mutter/cogl/cogl-quaternion.c

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/*
* 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>
*
* Various references relating to quaternions:
*
* http://www.cs.caltech.edu/courses/cs171/quatut.pdf
* http://mathworld.wolfram.com/Quaternion.html
* http://www.gamedev.net/reference/articles/article1095.asp
* http://www.cprogramming.com/tutorial/3d/quaternions.html
* http://www.isner.com/tutorials/quatSpells/quaternion_spells_12.htm
* http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q56
* 3D Maths Primer for Graphics and Game Development ISBN-10: 1556229119
*/
#include <cogl.h>
#include <cogl-quaternion.h>
#include <cogl-quaternion-private.h>
#include <cogl-matrix.h>
#include <cogl-vector.h>
#include <cogl-euler.h>
#include <string.h>
#include <math.h>
#define FLOAT_EPSILON 1e-03
static CoglQuaternion zero_quaternion =
{
0.0, 0.0, 0.0, 0.0,
};
static CoglQuaternion identity_quaternion =
{
1.0, 0.0, 0.0, 0.0,
};
void
_cogl_quaternion_print (CoglQuaternion *quaternion)
{
g_print ("[ %6.4f (%6.4f, %6.4f, %6.4f)]\n",
quaternion->w,
quaternion->x,
quaternion->y,
quaternion->z);
}
void
cogl_quaternion_init (CoglQuaternion *quaternion,
float angle,
float x,
float y,
float z)
{
CoglVector3 axis = { x, y, z};
cogl_quaternion_init_from_angle_vector (quaternion, angle, &axis);
}
void
cogl_quaternion_init_from_angle_vector (CoglQuaternion *quaternion,
float angle,
const CoglVector3 *axis_in)
{
/* NB: We are using quaternions to represent an axis (a), angle (𝜃) pair
* in this form:
* [w=cos(𝜃/2) ( x=sin(𝜃/2)*a.x, y=sin(𝜃/2)*a.y, z=sin(𝜃/2)*a.x )]
*/
CoglVector3 axis;
float half_angle;
float sin_half_angle;
/* XXX: Should we make cogl_vector3_normalize have separate in and
* out args? */
axis = *axis_in;
cogl_vector3_normalize (&axis);
half_angle = angle * _COGL_QUATERNION_DEGREES_TO_RADIANS * 0.5f;
sin_half_angle = sinf (half_angle);
quaternion->w = cosf (half_angle);
quaternion->x = axis.x * sin_half_angle;
quaternion->y = axis.y * sin_half_angle;
quaternion->z = axis.z * sin_half_angle;
cogl_quaternion_normalize (quaternion);
}
void
cogl_quaternion_init_identity (CoglQuaternion *quaternion)
{
quaternion->w = 1.0;
quaternion->x = 0.0;
quaternion->y = 0.0;
quaternion->z = 0.0;
}
void
cogl_quaternion_init_from_array (CoglQuaternion *quaternion,
const float *array)
{
quaternion->w = array[0];
quaternion->x = array[1];
quaternion->y = array[2];
quaternion->z = array[3];
}
void
cogl_quaternion_init_from_x_rotation (CoglQuaternion *quaternion,
float angle)
{
/* NB: We are using quaternions to represent an axis (a), angle (𝜃) pair
* in this form:
* [w=cos(𝜃/2) ( x=sin(𝜃/2)*a.x, y=sin(𝜃/2)*a.y, z=sin(𝜃/2)*a.x )]
*/
float half_angle = angle * _COGL_QUATERNION_DEGREES_TO_RADIANS * 0.5f;
quaternion->w = cosf (half_angle);
quaternion->x = sinf (half_angle);
quaternion->y = 0.0f;
quaternion->z = 0.0f;
}
void
cogl_quaternion_init_from_y_rotation (CoglQuaternion *quaternion,
float angle)
{
/* NB: We are using quaternions to represent an axis (a), angle (𝜃) pair
* in this form:
* [w=cos(𝜃/2) ( x=sin(𝜃/2)*a.x, y=sin(𝜃/2)*a.y, z=sin(𝜃/2)*a.x )]
*/
float half_angle = angle * _COGL_QUATERNION_DEGREES_TO_RADIANS * 0.5f;
quaternion->w = cosf (half_angle);
quaternion->x = 0.0f;
quaternion->y = sinf (half_angle);
quaternion->z = 0.0f;
}
void
cogl_quaternion_init_from_z_rotation (CoglQuaternion *quaternion,
float angle)
{
/* NB: We are using quaternions to represent an axis (a), angle (𝜃) pair
* in this form:
* [w=cos(𝜃/2) ( x=sin(𝜃/2)*a.x, y=sin(𝜃/2)*a.y, z=sin(𝜃/2)*a.x )]
*/
float half_angle = angle * _COGL_QUATERNION_DEGREES_TO_RADIANS * 0.5f;
quaternion->w = cosf (half_angle);
quaternion->x = 0.0f;
quaternion->y = 0.0f;
quaternion->z = sinf (half_angle);
}
void
cogl_quaternion_init_from_euler (CoglQuaternion *quaternion,
const CoglEuler *euler)
{
/* NB: We are using quaternions to represent an axis (a), angle (𝜃) pair
* in this form:
* [w=cos(𝜃/2) ( x=sin(𝜃/2)*a.x, y=sin(𝜃/2)*a.y, z=sin(𝜃/2)*a.x )]
*/
float sin_heading =
sinf (euler->heading * _COGL_QUATERNION_DEGREES_TO_RADIANS * 0.5f);
float sin_pitch =
sinf (euler->pitch * _COGL_QUATERNION_DEGREES_TO_RADIANS * 0.5f);
float sin_roll =
sinf (euler->roll * _COGL_QUATERNION_DEGREES_TO_RADIANS * 0.5f);
float cos_heading =
cosf (euler->heading * _COGL_QUATERNION_DEGREES_TO_RADIANS * 0.5f);
float cos_pitch =
cosf (euler->pitch * _COGL_QUATERNION_DEGREES_TO_RADIANS * 0.5f);
float cos_roll =
cosf (euler->roll * _COGL_QUATERNION_DEGREES_TO_RADIANS * 0.5f);
quaternion->w =
cos_heading * cos_pitch * cos_roll +
sin_heading * sin_pitch * sin_roll;
quaternion->x =
cos_heading * sin_pitch * cos_roll +
sin_heading * cos_pitch * sin_roll;
quaternion->y =
sin_heading * cos_pitch * cos_roll -
cos_heading * sin_pitch * sin_roll;
quaternion->z =
cos_heading * cos_pitch * sin_roll -
sin_heading * sin_pitch * cos_roll;
}
void
cogl_quaternion_init_from_quaternion (CoglQuaternion *quaternion,
CoglQuaternion *src)
{
memcpy (quaternion, src, sizeof (float) * 4);
}
/* XXX: it could be nice to make something like this public... */
/*
* COGL_MATRIX_READ:
* @MATRIX: A 4x4 transformation matrix
* @ROW: The row of the value you want to read
* @COLUMN: The column of the value you want to read
*
* Reads a value from the given matrix using integers to index
* into the matrix.
*/
#define COGL_MATRIX_READ(MATRIX, ROW, COLUMN) \
(((const float *)matrix)[COLUMN * 4 + ROW])
/**
* 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: 1.4
*/
void
cogl_quaternion_init_from_matrix (CoglQuaternion *quaternion,
const CoglMatrix *matrix)
{
/* Algorithm devised by Ken Shoemake, Ref:
* http://campar.in.tum.de/twiki/pub/Chair/DwarfTutorial/quatut.pdf
*/
/* 3D maths literature refers to the diagonal of a matrix as the
* "trace" of a matrix... */
float trace = matrix->xx + matrix->yy + matrix->zz;
float root;
if (trace > 0.0f)
{
root = sqrtf (trace + 1);
quaternion->w = root * 0.5f;
root = 0.5f / root;
quaternion->x = (matrix->zy - matrix->yz) * root;
quaternion->y = (matrix->xz - matrix->zx) * root;
quaternion->z = (matrix->yx - matrix->xy) * root;
}
else
{
#define X 0
#define Y 1
#define Z 2
#define W 3
int h = X;
if (matrix->yy > matrix->xx)
h = Y;
if (matrix->zz > COGL_MATRIX_READ (matrix, h, h))
h = Z;
switch (h)
{
#define CASE_MACRO(i, j, k, I, J, K) \
case I: \
root = sqrtf ((COGL_MATRIX_READ (matrix, I, I) - \
(COGL_MATRIX_READ (matrix, J, J) + \
COGL_MATRIX_READ (matrix, K, K))) + \
COGL_MATRIX_READ (matrix, W, W)); \
quaternion->i = root * 0.5f;\
root = 0.5f / root;\
quaternion->j = (COGL_MATRIX_READ (matrix, I, J) + \
COGL_MATRIX_READ (matrix, J, I)) * root; \
quaternion->k = (COGL_MATRIX_READ (matrix, K, I) + \
COGL_MATRIX_READ (matrix, I, K)) * root; \
quaternion->w = (COGL_MATRIX_READ (matrix, K, J) - \
COGL_MATRIX_READ (matrix, J, K)) * root;\
break
CASE_MACRO (x, y, z, X, Y, Z);
CASE_MACRO (y, z, x, Y, Z, X);
CASE_MACRO (z, x, y, Z, X, Y);
#undef CASE_MACRO
#undef X
#undef Y
#undef Z
}
}
if (matrix->ww != 1.0f)
{
float s = 1.0 / sqrtf (matrix->ww);
quaternion->w *= s;
quaternion->x *= s;
quaternion->y *= s;
quaternion->z *= s;
}
}
gboolean
cogl_quaternion_equal (gconstpointer v1, gconstpointer v2)
{
const CoglQuaternion *a = v1;
const CoglQuaternion *b = v2;
g_return_val_if_fail (v1 != NULL, FALSE);
g_return_val_if_fail (v2 != NULL, FALSE);
if (v1 == v2)
return TRUE;
return (a->w == b->w &&
a->x == b->x &&
a->y == b->y &&
a->z == b->z);
}
CoglQuaternion *
cogl_quaternion_copy (const CoglQuaternion *src)
{
if (G_LIKELY (src))
{
CoglQuaternion *new = g_slice_new (CoglQuaternion);
memcpy (new, src, sizeof (float) * 4);
return new;
}
else
return NULL;
}
void
cogl_quaternion_free (CoglQuaternion *quaternion)
{
g_slice_free (CoglQuaternion, quaternion);
}
float
cogl_quaternion_get_rotation_angle (const CoglQuaternion *quaternion)
{
/* NB: We are using quaternions to represent an axis (a), angle (𝜃) pair
* in this form:
* [w=cos(𝜃/2) ( x=sin(𝜃/2)*a.x, y=sin(𝜃/2)*a.y, z=sin(𝜃/2)*a.x )]
*/
/* FIXME: clamp [-1, 1] */
return 2.0f * acosf (quaternion->w) * _COGL_QUATERNION_RADIANS_TO_DEGREES;
}
void
cogl_quaternion_get_rotation_axis (const CoglQuaternion *quaternion,
CoglVector3 *vector)
{
float sin_half_angle_sqr;
float one_over_sin_angle_over_2;
/* NB: We are using quaternions to represent an axis (a), angle (𝜃) pair
* in this form:
* [w=cos(𝜃/2) ( x=sin(𝜃/2)*a.x, y=sin(𝜃/2)*a.y, z=sin(𝜃/2)*a.x )]
*/
/* NB: sin²(𝜃) + cos²(𝜃) = 1 */
sin_half_angle_sqr = 1.0f - quaternion->w * quaternion->w;
if (sin_half_angle_sqr <= 0.0f)
{
/* Either an identity quaternion or numerical imprecision.
* Either way we return an arbitrary vector. */
vector->x = 1;
vector->y = 0;
vector->z = 0;
return;
}
/* Calculate 1 / sin(𝜃/2) */
one_over_sin_angle_over_2 = 1.0f / sqrtf (sin_half_angle_sqr);
vector->x = quaternion->x * one_over_sin_angle_over_2;
vector->y = quaternion->y * one_over_sin_angle_over_2;
vector->z = quaternion->z * one_over_sin_angle_over_2;
}
void
cogl_quaternion_normalize (CoglQuaternion *quaternion)
{
float slen = _COGL_QUATERNION_NORM (quaternion);
float factor = 1.0f / sqrtf (slen);
quaternion->x *= factor;
quaternion->y *= factor;
quaternion->z *= factor;
quaternion->w *= factor;
return;
}
float
cogl_quaternion_dot_product (const CoglQuaternion *a,
const CoglQuaternion *b)
{
return a->w * b->w + a->x * b->x + a->y * b->y + a->z * b->z;
}
void
cogl_quaternion_invert (CoglQuaternion *quaternion)
{
quaternion->x = -quaternion->x;
quaternion->y = -quaternion->y;
quaternion->z = -quaternion->z;
}
void
cogl_quaternion_multiply (CoglQuaternion *result,
const CoglQuaternion *a,
const CoglQuaternion *b)
{
result->w = a->w * b->w - a->x * b->x - a->y * b->y - a->z * b->z;
result->x = a->w * b->x + a->x * b->w + a->y * b->z - a->z * b->y;
result->y = a->w * b->y + a->y * b->w + a->z * b->x - a->x * b->z;
result->z = a->w * b->z + a->z * b->w + a->x * b->y - a->y * b->x;
}
void
cogl_quaternion_pow (CoglQuaternion *quaternion, float exponent)
{
float half_angle;
float new_half_angle;
float factor;
/* Try and identify and nop identity quaternions to avoid
* dividing by zero */
if (fabs (quaternion->w) > 0.9999f)
return;
/* NB: We are using quaternions to represent an axis (a), angle (𝜃) pair
* in this form:
* [w=cos(𝜃/2) ( x=sin(𝜃/2)*a.x, y=sin(𝜃/2)*a.y, z=sin(𝜃/2)*a.x )]
*/
/* FIXME: clamp [-1, 1] */
/* Extract 𝜃/2 from w */
half_angle = acosf (quaternion->w);
/* Compute the new 𝜃/2 */
new_half_angle = half_angle * exponent;
/* Compute the new w value */
quaternion->w = cosf (new_half_angle);
/* And new xyz values */
factor = sinf (new_half_angle) / sinf (half_angle);
quaternion->x *= factor;
quaternion->y *= factor;
quaternion->z *= factor;
}
void
cogl_quaternion_slerp (CoglQuaternion *result,
const CoglQuaternion *a,
const CoglQuaternion *b,
float t)
{
float cos_difference;
float qb_w;
float qb_x;
float qb_y;
float qb_z;
float fa;
float fb;
g_return_if_fail (t >=0 && t <= 1.0f);
if (t == 0)
{
*result = *a;
return;
}
else if (t == 1)
{
*result = *b;
return;
}
/* compute the cosine of the angle between the two given quaternions */
cos_difference = cogl_quaternion_dot_product (a, b);
/* If negative, use -b. Two quaternions q and -q represent the same angle but
* may produce a different slerp. We choose b or -b to rotate using the acute
* angle.
*/
if (cos_difference < 0.0f)
{
qb_w = -b->w;
qb_x = -b->x;
qb_y = -b->y;
qb_z = -b->z;
cos_difference = -cos_difference;
}
else
{
qb_w = b->w;
qb_x = b->x;
qb_y = b->y;
qb_z = b->z;
}
/* If we have two unit quaternions the dot should be <= 1.0 */
g_assert (cos_difference < 1.1f);
/* Determine the interpolation factors for each quaternion, simply using
* linear interpolation for quaternions that are nearly exactly the same.
* (this will avoid divisions by zero)
*/
if (cos_difference > 0.9999f)
{
fa = 1.0f - t;
fb = t;
/* XXX: should we also normalize() at the end in this case? */
}
else
{
/* Calculate the sin of the angle between the two quaternions using the
* trig identity: sin²(𝜃) + cos²(𝜃) = 1
*/
float sin_difference = sqrtf (1.0f - cos_difference * cos_difference);
float difference = atan2f (sin_difference, cos_difference);
float one_over_sin_difference = 1.0f / sin_difference;
fa = sinf ((1.0f - t) * difference) * one_over_sin_difference;
fb = sinf (t * difference) * one_over_sin_difference;
}
/* Finally interpolate the two quaternions */
result->x = fa * a->x + fb * qb_x;
result->y = fa * a->y + fb * qb_y;
result->z = fa * a->z + fb * qb_z;
result->w = fa * a->w + fb * qb_w;
}
void
cogl_quaternion_nlerp (CoglQuaternion *result,
const CoglQuaternion *a,
const CoglQuaternion *b,
float t)
{
float cos_difference;
float qb_w;
float qb_x;
float qb_y;
float qb_z;
float fa;
float fb;
g_return_if_fail (t >=0 && t <= 1.0f);
if (t == 0)
{
*result = *a;
return;
}
else if (t == 1)
{
*result = *b;
return;
}
/* compute the cosine of the angle between the two given quaternions */
cos_difference = cogl_quaternion_dot_product (a, b);
/* If negative, use -b. Two quaternions q and -q represent the same angle but
* may produce a different slerp. We choose b or -b to rotate using the acute
* angle.
*/
if (cos_difference < 0.0f)
{
qb_w = -b->w;
qb_x = -b->x;
qb_y = -b->y;
qb_z = -b->z;
cos_difference = -cos_difference;
}
else
{
qb_w = b->w;
qb_x = b->x;
qb_y = b->y;
qb_z = b->z;
}
/* If we have two unit quaternions the dot should be <= 1.0 */
g_assert (cos_difference < 1.1f);
fa = 1.0f - t;
fb = t;
result->x = fa * a->x + fb * qb_x;
result->y = fa * a->y + fb * qb_y;
result->z = fa * a->z + fb * qb_z;
result->w = fa * a->w + fb * qb_w;
cogl_quaternion_normalize (result);
}
/**
* cogl_quaternion_squad:
*
*/
void
cogl_quaternion_squad (CoglQuaternion *result,
const CoglQuaternion *prev,
const CoglQuaternion *a,
const CoglQuaternion *b,
const CoglQuaternion *next,
float t)
{
CoglQuaternion slerp0;
CoglQuaternion slerp1;
cogl_quaternion_slerp (&slerp0, a, b, t);
cogl_quaternion_slerp (&slerp1, prev, next, t);
cogl_quaternion_slerp (result, &slerp0, &slerp1, 2.0f * t * (1.0f - t));
}
const CoglQuaternion *
cogl_get_static_identity_quaternion (void)
{
return &identity_quaternion;
}
const CoglQuaternion *
cogl_get_static_zero_quaternion (void)
{
return &zero_quaternion;
}