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SYNOPSIS

#include <agar/math.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 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() 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 spherical linear interpolation (SLERP) between q1 and q2, by factor c, and returns the result.

HISTORY

The M_Quaternion structure first appeared in Agar 1.3.4.