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M_QUATERNION(3)		    Library Functions Manual	       M_QUATERNION(3)

NAME
       M_Quaternion -- Agar-Math quaternion

SYNOPSIS
       #include	<agar/core.h>
       #include	<agar/gui.h>
       #include	<agar/math/m.h>

DESCRIPTION
       The  M_Quaternion  structure describes a	quaternion.  Quaternions are a
       non-commutative	extension  of  complex	numbers	 (see	M_Complex(3)).
       Quaternions  provide a convenient way of	representing and concatenating
       rotations.  The structure is defined as:

       typedef struct m_quaternion {
	       M_Real w, x, y, z;
       } M_Quaternion;

INITIALIZATION
       M_Quaternion M_QuaternionMultIdentity(void)

       M_Quaternion M_QuaternionAddIdentity(void)

       M_Quaternion M_ReadQuaternion(AG_DataSource *ds)

       void M_WriteQuaternion(AG_DataSource *ds, M_Quaternion q)

       The M_QuaternionMultIdentity() routine returns the multiplicative iden-
       tity (1,0,0,0).	M_QuaternionAddIdentity() returns the  additive	 iden-
       tity (0,0,0,0).

       The   M_ReadQuaternion()	  function   reads   a	 quaternion   from  an
       AG_DataSource(3)	and returns it.	 M_WriteQuaternion() writes a  quater-
       nion to a data source.

CONVERSION ROUTINES
       void  M_QuaternionpToAxisAngle(const  M_Quaternion *q, M_Vector3	*axis,
       M_Real *theta)

       void M_QuaternionpToAxisAngle3(const M_Quaternion  *q,  M_Real  *theta,
       M_Real *x, M_Real *y, M_Real *z)

       M_Quaternion M_QuaternionFromAxisAngle(M_Vector3	axis, M_Real theta)

       M_Quaternion  M_QuaternionFromAxisAngle3(M_Real theta, M_Real x,	M_Real
       y, M_Real z)

       void M_QuaternionpFromAxisAngle(M_Quaternion *q,	M_Vector3 axis,	M_Real
       theta)

       void M_QuaternionpFromAxisAngle3(M_Quaternion *q, M_Real	theta,	M_Real
       x, M_Real y, M_Real z)

       void  M_QuaternionFromEulv(M_Quaternion	*q, M_Real a, M_Real b,	M_Real
       c)

       M_Quaternion M_QuaternionFromEul(M_Real a, M_Real b, M_Real c)

       void M_QuaternionToMatrix44(M_Matrix44 *A, const	M_Quaternion *q)

       The M_QuaternionpToAxisAngle() function obtains a rotation in  axis-an-
       gle  format from	a quaternion q.	 The axis is returned into v and angle
       into theta.  The	M_QuaternionpToAxisAngle3() variant returns  the  axis
       into x, y and z.

       M_QuaternionFromAxisAngle()  returns a quaternion describing a rotation
       of    theta     radians	   about     the     axis     vector.	   The
       M_QuaternionFromAxisAngle3() form accepts individual x, y, z arguments.

       The   M_QuaternionpFromAxisAngle()   and	 M_QuaternionpFromAxisAngle3()
       variants	write the resulting quaternion into q as opposed to  returning
       it.

       M_QuaternionFromEulv()  and  M_QuaternionFromEul()  return a quaternion
       describing a rotation given the set of Euler angles.

       M_QuaternionToMatrix44()	converts the rotation described	by  quaternion
       q into a	4x4 matrix A.

ARITHMETIC OPERATIONS
       void M_Quaternion M_QuaternionConj(M_Quaternion q)

       M_Quaternion M_QuaternionConjp(const M_Quaternion *q)

       void M_QuaternionConjv(M_Quaternion *q)

       M_Quaternion M_QuaternionScale(M_Quaternion q, M_Real c)

       M_Quaternion M_QuaternionScalep(const M_Quaternion *q, M_Real c)

       void M_QuaternionScalev(M_Quaternion *q,	M_Real c)

       M_Quaternion    M_QuaternionConcat(const	   M_Quaternion	  *q1,	 const
       M_Quaternion *q2)

       M_Quaternion M_QuaternionMult(M_Quaternion q1, M_Quaternion q2)

       M_Quaternion   M_QuaternionMultp(const	 M_Quaternion	 *q1,	 const
       M_Quaternion *q2)

       void  M_QuaternionMultv(M_Quaternion  *q, const M_Quaternion *q1, const
       M_Quaternion *q2)

       M_Quaternion M_QuaternionNormp(const M_Quaternion *q)

       void M_QuaternionNormv(M_Quaternion *q)

       M_Quaternion M_QuaternionInverse(M_Quaternion q)

       M_Quaternion M_QuaternionInversep(const M_Quaternion *q)

       void M_QuaternionInversev(M_Quaternion *q)

       M_Quaternion M_QuaternionSLERP(M_Quaternion q1, M_Quaternion q2,	M_Real
       c)

       M_Quaternion   M_QuaternionSLERPp(const	 M_Quaternion	 *q1,	 const
       M_Quaternion *q2, M_Real	c)

       M_QuaternionConj(),  M_QuaternionConjp()	and M_QuaternionConjv()	return
       the conjugate of	q.

       M_QuaternionScale(), M_QuaternionScalep() and M_QuaternionScalev()  re-
       turn the	quaternion q scaled by factor c.

       M_QuaternionConcat()  concatenates the rotations	described by q1	and q2
       and returns the resulting quaternion.

       M_QuaternionMult(), M_QuaternionMultp() and M_QuaternionMultv() compute
       the product of q1 and q2.

       M_QuaternionNormp() and M_QuaternionNormv() return the normalized  form
       of q (equivalent	to normalizing q as a vector).

       M_QuaternionInverse(),		 M_QuaternionInversep()		   and
       M_QuaternionInversev() return the inverse (i.e.,	the normalized form of
       the conjugate) of q.

       The  functions  M_QuaternionSLERP()  and	 M_QuaternionSLERPp()  perform
       spherical  linear interpolation (SLERP) between q1 and q2, by factor c,
       and returns the result.

SEE ALSO
       AG_DataSource(3), AG_Intro(3),  M_Complex(3),  M_Matrix(3),  M_Real(3),
       M_Vector(3)

HISTORY
       The M_Quaternion	structure first	appeared in Agar 1.3.4.

Agar 1.7		       December	21, 2022	       M_QUATERNION(3)

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