#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 13 of file quaternion.h.

Constructor & Destructor Documentation

◆ Quaternion() [1/3]

impeller::Quaternion::Quaternion ( )

inline

Definition at line 24 of file quaternion.h.

24 {}

◆ Quaternion() [2/3]

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

inline

Definition at line 26 of file quaternion.h.

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

◆ Quaternion() [3/3]

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

inline

Definition at line 29 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 37 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 48 of file quaternion.h.

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

References w, x, y, and z.

Referenced by impeller::scene::RotationTimelineResolver::Apply().

◆ Length()

Scalar impeller::Quaternion::Length ( ) const

inline

Definition at line 41 of file quaternion.h.

41 { 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 43 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 84 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 52 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 61 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 65 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 72 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 76 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 80 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();
   }
 }