/*
* Cogl
*
* An object oriented GL/GLES Abstraction/Utility Layer
*
* Copyright (C) 2010 Intel Corporation.
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the
* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
* Boston, MA 02111-1307, USA.
*
* Authors:
* Robert Bragg <robert@linux.intel.com>
*/
#if !defined(__COGL_H_INSIDE__) && !defined(COGL_COMPILATION)
#error "Only <cogl/cogl.h> can be included directly."
#endif
#ifndef __COGL_QUATERNION_H__
#define __COGL_QUATERNION_H__
#include <cogl/cogl-types.h>
#include <cogl/cogl-vector.h>
COGL_BEGIN_DECLS
/**
* SECTION:cogl-quaternion
* @short_description: Functions for initializing and manipulating
* quaternions.
*
* Quaternions have become a standard form for representing 3D
* rotations and have some nice properties when compared with other
* representation such as (roll,pitch,yaw) Euler angles. They can be
* used to interpolate between different rotations and they don't
* suffer from a problem called
* <ulink url="http://en.wikipedia.org/wiki/Gimbal_lock">"Gimbal lock"</ulink>
* where two of the axis of rotation may become aligned and you loose a
* degree of freedom.
* .
*/
#include <cogl/cogl-vector.h>
#include <cogl/cogl-euler.h>
/**
* CoglQuaternion:
*
* A quaternion is comprised of a scalar component and a 3D vector
* component. The scalar component is normally referred to as w and the
* vector might either be referred to as v or a (for axis) or expanded
* with the individual components: (x, y, z) A full quaternion would
* then be written as <literal>[w (x, y, z)]</literal>.
*
* Quaternions can be considered to represent an axis and angle
* pair although sadly these numbers are buried somewhat under some
* maths...
*
* For the curious you can see here that a given axis (a) and angle (š)
* pair are represented in a quaternion as follows:
* |[
* [w=cos(š/2) ( x=sin(š/2)*a.x, y=sin(š/2)*a.y, z=sin(š/2)*a.x )]
* ]|
*
* Unit Quaternions:
* When using Quaternions to represent spatial orientations for 3D
* graphics it's always assumed you have a unit quaternion. The
* magnitude of a quaternion is defined as:
* |[
* sqrt (wĀ² + xĀ² + yĀ² + zĀ²)
* ]|
* and a unit quaternion satisfies this equation:
* |[
* wĀ² + xĀ² + yĀ² + zĀ² = 1
* ]|
*
* Thankfully most of the time we don't actually have to worry about
* the maths that goes on behind the scenes but if you are curious to
* learn more here are some external references:
*
* <itemizedlist>
* <listitem>
* <ulink url="http://mathworld.wolfram.com/Quaternion.html"/>
* </listitem>
* <listitem>
* <ulink url="http://www.gamedev.net/reference/articles/article1095.asp"/>
* </listitem>
* <listitem>
* <ulink url="http://www.cprogramming.com/tutorial/3d/quaternions.html"/>
* </listitem>
* <listitem>
* <ulink url="http://www.isner.com/tutorials/quatSpells/quaternion_spells_12.htm"/>
* </listitem>
* <listitem>
* 3D Maths Primer for Graphics and Game Development ISBN-10: 1556229119
* </listitem>
* <listitem>
* <ulink url="http://www.cs.caltech.edu/courses/cs171/quatut.pdf"/>
* </listitem>
* <listitem>
* <ulink url="http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q56"/>
* </listitem>
* </itemizedlist>
*
* @w: based on the angle of rotation it is cos(š/2)
* @x: based on the angle of rotation and x component of the axis of
* rotation it is sin(š/2)*axis.x
* @y: based on the angle of rotation and y component of the axis of
* rotation it is sin(š/2)*axis.y
* @z: based on the angle of rotation and z component of the axis of
* rotation it is sin(š/2)*axis.z
*/
struct _CoglQuaternion
{
float w;
float x;
float y;
float z;
/*< private >*/
float padding0;
float padding1;
float padding2;
float padding3;
};
COGL_STRUCT_SIZE_ASSERT (CoglQuaternion, 32);
/**
* cogl_quaternion_init:
* @quaternion: An uninitialized #CoglQuaternion
* @angle: The angle you want to rotate around the given axis
* @x: The x component of your axis vector about which you want to
* rotate.
* @y: The y component of your axis vector about which you want to
* rotate.
* @z: The z component of your axis vector about which you want to
* rotate.
*
* Initializes a quaternion that rotates @angle degrees around the
* axis vector (@x, @y, @z). The axis vector does not need to be
* normalized.
*
* Returns: A normalized, unit quaternion representing an orientation
* rotated @angle degrees around the axis vector (@x, @y, @z)
*
* Since: 2.0
*/
void
cogl_quaternion_init (CoglQuaternion *quaternion,
float angle,
float x,
float y,
float z);
/**
* cogl_quaternion_init_from_angle_vector:
* @quaternion: An uninitialized #CoglQuaternion
* @angle: The angle to rotate around @axis3f
* @axis3f: your 3 component axis vector about which you want to rotate.
*
* Initializes a quaternion that rotates @angle degrees around the
* given @axis vector. The axis vector does not need to be
* normalized.
*
* Returns: A normalized, unit quaternion representing an orientation
* rotated @angle degrees around the given @axis vector.
*
* Since: 2.0
*/
void
cogl_quaternion_init_from_angle_vector (CoglQuaternion *quaternion,
float angle,
const float *axis3f);
/**
* cogl_quaternion_init_identity:
* @quaternion: An uninitialized #CoglQuaternion
*
* Initializes the quaternion with the canonical quaternion identity
* [1 (0, 0, 0)] which represents no rotation. Multiplying a
* quaternion with this identity leaves the quaternion unchanged.
*
* You might also want to consider using
* cogl_get_static_identity_quaternion().
*
* Since: 2.0
*/
void
cogl_quaternion_init_identity (CoglQuaternion *quaternion);
/**
* cogl_quaternion_init_from_array:
* @quaternion: A #CoglQuaternion
* @array: An array of 4 floats w,(x,y,z)
*
* Initializes a [w (x, y,z)] quaternion directly from an array of 4
* floats: [w,x,y,z].
*
* Since: 2.0
*/
void
cogl_quaternion_init_from_array (CoglQuaternion *quaternion,
const float *array);
/**
* cogl_quaternion_init_from_x_rotation:
* @quaternion: An uninitialized #CoglQuaternion
* @angle: The angle to rotate around the x axis
*
* XXX: check which direction this rotates
*
* Since: 2.0
*/
void
cogl_quaternion_init_from_x_rotation (CoglQuaternion *quaternion,
float angle);
/**
* cogl_quaternion_init_from_y_rotation:
* @quaternion: An uninitialized #CoglQuaternion
* @angle: The angle to rotate around the y axis
*
*
* Since: 2.0
*/
void
cogl_quaternion_init_from_y_rotation (CoglQuaternion *quaternion,
float angle);
/**
* cogl_quaternion_init_from_z_rotation:
* @quaternion: An uninitialized #CoglQuaternion
* @angle: The angle to rotate around the z axis
*
*
* Since: 2.0
*/
void
cogl_quaternion_init_from_z_rotation (CoglQuaternion *quaternion,
float angle);
/**
* cogl_quaternion_init_from_euler:
* @quaternion: A #CoglQuaternion
* @euler: A #CoglEuler with which to initialize the quaternion
*
* Since: 2.0
*/
void
cogl_quaternion_init_from_euler (CoglQuaternion *quaternion,
const CoglEuler *euler);
/**
* cogl_quaternion_init_from_quaternion:
* @quaternion: A #CoglQuaternion
* @src: A #CoglQuaternion with which to initialize @quaternion
*
* Since: 2.0
*/
void
cogl_quaternion_init_from_quaternion (CoglQuaternion *quaternion,
CoglQuaternion *src);
/**
* cogl_quaternion_init_from_matrix:
* @quaternion: A Cogl Quaternion
* @matrix: A rotation matrix with which to initialize the quaternion
*
* Initializes a quaternion from a rotation matrix.
*
* Since: 1.10
* Stability: unstable
*/
void
cogl_quaternion_init_from_matrix (CoglQuaternion *quaternion,
const CoglMatrix *matrix);
/**
* cogl_quaternion_equal:
* @v1: A #CoglQuaternion
* @v2: A #CoglQuaternion
*
* Compares that all the components of quaternions @a and @b are
* equal.
*
* An epsilon value is not used to compare the float components, but
* the == operator is at least used so that 0 and -0 are considered
* equal.
*
* Returns: %TRUE if the quaternions are equal else %FALSE.
*
* Since: 2.0
*/
CoglBool
cogl_quaternion_equal (const void *v1, const void *v2);
/**
* cogl_quaternion_copy:
* @src: A #CoglQuaternion
*
* Allocates a new #CoglQuaternion on the stack and initializes it with
* the same values as @src.
*
* Returns: A newly allocated #CoglQuaternion which should be freed
* using cogl_quaternion_free()
*
* Since: 2.0
*/
CoglQuaternion *
cogl_quaternion_copy (const CoglQuaternion *src);
/**
* cogl_quaternion_free:
* @quaternion: A #CoglQuaternion
*
* Frees a #CoglQuaternion that was previously allocated via
* cogl_quaternion_copy().
*
* Since: 2.0
*/
void
cogl_quaternion_free (CoglQuaternion *quaternion);
/**
* cogl_quaternion_get_rotation_angle:
* @quaternion: A #CoglQuaternion
*
*
* Since: 2.0
*/
float
cogl_quaternion_get_rotation_angle (const CoglQuaternion *quaternion);
/**
* cogl_quaternion_get_rotation_axis:
* @quaternion: A #CoglQuaternion
* @vector3: (out): an allocated 3-float array
*
* Since: 2.0
*/
void
cogl_quaternion_get_rotation_axis (const CoglQuaternion *quaternion,
float *vector3);
/**
* cogl_quaternion_normalize:
* @quaternion: A #CoglQuaternion
*
*
* Since: 2.0
*/
void
cogl_quaternion_normalize (CoglQuaternion *quaternion);
/**
* cogl_quaternion_dot_product:
* @a: A #CoglQuaternion
* @b: A #CoglQuaternion
*
* Since: 2.0
*/
float
cogl_quaternion_dot_product (const CoglQuaternion *a,
const CoglQuaternion *b);
/**
* cogl_quaternion_invert:
* @quaternion: A #CoglQuaternion
*
*
* Since: 2.0
*/
void
cogl_quaternion_invert (CoglQuaternion *quaternion);
/**
* cogl_quaternion_multiply:
* @result: The destination #CoglQuaternion
* @left: The second #CoglQuaternion rotation to apply
* @right: The first #CoglQuaternion rotation to apply
*
* This combines the rotations of two quaternions into @result. The
* operation is not commutative so the order is important because AxB
* != BxA. Cogl follows the standard convention for quaternions here
* so the rotations are applied @right to @left. This is similar to the
* combining of matrices.
*
* <note>It is possible to multiply the @a quaternion in-place, so
* @result can be equal to @a but can't be equal to @b.</note>
*
* Since: 2.0
*/
void
cogl_quaternion_multiply (CoglQuaternion *result,
const CoglQuaternion *left,
const CoglQuaternion *right);
/**
* cogl_quaternion_pow:
* @quaternion: A #CoglQuaternion
* @exponent: the exponent
*
*
* Since: 2.0
*/
void
cogl_quaternion_pow (CoglQuaternion *quaternion, float exponent);
/**
* cogl_quaternion_slerp:
* @result: The destination #CoglQuaternion
* @a: The first #CoglQuaternion
* @b: The second #CoglQuaternion
* @t: The factor in the range [0,1] used to interpolate between
* quaternion @a and @b.
*
* Performs a spherical linear interpolation between two quaternions.
*
* Noteable properties:
* <itemizedlist>
* <listitem>
* commutative: No
* </listitem>
* <listitem>
* constant velocity: Yes
* </listitem>
* <listitem>
* torque minimal (travels along the surface of the 4-sphere): Yes
* </listitem>
* <listitem>
* more expensive than cogl_quaternion_nlerp()
* </listitem>
* </itemizedlist>
*/
void
cogl_quaternion_slerp (CoglQuaternion *result,
const CoglQuaternion *a,
const CoglQuaternion *b,
float t);
/**
* cogl_quaternion_nlerp:
* @result: The destination #CoglQuaternion
* @a: The first #CoglQuaternion
* @b: The second #CoglQuaternion
* @t: The factor in the range [0,1] used to interpolate between
* quaterion @a and @b.
*
* Performs a normalized linear interpolation between two quaternions.
* That is it does a linear interpolation of the quaternion components
* and then normalizes the result. This will follow the shortest arc
* between the two orientations (just like the slerp() function) but
* will not progress at a constant speed. Unlike slerp() nlerp is
* commutative which is useful if you are blending animations
* together. (I.e. nlerp (tmp, a, b) followed by nlerp (result, tmp,
* d) is the same as nlerp (tmp, a, d) followed by nlerp (result, tmp,
* b)). Finally nlerp is cheaper than slerp so it can be a good choice
* if you don't need the constant speed property of the slerp() function.
*
* Notable properties:
* <itemizedlist>
* <listitem>
* commutative: Yes
* </listitem>
* <listitem>
* constant velocity: No
* </listitem>
* <listitem>
* torque minimal (travels along the surface of the 4-sphere): Yes
* </listitem>
* <listitem>
* faster than cogl_quaternion_slerp()
* </listitem>
* </itemizedlist>
*/
void
cogl_quaternion_nlerp (CoglQuaternion *result,
const CoglQuaternion *a,
const CoglQuaternion *b,
float t);
/**
* cogl_quaternion_squad:
* @result: The destination #CoglQuaternion
* @prev: A #CoglQuaternion used before @a
* @a: The first #CoglQuaternion
* @b: The second #CoglQuaternion
* @next: A #CoglQuaternion that will be used after @b
* @t: The factor in the range [0,1] used to interpolate between
* quaternion @a and @b.
*
*
* Since: 2.0
*/
void
cogl_quaternion_squad (CoglQuaternion *result,
const CoglQuaternion *prev,
const CoglQuaternion *a,
const CoglQuaternion *b,
const CoglQuaternion *next,
float t);
/**
* cogl_get_static_identity_quaternion:
*
* Returns a pointer to a singleton quaternion constant describing the
* canonical identity [1 (0, 0, 0)] which represents no rotation.
*
* If you multiply a quaternion with the identity quaternion you will
* get back the same value as the original quaternion.
*
* Returns: A pointer to an identity quaternion
*
* Since: 2.0
*/
const CoglQuaternion *
cogl_get_static_identity_quaternion (void);
/**
* cogl_get_static_zero_quaternion:
*
* Returns: a pointer to a singleton quaternion constant describing a
* rotation of 180 degrees around a degenerate axis:
* [0 (0, 0, 0)]
*
* Since: 2.0
*/
const CoglQuaternion *
cogl_get_static_zero_quaternion (void);
COGL_END_DECLS
#endif /* __COGL_QUATERNION_H__ */