=encoding UTF-8


=head1 NAME

BH_Quat - Quaternion


=head1 SYNTAX

 #include <BH/Math/Quat.h>

 cc prog.c -o prog -lbh


=head1 DESCRIPTION

This module provides a set of functions for working with quaternions.
Quaternions are used to represent rotations in three-dimensional space and have
advantages over other methods, such as rotation matrices or Euler angles, in
terms of stability against error accumulation during multiple rotation
operations.


=head1 API CALLS


=head2 BH_Quat4fAdd

 #define BH_Quat4fAdd(a, b, out) \
     BH_Vec4fAdd(a, b, out)

Calculates the sum of two quaternions I<a> and I<b>.

The parameter I<out> describes the resulting quaternion.


=head2 BH_Quat4fSub

 #define BH_Quat4fSub(a, b, out) \
     BH_Vec4fSub(a, b, out)

Calculates the difference between two quaternions I<a> and I<b>.

The parameter I<out> describes the resulting quaternion.


=head2 BH_Quat4fScale

 #define BH_Quat4fScale(a, b, out) \
     BH_Vec4fScale(a, b, out)

Calculates the result of multiplying quaternion I<a> by value I<b>.

The parameter I<out> describes the resulting quaternion.


=head2 BH_Quat4fNegate

 #define BH_Quat4fNegate(in, out) \
     BH_Vec4fNegate(in, out)

Calculates the opposite quaternion from quaternion I<in>.

The parameter I<out> describes the resulting quaternion.


=head2 BH_Quat4fDot

 #define BH_Quat4fDot(a, b) \
     BH_Vec4fDot(a, b)

Calculates the dot product of quaternions I<a> and I<b>.


=head2 BH_Quat4fLength

 #define BH_Quat4fLength(in) \
     BH_Vec4fLength(in)

float BH_Vec4fLength(const float in[4]);

Calculates the length of quaternion I<in>.


=head2 BH_Quat4fNormal

 #define BH_Quat4fNormal(in, out) \
     BH_Vec4fNormal(in, out)

Calculates the normalized form of quaternion I<in>.

The parameter I<out> describes the resulting quaternion.


=head2 BH_Quat4fLerp

 #define BH_Quat4fLerp(a, b, t, out) \
     BH_Vec4fLerp(a, b, t, out)

Performs linear interpolation between two quaternions I<a> and I<b> with
parameter I<t>.

The parameter I<out> describes the resulting quaternion.


=head2 BH_Quat4fIdentity

 void BH_Quat4fIdentity(float out[4]);

Writes the identity quaternion to I<out>.


=head2 BH_Quat4fConjugate

 void BH_Quat4fConjugate(const float in[4],
                         float out[4]);

Calculates the conjugate quaternion from I<in>.

The parameter I<out> describes the resulting quaternion.


=head2 BH_Quat4fInverse

 void BH_Quat4fInverse(const float in[4],
                       float out[4]);

Calculates the inverse quaternion from I<in>.

The parameter I<out> describes the resulting quaternion.


=head2 BH_Quat4fMul

 void BH_Quat4fMul(const float a[4],
                   const float b[4],
                   float out[4]);

Calculates the result of multiplying two quaternions I<a> and I<b>.

The parameter I<out> describes the resulting quaternion.


=head2 BH_Quat4fSlerp

 void BH_Quat4fSlerp(const float a[4],
                     const float b[4],
                     float t,
                     float out[4]);

Performs spherical linear interpolation between two quaternions I<a> and I<b>
with parameter I<t>.

The parameter I<out> describes the resulting quaternion.


=head2 BH_Quat4fFromEuler

 void BH_Quat4fFromEuler(float roll,
                         float pitch,
                         float yaw,
                         float out[4]);

Calculates the quaternion from the angles of the associated coordinate system
I<roll>, I<pitch>, and I<yaw>.

The order of rotation application is ZYX (yaw, pitch, roll).

The parameter I<out> describes the resulting quaternion.


=head2 BH_Quat4fFromAxis

 void BH_Quat4fFromAxis(const float axis[3],
                        float angle,
                        float out[4]);

Calculates the quaternion from rotation around the I<axis> with the given
I<angle>.

The parameter I<out> describes the resulting quaternion.


=head2 BH_Quat4fToEuler

 void BH_Quat4fToEuler(const float in[4],
                       float *roll,
                       float *pitch,
                       float *yaw);

Calculates the angles of the associated coordinate system I<roll>, I<pitch>,
and I<yaw> from quaternion I<in>.

The order of rotation application is ZYX (yaw, pitch, roll).


=head2 BH_Quat4fToAxis

 void BH_Quat4fToAxis(const float in[4],
                      float axis[3],
                      float *angle);

Calculates the rotation I<axis> and I<angle> from quaternion I<in>.


=head2 BH_Quat4fToMat4f

 void BH_Quat4fToMat4f(const float in[4],
                       float out[16]);

Calculates the rotation matrix from quaternion I<in>.

The parameter I<out> describes the resulting matrix.


=head1 SEE ALSO

L<BH>