Quaternion Rotations

Functions
template<class T>
constexpr vec< T, 3 >	qxdir (const vec< T, 4 > &q)
	efficient shorthand for qrot(q, {1,0,0})
template<class T>
constexpr vec< T, 3 >	qydir (const vec< T, 4 > &q)
	efficient shorthand for qrot(q, {0,1,0})
template<class T>
constexpr vec< T, 3 >	qzdir (const vec< T, 4 > &q)
	efficient shorthand for qrot(q, {0,0,1})
template<class T>
constexpr mat< T, 3, 3 >	qmat (const vec< T, 4 > &q)
	Create an equivalent mat3 rotation matrix from the input quaternion.
template<class T>
constexpr vec< T, 3 >	qrot (const vec< T, 4 > &q, const vec< T, 3 > &v)
	Rotate a vector by a quaternion.
template<class T>
T	qangle (const vec< T, 4 > &q)
	Return the angle in radians of the axis-angle representation of the input normalized quaternion.
template<class T>
vec< T, 3 >	qaxis (const vec< T, 4 > &q)
	Return the normalized axis of the axis-angle representation of the input normalized quaternion.
template<class T>
vec< T, 4 >	qnlerp (const vec< T, 4 > &a, const vec< T, 4 > &b, T t)
	Linear interpolation that takes the shortest path - this is not geometrically sensible, consider qslerp instead.
template<class T>
vec< T, 4 >	qslerp (const vec< T, 4 > &a, const vec< T, 4 > &b, T t)
	Spherical linear interpolation that takes the shortest path.
template<class T>
vec< T, 4 > constexpr	rotation_quat (const vec< T, 3 > &axis, T angle)
	Returns a normalized quaternion representing a rotation by angle in radians about the provided axis.
template<class T>
vec< T, 4 >	rotation_quat (const vec< T, 3 > &orig, const vec< T, 3 > &dest)
	Returns a normalized quaternion representing the shortest rotation from orig vector to dest vector.
template<class T>
vec< T, 4 >	rotation_quat (const mat< T, 3, 3 > &m)
	Returns a normalized quaternion representing the input rotation matrix, which should be orthonormal.

Detailed Description

Support for 3D spatial rotations using normalized quaternions.