impeller::Quaternion Struct Reference

#include <quaternion.h>

Public Member Functions
	Quaternion ()
	Quaternion (Scalar px, Scalar py, Scalar pz, Scalar pw)
	Quaternion (const Vector3 &axis, Scalar angle)
Scalar	Dot (const Quaternion &q) const
Scalar	Length () const
Quaternion	Normalize () const
Quaternion	Invert () const
Quaternion	Slerp (const Quaternion &to, double time) const
Quaternion	operator* (const Quaternion &o) const
Quaternion	operator* (Scalar scale) const
Vector3	operator* (Vector3 vector) const
Quaternion	operator+ (const Quaternion &o) const
Quaternion	operator- (const Quaternion &o) const
bool	operator== (const Quaternion &o) const
bool	operator!= (const Quaternion &o) const

Public Attributes
union {
struct {
Scalar   x = 0.0
Scalar   y = 0.0
Scalar   z = 0.0
Scalar   w = 1.0
}
Scalar   e [4]
};

Detailed Description

Definition at line 14 of file quaternion.h.

Constructor & Destructor Documentation

Quaternion() [1/3]

impeller::Quaternion::Quaternion ( )

inline

Definition at line 25 of file quaternion.h.

{}

Quaternion() [2/3]

impeller::Quaternion::Quaternion ( Scalar  px, Scalar  py, Scalar  pz, Scalar  pw  )

inline

Definition at line 27 of file quaternion.h.

      : x(px), y(py), z(pz), w(pw) {}

Quaternion() [3/3]

impeller::Quaternion::Quaternion ( const Vector3 &  axis, Scalar  angle  )

inline

Definition at line 30 of file quaternion.h.

                                                {
    const auto sine = sin(angle * 0.5f);
    x = sine * axis.x;
    y = sine * axis.y;
    z = sine * axis.z;
    w = cos(angle * 0.5f);
  }

References w, x, impeller::Vector3::x, y, impeller::Vector3::y, z, and impeller::Vector3::z.

Member Function Documentation

Dot()

Scalar impeller::Quaternion::Dot ( const Quaternion &  q ) const

inline

Definition at line 38 of file quaternion.h.

                                        {
    return x * q.x + y * q.y + z * q.z + w * q.w;
  }

References w, x, y, and z.

Referenced by Slerp().

Invert()

Quaternion impeller::Quaternion::Invert ( ) const

inline

Definition at line 49 of file quaternion.h.

{ return {-x, -y, -z, w}; }

References w, x, y, and z.

Length()

Scalar impeller::Quaternion::Length ( ) const

inline

Definition at line 42 of file quaternion.h.

{ return sqrt(x * x + y * y + z * z + w * w); }

References w, x, y, and z.

Referenced by Normalize().

Normalize()

Quaternion impeller::Quaternion::Normalize ( ) const

inline

Definition at line 44 of file quaternion.h.

                               {
    auto m = 1.0f / Length();
    return {x * m, y * m, z * m, w * m};
  }

References Length(), w, x, y, and z.

Referenced by Slerp().

operator!=()

bool impeller::Quaternion::operator!= ( const Quaternion &  o ) const

inline

Definition at line 85 of file quaternion.h.

                                             {
    return x != o.x || y != o.y || z != o.z || w != o.w;
  }

References w, x, y, and z.

operator*() [1/3]

Quaternion impeller::Quaternion::operator* ( const Quaternion &  o ) const

inline

Definition at line 53 of file quaternion.h.

                                                  {
    return {
        w * o.x + x * o.w + y * o.z - z * o.y,
        w * o.y + y * o.w + z * o.x - x * o.z,
        w * o.z + z * o.w + x * o.y - y * o.x,
        w * o.w - x * o.x - y * o.y - z * o.z,
    };
  }

References w, x, y, and z.

operator*() [2/3]

Quaternion impeller::Quaternion::operator* ( Scalar  scale ) const

inline

Definition at line 62 of file quaternion.h.

                                           {
    return {scale * x, scale * y, scale * z, scale * w};
  }

References w, x, y, and z.

operator*() [3/3]

Vector3 impeller::Quaternion::operator* ( Vector3  vector ) const

inline

Definition at line 66 of file quaternion.h.

                                          {
    Vector3 v(x, y, z);
    return v * v.Dot(vector) * 2 +        //
           vector * (w * w - v.Dot(v)) +  //
           v.Cross(vector) * 2 * w;
  }

References impeller::Vector3::Cross(), impeller::Vector3::Dot(), w, x, y, and z.

operator+()

Quaternion impeller::Quaternion::operator+ ( const Quaternion &  o ) const

inline

Definition at line 73 of file quaternion.h.

                                                  {
    return {x + o.x, y + o.y, z + o.z, w + o.w};
  }

References w, x, y, and z.

operator-()

Quaternion impeller::Quaternion::operator- ( const Quaternion &  o ) const

inline

Definition at line 77 of file quaternion.h.

                                                  {
    return {x - o.x, y - o.y, z - o.z, w - o.w};
  }

References w, x, y, and z.

operator==()

bool impeller::Quaternion::operator== ( const Quaternion &  o ) const

inline

Definition at line 81 of file quaternion.h.

                                             {
    return x == o.x && y == o.y && z == o.z && w == o.w;
  }

References w, x, y, and z.

Slerp()

Quaternion impeller::Quaternion::Slerp	(	const Quaternion &	to,
		double	time
	)		const

Definition at line 10 of file quaternion.cc.

                                                                    {
  double cosine = Dot(to);
  if (fabs(cosine) < 1.0 - 1e-3 /* epsilon */) {
    /*
     *  Spherical Interpolation.
     */
    auto sine = sqrt(1.0 - cosine * cosine);
    auto angle = atan2(sine, cosine);
    auto sineInverse = 1.0 / sine;
    auto c0 = sin((1.0 - time) * angle) * sineInverse;
    auto c1 = sin(time * angle) * sineInverse;
    return *this * c0 + to * c1;
  } else {
    /*
     *  Linear Interpolation.
     */
    return (*this * (1.0 - time) + to * time).Normalize();
  }
}

References Dot(), e, and Normalize().

Member Data Documentation

union { ... }

e

Scalar impeller::Quaternion::e[4]

Definition at line 22 of file quaternion.h.

Referenced by Slerp().

w

Scalar impeller::Quaternion::w = 1.0

Definition at line 20 of file quaternion.h.

Referenced by impeller::Matrix::Decompose(), Dot(), Invert(), Length(), impeller::Matrix::MakeRotation(), impeller::Matrix::Matrix(), Normalize(), operator!=(), operator*(), operator+(), operator-(), std::operator<<(), operator==(), Quaternion(), and QuaternionNear().

x

Scalar impeller::Quaternion::x = 0.0

Definition at line 17 of file quaternion.h.

Referenced by impeller::Matrix::Decompose(), Dot(), Invert(), Length(), impeller::Matrix::MakeRotation(), impeller::Matrix::Matrix(), Normalize(), operator!=(), operator*(), operator+(), operator-(), std::operator<<(), operator==(), Quaternion(), and QuaternionNear().

y

Scalar impeller::Quaternion::y = 0.0

Definition at line 18 of file quaternion.h.

Referenced by impeller::Matrix::Decompose(), Dot(), Invert(), Length(), impeller::Matrix::MakeRotation(), impeller::Matrix::Matrix(), Normalize(), operator!=(), operator*(), operator+(), operator-(), std::operator<<(), operator==(), Quaternion(), and QuaternionNear().

z

Scalar impeller::Quaternion::z = 0.0

Definition at line 19 of file quaternion.h.

Referenced by impeller::Matrix::Decompose(), Dot(), Invert(), Length(), impeller::Matrix::MakeRotation(), impeller::Matrix::Matrix(), Normalize(), operator!=(), operator*(), operator+(), operator-(), std::operator<<(), operator==(), Quaternion(), and QuaternionNear().

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The documentation for this struct was generated from the following files:

• impeller/geometry/quaternion.h
• impeller/geometry/quaternion.cc