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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	identity
     (1,0,0,0).    M_QuaternionAddIdentity()   returns	 the  additive	identity
     (0,0,0,0).

     The M_ReadQuaternion() function reads a quaternion from an AG_DataSource(3)
     and returns it.  M_WriteQuaternion() writes a quaternion 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-angle
     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  de-
     scribing 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() return
     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  spheri-
     cal  linear  interpolation  (SLERP) between q1 and q2, by factor c, and re-
     turns the result.

SEE ALSO
     AG_DataSource(3), AG_Intro(3), M_Complex(3), M_Matrix(3), M_Real(3), M_Vec-
     tor(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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