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Euler

Euler — Euler angles

Types and Values

Includes

#include <graphene.h>

Description

The graphene_euler_t structure defines a rotation along three axis using three angles. It also optionally can describe the order of the rotations.

Rotations described Euler angles are immediately understandable, compared to rotations expressed using quaternions, but they are susceptible of "Gimbal lock" — the loss of one degree of freedom caused by two axis on the same plane. You typically should use graphene_euler_t to expose rotation angles in your API, or to store them, but use graphene_quaternion_t to apply rotations to modelview matrices, or interpolate between initial and final rotation transformations.

See also: graphene_quaternion_t.

Functions

graphene_euler_alloc ()

graphene_euler_t *
graphene_euler_alloc (void);

Allocates a new graphene_euler_t.

The contents of the returned structure are undefined.

[constructor]

Returns

the newly allocated graphene_euler_t.

[transfer full]

Since: 1.2


graphene_euler_free ()

void
graphene_euler_free (graphene_euler_t *e);

Frees the resources allocated by graphene_euler_alloc().

Parameters

Since: 1.2


graphene_euler_init ()

graphene_euler_t *
graphene_euler_init (graphene_euler_t *e,
                     float x,
                     float y,
                     float z);

Initializes a graphene_euler_t using the given angles.

The order of the rotations is GRAPHENE_EULER_ORDER_DEFAULT.

Parameters

e

the graphene_euler_t to initialize

 

x

rotation angle on the X axis, in degrees

 

y

rotation angle on the Y axis, in degrees

 

z

rotation angle on the Z axis, in degrees

 

Returns

the initialized graphene_euler_t.

[transfer none]

Since: 1.2


graphene_euler_init_with_order ()

graphene_euler_t *
graphene_euler_init_with_order (graphene_euler_t *e,
                                float x,
                                float y,
                                float z,
                                graphene_euler_order_t order);

Initializes a graphene_euler_t with the given angles and order .

Parameters

e

the graphene_euler_t to initialize

 

x

rotation angle on the X axis, in degrees

 

y

rotation angle on the Y axis, in degrees

 

z

rotation angle on the Z axis, in degrees

 

order

the order used to apply the rotations

 

Returns

the initialized graphene_euler_t.

[transfer none]

Since: 1.2


graphene_euler_init_from_matrix ()

graphene_euler_t *
graphene_euler_init_from_matrix (graphene_euler_t *e,
                                 const graphene_matrix_t *m,
                                 graphene_euler_order_t order);

Initializes a graphene_euler_t using the given rotation matrix.

If the graphene_matrix_t m is NULL, the graphene_euler_t will be initialized with all angles set to 0.

Parameters

e

the graphene_euler_t to initialize

 

m

a rotation matrix.

[nullable]

order

the order used to apply the rotations

 

Returns

the initialized graphene_euler_t.

[transfer none]

Since: 1.2


graphene_euler_init_from_quaternion ()

graphene_euler_t *
graphene_euler_init_from_quaternion (graphene_euler_t *e,
                                     const graphene_quaternion_t *q,
                                     graphene_euler_order_t order);

Initializes a graphene_euler_t using the given normalized quaternion.

If the graphene_quaternion_t q is NULL, the graphene_euler_t will be initialized with all angles set to 0.

Parameters

e

a graphene_euler_t

 

q

a normalized graphene_quaternion_t.

[nullable]

order

the order used to apply the rotations

 

Returns

the initialized graphene_euler_t.

[transfer none]

Since: 1.2


graphene_euler_init_from_vec3 ()

graphene_euler_t *
graphene_euler_init_from_vec3 (graphene_euler_t *e,
                               const graphene_vec3_t *v,
                               graphene_euler_order_t order);

Initializes a graphene_euler_t using the angles contained in a graphene_vec3_t.

If the graphene_vec3_t v is NULL, the graphene_euler_t will be initialized with all angles set to 0.

Parameters

e

the graphene_euler_t to initialize

 

v

a graphene_vec3_t containing the rotation angles in degrees.

[nullable]

order

the order used to apply the rotations

 

Returns

the initialized graphene_euler_t.

[transfer none]

Since: 1.2


graphene_euler_init_from_euler ()

graphene_euler_t *
graphene_euler_init_from_euler (graphene_euler_t *e,
                                const graphene_euler_t *src);

Initializes a graphene_euler_t using the angles and order of another graphene_euler_t.

If the graphene_euler_t src is NULL, this function is equivalent to calling graphene_euler_init() with all angles set to 0.

Parameters

e

the graphene_euler_t to initialize

 

src

a graphene_euler_t.

[nullable]

Returns

the initialized graphene_euler_t.

[transfer none]

Since: 1.2


graphene_euler_equal ()

bool
graphene_euler_equal (const graphene_euler_t *a,
                      const graphene_euler_t *b);

Checks if two graphene_euler_t are equal.

Parameters

Returns

true if the two graphene_euler_t are equal

Since: 1.2


graphene_euler_get_x ()

float
graphene_euler_get_x (const graphene_euler_t *e);

Retrieves the rotation angle on the X axis, in degrees.

Parameters

Returns

the rotation angle

Since: 1.2


graphene_euler_get_y ()

float
graphene_euler_get_y (const graphene_euler_t *e);

Retrieves the rotation angle on the Y axis, in degrees.

Parameters

Returns

the rotation angle

Since: 1.2


graphene_euler_get_z ()

float
graphene_euler_get_z (const graphene_euler_t *e);

Retrieves the rotation angle on the Z axis, in degrees.

Parameters

Returns

the rotation angle

Since: 1.2


graphene_euler_get_order ()

graphene_euler_order_t
graphene_euler_get_order (const graphene_euler_t *e);

Retrieves the order used to apply the rotations described in the graphene_euler_t structure, when converting to and from other structures, like graphene_quaternion_t and graphene_matrix_t.

This function does not return the GRAPHENE_EULER_ORDER_DEFAULT enumeration value; it will return the effective order of rotation instead.

Parameters

Returns

the order used to apply the rotations

Since: 1.2


graphene_euler_to_vec3 ()

void
graphene_euler_to_vec3 (const graphene_euler_t *e,
                        graphene_vec3_t *res);

Retrieves the angles of a graphene_euler_t and initializes a graphene_vec3_t with them.

Parameters

e

a graphene_euler_t

 

res

return location for a graphene_vec3_t.

[out caller-allocates]

Since: 1.2


graphene_euler_to_matrix ()

void
graphene_euler_to_matrix (const graphene_euler_t *e,
                          graphene_matrix_t *res);

Converts a graphene_euler_t into a transformation matrix expressing the extrinsic composition of rotations described by the Euler angles.

The rotations are applied over the reference frame axes in the order associated with the graphene_euler_t; for instance, if the order used to initialize e is GRAPHENE_EULER_ORDER_XYZ:

  • the first rotation moves the body around the X axis with an angle φ

  • the second rotation moves the body around the Y axis with an angle of ϑ

  • the third rotation moves the body around the Z axis with an angle of ψ

The rotation sign convention is left-handed, to preserve compatibility between Euler-based, quaternion-based, and angle-axis-based rotations.

Parameters

e

a graphene_euler_t

 

res

return location for a graphene_matrix_t.

[out caller-allocates]

Since: 1.2


graphene_euler_reorder ()

void
graphene_euler_reorder (const graphene_euler_t *e,
                        graphene_euler_order_t order,
                        graphene_euler_t *res);

Reorders a graphene_euler_t using order .

This function is equivalent to creating a graphene_quaternion_t from the given graphene_euler_t, and then converting the quaternion into another graphene_euler_t.

Parameters

e

a graphene_euler_t

 

order

the new order

 

res

return location for the reordered graphene_euler_t.

[out caller-allocates]

Since: 1.2

Types and Values

graphene_euler_t

typedef struct {
} graphene_euler_t;

Describe a rotation using Euler angles.

The contents of the graphene_euler_t structure are private and should never be accessed directly.

Since: 1.2


enum graphene_euler_order_t

Specify the order of the rotations on each axis.

The GRAPHENE_EULER_ORDER_DEFAULT value is special, and is used as an alias for one of the other orders.

Members

GRAPHENE_EULER_ORDER_DEFAULT

Rotate in the default order; the default order is one of the following enumeration values

 

GRAPHENE_EULER_ORDER_XYZ

Rotate in the X, Y, and Z order

 

GRAPHENE_EULER_ORDER_YZX

Rotate in the Y, Z, and X order

 

GRAPHENE_EULER_ORDER_ZXY

Rotate in the Z, X, and Y order

 

GRAPHENE_EULER_ORDER_XZY

Rotate in the X, Z, and Y order

 

GRAPHENE_EULER_ORDER_YXZ

Rotate in the Y, X, and Z order

 

GRAPHENE_EULER_ORDER_ZYX

Rotate in the Z, Y, and X order

 

Since: 1.2

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