Quaternions: mialm Reference Manual

Quaternions

Quaternions — Quaternions to describe rotations in 3D space

Functions

MiaQuaternion *	mia_quaternion_new ()
MiaQuaternion *	mia_quaternion_new_from_eulerrot ()
MiaQuaternion *	mia_quaternion_copy ()
MiaQuaternion *	mia_quaternion_dup ()
void	mia_quaternion_get_rotation ()
gboolean	mia_quaternion_equal ()
void	mia_quaternion_normalize ()
gfloat	mia_quaternion_norm ()
MiaQuaternion *	mia_quaternion_multby ()
void	mia_quaternion_xmlio_read ()
gboolean	mia_quaternion_xmlio_write ()
gboolean	mia_quaternion_test ()

Types and Values

struct	MiaQuaternion
typedef	RotMatrix

Description

MiaQuaternion and the related functions describe and handle rotations in 3D space that are specifically suited for visualization.

Functions

mia_quaternion_new ()

MiaQuaternion *
mia_quaternion_new (gfloat x,
                    gfloat y,
                    gfloat z,
                    gfloat w);

Create a quaternion q = w + x *i + y * j + z * k.

Parameters

x	x-component of rotation axis
y	y-component of rotation axis
z	z-component of rotation axis
w	scalar part of the quaternion

Returns

a newly created quaternion representing the rotation

mia_quaternion_new_from_eulerrot ()

MiaQuaternion *
mia_quaternion_new_from_eulerrot (const MiaVector3d *axis,
                                  gfloat angle);

Create a quaternion that represents a rotation around the given axis by the given angle. The returned quaternion must be destroyed by calling g_object_unref()

Parameters

axis	the rotation axis
angle	the rotation angle

Returns

a newly created quaternion

mia_quaternion_copy ()

MiaQuaternion *
mia_quaternion_copy (MiaQuaternion *dest,
                     const MiaQuaternion *src);

Copy one quaternion into another one. The destination quaternion must already be properly created.

Parameters

dest	destination quaternion to copy to
src	source quaternion to copy from

Returns

the destination quaternion

mia_quaternion_dup ()

MiaQuaternion *
mia_quaternion_dup (const MiaQuaternion *org);

Create a duplicate of a quaternion. It must be destroyed by calling calling g_object_unref()

Parameters

org

a quaterion

Returns

a newly created copy of the quaternion.

mia_quaternion_get_rotation ()

void
mia_quaternion_get_rotation (MiaQuaternion *self,
                             RotMatrix m);

Evaluate the 4x4 Matrix corresponding to the 3D rotation.

Parameters

self	the quaternion desctibing the rotation
m	The result will be stored in this matrix.

mia_quaternion_equal ()

gboolean
mia_quaternion_equal (const MiaQuaternion *a,
                      const MiaQuaternion *b);

Test if two quaternions are exactly equal.

Parameters

a	left hand value for comparison
b	right hand value for comparison

Returns

TRUE if equal, FALSE otherwise

mia_quaternion_normalize ()

void
mia_quaternion_normalize (MiaQuaternion *self);

Normalize a quaternion if it's norm is not zero.

Parameters

self

the quaternion to be normalized

mia_quaternion_norm ()

gfloat
mia_quaternion_norm (const MiaQuaternion *self);

Evaluate the quaternions norm.

Parameters

self

the quaternion

Returns

the Euclidian norm

mia_quaternion_multby ()

MiaQuaternion *
mia_quaternion_multby (MiaQuaternion *self,
                       MiaQuaternion *other);

Multiply the quaternion dest by a quaternion other as in dest *= other

Parameters

self	destination quaternion
other	other quaternion to multiply by

Returns

the quaternion self

mia_quaternion_xmlio_read ()

void
mia_quaternion_xmlio_read (ParserState *state,
                           const gchar *property);

Helper function to read a quaternion from a XML file

Parameters

state	XML parser state holding the parent object and the values
property	property name the quaternion has in the parent class

mia_quaternion_xmlio_write ()

gboolean
mia_quaternion_xmlio_write (xmlNodePtr root,
                            xmlNsPtr ns,
                            const gchar *tag,
                            const MiaQuaternion *q);

Helper function to write a quaternion to a XML file

Parameters

root	xml node this quaternion will be attached to
ns	name space
tag	the xml tag to store this quaternion under
q	the quaternion

Returns

true if the node creation was successfu, otherwise false.

mia_quaternion_test ()

gboolean
mia_quaternion_test (void);

Test the quaternion implementation

Returns

TRUE if all tests pass, FALSE otherwise.

Types and Values

struct MiaQuaternion

struct MiaQuaternion {
	MiaVector3d parent;
	/* add your class instance elements here */
	gfloat r;
};

This defines a Quaternion and is used to describe a rotation in 3D space.

RotMatrix

typedef float RotMatrix[4][4];

A 4x4 matrix used for rotations.