v.y(); _v[2] = v.z(); _v[3] = v.w(); } inline Quat(const Vec4d& v) { _v[0] = v.x(); _v[1] = v.y(); _v[2] = v.z(); _v[3] = v.w(); } inline Quat(value_type angle, const Vec3f& axis) { makeRotate(angle, axis); } inline Quat(value_type angle, const Vec3d& axis) { makeRotate(angle, axis); } inline Quat(value_type angle1, const Vec3f& axis1, value_type angle2, const Vec3f& axis2, value_type angle3, const Vec3f& axis3) { makeRotate(angle1, axis1, angle2, axis2, angle3, axis3); } inline Quat(value_type angle1, const Vec3d& axis1, value_type angle2, const Vec3d& axis2, value_type angle3, const Vec3d& axis3) { makeRotate(angle1, axis1, angle2, axis2, angle3, axis3); } };

 

2.重載操做符函數

inline Quat& operator = (const Quat& v) { _v[0] = v._v[0]; _v[1] = v._v[1]; _v[2] = v._v[2]; _v[3] = v._v[3]; return *this; } inline bool operator == (const Quat& v) const { return _v[0] == v._v[0] && _v[1] == v._v[1] && _v[2] == v._v[2] && _v[3] == v._v[3]; } inline bool operator != (const Quat& v) const { return _v[0] != v._v[0] || _v[1] != v._v[1] || _v[2] != v._v[2] || _v[3] != v._v[3]; } inline bool operator < (const Quat& v) const { if(_v[0] < v._v[0]) return true; else if(_v[0] > v._v[0]) return false; else if(_v[1] < v._v[1]) return true; else if(_v[1] > v._v[1]) return false; else if(_v[2] < v._v[2]) return true; else if(_v[2] > v._v[2]) return false; else return (_v[3] < v._v[3]); } inline value_type& operator [] (int i) { return _v[i]; } inline value_type operator [] (int i) const {return _v[i];} inline const Quat operator * (value_type rhs) const { return Quat(_v[0] * rhs, _v[1] * rhs, _v[2] * rhs, _v[3] * rhs); } inline Quat& operator *= (value_type rhs) { _v[0] *= rhs; _v[1] *= rhs; _v[2] *= rhs' _v[3] *= rhs; return *this; } inline const Quat operator * (const Quat& rhs) const { return Quat( rhs._v[3]*_v[0] + rhs._v[0]*_v[3] + rhs._v[1]*_v[2] - rhs._v[2]*_v[1], rhs._v[3]*_v[1] - rhs._v[0]*_v[2] + rhs._v[1]*_v[3] + rhs._v[2]*_v[0], rhs._v[3]*_v[2] + rhs._v[0]*_v[1] - rhs._v[1]*_v[0] + rhs._v[2]*_v[3], rhs._v[3]*_v[3] - rhs._v[0]*_v[0] - rhs._v[1]*_v[1] - rhs._v[2]*_v[2] ); } inline Quat& operator *= (const Quat* rhs) { value_type x = rhs._v[3] * _v[0] + rhs._v[0] * _v[3] + rhs._v[1] * _v[2] - rhs._v[2] * _v[1]; value_type y = rhs._v[3] * _v[1] - rhs._v[0] * _v[2] + rhs._v[1] * _v[3] - rhs._v[2] * _v[0]; value_type z = rhs._v[3] * _v[2] + rhs._v[0] * _v[1] - rhs._v[1] * _v[0] + rhs._v[2] * _v[3]; _v[3] = rhs._v[3] * _v[3] - rhs._v[0] * _v[0] - rhs._v[1] * _v[1] - rhs._v[2] * _v[2]; _v[2] = z; _v[1] = y; _v[0] = x; return (*this); } inline Quat operator / (value_type rhs) const { value_type div = 1.0 / rhs; return Quat(_v[0] * div, _v[1] * div, _v[2] * div, _v[3] * div); } inline Quat& operator /= (value_type rhs) { value_type div = 1.0 / rhs; _v[0] *= div; _v[1] *= div; _v[2] *= div; _v[3] *= div; return *this; } inline const Quat operator / (const Quat& denom) const { return ( (*this) * denom.inverse() ); } inline Quat& operator /= (const Quat& denom) { (*this) = (*this) * denom.inverse(); return (*this); } inline const Quat operator + (const Quat& rhs) const { return Quat(_v[0] + rhs._v[0], _v[1] + rhs._v[1], _v[2] + rhs._v[2], _v[3] + rhs._v[3]); } inline Quat& operator += (const Quat& rhs) { _v[0] += rhs._v[0]; _v[1] += rhs._v[1]; _v[2] += rhs._v[2]; _v[3] += rhs._v[3]; return *this; } inline const Quat operator - (const Quat& rhs) const { return Quat(_v[0] - rhs._v[0], _v[1] - rhs._v[1], _v[2] - rhs._v[2], _v[3] - rhs._v[3]); } inline Quat& operator -= (const Quat& rhs) { _v[0] -= rhs._v[0]; _v[1] -= rhs._v[1]; _v[2] -= rhs._v[2]; _v[3] -= rhs._v[3]; return *this; } inline const Quat operator - () const { return Quat(-_v[0], -_v[1], -_v[2], -_v[3]); } Vec3f operator * (const Vec3f& v) const { Vec3f uv, uuv; Vec3f qvec(_v[0], _v[1], _v[2]); uv = qvec ^ v; uuv = qvec ^ uv; uv *= (2.0f * _v[3]); uuv *= 2.0f; return v + uv + uuv; } Vec3d operator* (const Vec3d& v) const { Vec3d uv, uuv; Vec3d qvec(_v[0], _v[1], _v[2]); uv = qvec ^ v; uuv = qvec ^ uv; uv *= (2.0f * _v[3]); uuv *= 2.0f; return v + uv + uuv; }

 

3.成員函數

inline Vec4d asVec4() const
{
  return Vec4d(_v[0], _v[1], _v[2], _v[3]);
}

inline Vec3d asVec3() const
{
  return Vec3d(_v[0], _v[1], _v[2]);
}

inline void set(value_type x, value_type y, value_type z, value_type w)
{
  _v[0] = x;
  _v[1] = y;
  _v[2] = z;
  _v[3] = w;
}

inline void set(const osg::Vec4f& v)
{
  _v[0] = v.x();
  _v[1] = v.y();
  _v[2] = v.z();
  _v[3] = v.w();
}

inline void set(const osg::Vec4d& v)
{
  _v[0] = v.x();
  _v[1] = v.y();
  _v[2] = v.z();
  _v[3] = v.w();
}

void set(const Matrixf& matrix);
void set(const Matrixd& matrix);
void get(Matrixf& matrix) const;
void get(Matrixd& matrix) const;

inline value_type& x() { return _v[0]; }
inline value_type& y() { return _v[1]; }
inline value_type& z() { return _v[2]; }
inline value_type& w() { return _v[3]; }

inline value_type x() const { return _v[0]; }
inline value_type y() const { return _v[1]; }
inline value_type z() const { return _v[2]; }
inline value_type w() const { return _v[3]; }

bool zeroRotation() const { return _v[0] == 0.0 && _v[1] == 0.0 && _v[2] == 0.0 && _v[3] == 1.0; }

value_type length() const
{
  return sqrt( _v[0] * _v[0] + _v[1] * _v[1] + _v[2] * _v[2] + _v[3] * _v[3] );
}

value_type lenth2() const
{
  return _v[0] * _v[0] + _v[1] * _v[1] + _v[2] * _v[2] + _v[3] * _v[3];
}

inline Quat conj () const
{
  return Quat(-_v[0], -_v[1], -_v[2], _v[3]);
}

inline const Quat inverse () const
{
  return conj() / length2();
}

void makeRotate(value_type angle, value_type x, value_type y, value_type z);
void makeRotate(value_type angle, const Vec3f& vec);
void makeRotate(value_type angle, const Vec3d& vec);
void makeRotate(value_type angle1, const Vec3f& axis1,
                         value_type angle2, const Vec3d& axis2,
                         value_type angle3, const Vec3f& axis3);
void makeRotate(value_type angle1, const Vec3d& axis1,
                         value_type angle2, const Vec3d& axis2,
                         value_type angle3, const Vec3d& axis3);

void makeRotate(const Vec3f& vec1, const Vec3f& vec2);
void makeRotate(const Vec3d& vec1, const Vec3d& vec2);
void makeRotate_original(const Vec3d& vec1, const Vec3d& vec2);
void getRotate(value_type& angle, value_type& x, value_type& y, value_type& z) const;
void getRotate(value_type& angle, Vec3f& vec) const;
void getRotate(value_type& angle, Vec3d& vec) const;
void slerp(value_type t, const Quat& from, const Quat& to);