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math: Adds an experimental quaternion API

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This adds an experimental quaternion utility API. It's not yet fully
documented but it's complete enough that people can start to experiment
with using it. It adds the following functions:

    cogl_quaternion_init_identity
    cogl_quaternion_init
    cogl_quaternion_init_from_angle_vector
    cogl_quaternion_init_from_array
    cogl_quaternion_init_from_x_rotation
    cogl_quaternion_init_from_y_rotation
    cogl_quaternion_init_from_z_rotation
    cogl_quaternion_equal
    cogl_quaternion_copy
    cogl_quaternion_free
    cogl_quaternion_get_rotation_angle
    cogl_quaternion_get_rotation_axis
    cogl_quaternion_normalize
    cogl_quaternion_dot_product
    cogl_quaternion_invert
    cogl_quaternion_multiply
    cogl_quaternion_pow
    cogl_quaternion_slerp
    cogl_quaternion_nlerp
    cogl_quaternion_squad
    cogl_get_static_identity_quaternion
    cogl_get_static_zero_quaternion

Since it's experimental API you'll need to define
COGL_ENABLE_EXPERIMENTAL_API before including cogl.h.
This commit is contained in:
Robert Bragg 2010-02-25 01:40:29 +00:00
parent b316241612
commit d1434d1c33
14 changed files with 1278 additions and 2 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

2
cogl/Makefile.am
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@ -64,6 +64,7 @@ cogl_public_h = \
$(srcdir)/cogl-material-compat.h \
$(srcdir)/cogl-pipeline.h \
$(srcdir)/cogl-vector.h \
$(srcdir)/cogl-quaternion.h \
$(srcdir)/cogl-matrix.h \
$(srcdir)/cogl-offscreen.h \
$(srcdir)/cogl-primitives.h \
@ -230,6 +231,7 @@ cogl_sources_c = \
$(srcdir)/cogl-primitive.c \
$(srcdir)/cogl-matrix.c \
$(srcdir)/cogl-vector.c \
$(srcdir)/cogl-quaternion.c \
$(srcdir)/cogl-matrix-private.h \
$(srcdir)/cogl-matrix-stack.c \
$(srcdir)/cogl-matrix-stack.h \

38
cogl/cogl-matrix-mesa.c
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@ -70,6 +70,7 @@
*/
#include "cogl-matrix-mesa.h"
#include "cogl-quaternion-private.h"
#include <string.h>
#include <math.h>
@ -1586,6 +1587,43 @@ _math_matrix_init_from_array (CoglMatrix *matrix, const float *array)
matrix->flags = (MAT_FLAG_GENERAL | MAT_DIRTY_ALL);
}
/*
*/
void
_math_matrix_init_from_quaternion (CoglMatrix *matrix,
CoglQuaternion *quaternion)
{
float qnorm = _COGL_QUATERNION_NORM (quaternion);
float s = (qnorm > 0.0f) ? (2.0f / qnorm) : 0.0f;
float xs = quaternion->x * s;
float ys = quaternion->y * s;
float zs = quaternion->z * s;
float wx = quaternion->w * xs;
float wy = quaternion->w * ys;
float wz = quaternion->w * zs;
float xx = quaternion->x * xs;
float xy = quaternion->x * ys;
float xz = quaternion->x * zs;
float yy = quaternion->y * ys;
float yz = quaternion->y * zs;
float zz = quaternion->z * zs;
matrix->xx = 1.0f - (yy + zz);
matrix->yx = xy + wz;
matrix->zx = xz - wy;
matrix->xy = xy - wz;
matrix->yy = 1.0f - (xx + zz);
matrix->zy = yz + wx;
matrix->xz = xz + wy;
matrix->yz = yz - wx;
matrix->zz = 1.0f - (xx + yy);
matrix->xw = matrix->yw = matrix->zw = 0.0f;
matrix->wx = matrix->wy = matrix->wz = 0.0f;
matrix->ww = 1.0f;
matrix->flags = (MAT_FLAG_GENERAL | MAT_DIRTY_ALL);
}
/*@}*/

5
cogl/cogl-matrix-mesa.h
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@ -51,6 +51,7 @@
#define _M_MATRIX_H
#include <cogl-matrix.h>
#include <cogl-quaternion.h>
#include <glib.h>
@ -110,6 +111,10 @@ _math_matrix_multiply_array (CoglMatrix *result, const float *b);
void
_math_matrix_init_from_array (CoglMatrix *matrix, const float *array);
void
_math_matrix_init_from_quaternion (CoglMatrix *matrix,
CoglQuaternion *quaternion);
void
_math_matrix_translate (CoglMatrix *matrix, float x, float y, float z);

9
cogl/cogl-matrix.c
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@ -32,6 +32,8 @@
#include <cogl.h>
#include "cogl-debug.h"
#include <cogl-quaternion.h>
#include <cogl-quaternion-private.h>
#include <cogl-matrix.h>
#include <cogl-matrix-private.h>
#ifdef USE_MESA_MATRIX_API
@ -73,6 +75,13 @@ cogl_matrix_init_identity (CoglMatrix *matrix)
_COGL_MATRIX_DEBUG_PRINT (matrix);
}
void
cogl_matrix_init_from_quaternion (CoglMatrix *matrix,
CoglQuaternion *quaternion)
{
_math_matrix_init_from_quaternion (matrix, quaternion);
}
void
cogl_matrix_multiply (CoglMatrix *result,
const CoglMatrix *a,

21
cogl/cogl-matrix.h
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@ -30,6 +30,10 @@
#include <glib.h>
#include "cogl-types.h"
#ifdef COGL_ENABLE_EXPERIMENTAL_API
#include "cogl-quaternion.h"
#endif
G_BEGIN_DECLS
/**
@ -41,8 +45,6 @@ G_BEGIN_DECLS
* be used for direct manipulation of these matrices.
*/
typedef struct _CoglMatrix CoglMatrix;
/**
* CoglMatrix:
*
@ -360,6 +362,21 @@ cogl_matrix_init_from_array (CoglMatrix *matrix,
G_CONST_RETURN float *
cogl_matrix_get_array (const CoglMatrix *matrix);
#ifdef COGL_ENABLE_EXPERIMENTAL_API
/**
* cogl_matrix_init_from_quaternion:
* @matrix: A 4x4 transformation matrix
* @quaternion: A #CoglQuaternion
*
* Initializes @matrix from a #CoglQuaternion rotation.
*
* Return value: a pointer to the float array
*/
void
cogl_matrix_init_from_quaternion (CoglMatrix *matrix,
CoglQuaternion *quaternion);
#endif
/**
* cogl_matrix_equal:
* @v1: A 4x4 transformation matrix

39
cogl/cogl-quaternion-private.h Normal file
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@ -0,0 +1,39 @@
/*
* Cogl
*
* An object oriented GL/GLES Abstraction/Utility Layer
*
* Copyright (C) 2008,2009 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>
*/
#ifndef __COGL_QUATERNION_PRIVATE_H__
#define __COGL_QUATERNION_PRIVATE_H__
#include <glib.h>
/* squared length */
#define _COGL_QUATERNION_NORM(Q) \
((Q)->x*(Q)->x + (Q)->y*(Q)->y + (Q)->z*(Q)->z + (Q)->w*(Q)->w)
#define _COGL_QUATERNION_DEGREES_TO_RADIANS (G_PI / 180.0f)
#define _COGL_QUATERNION_RADIANS_TO_DEGREES (180.0f / G_PI)
#endif /* __COGL_QUATERNION_PRIVATE_H__ */

617
cogl/cogl-quaternion.c Normal file
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@ -0,0 +1,617 @@
/*
* 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 <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)
{
memcpy (&quaternion->x, array, sizeof (float) * 4);
}
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_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->x = quaternion->x * one_over_sin_angle_over_2;
vector->x = quaternion->x * 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;
}

486
cogl/cogl-quaternion.h Normal file
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@ -0,0 +1,486 @@
/*
* 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(CLUTTER_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>
G_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 "Gimbal lock" where two of the axis of
* rotation may become aligned and you loose a degree of freedom.
* (<ulink url="http://en.wikipedia.org/wiki/Gimbal_lock"/>).
*/
/**
* 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 <pre>[w (x, y, z)]</pre>.
*
* 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 (𝜃)
* pair are represented in a quaternion as follows:
* |[
* [w=cos(𝜃/2) ( x=sin(𝜃/2)*a.x, y=sin(𝜃/2)*a.y, z=sin(𝜃/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 (w² + x² + y² + z²)
* ]|
* and a unit quaternion satisfies this equation:
* |[
* w² + x² + y² + z² = 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(𝜃/2)
* @x: based on the angle of rotation and x component of the axis of
* rotation it is sin(𝜃/2)*axis.x
* @y: based on the angle of rotation and y component of the axis of
* rotation it is sin(𝜃/2)*axis.y
* @z: based on the angle of rotation and z component of the axis of
* rotation it is sin(𝜃/2)*axis.z
*/
struct _CoglQuaternion
{
float w;
float x;
float y;
float z;
float padding0;
float padding1;
float padding2;
float padding3;
};
/**
* 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
* @axis: your 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 CoglVector3 *axis);
/**
* 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 (x,y,z),w
*
* 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 y axis
*
*
* Since: 2.0
*/
void
cogl_quaternion_init_from_z_rotation (CoglQuaternion *quaternion,
float angle);
/**
* cogl_quaternion_equal:
* @a: A #CoglQuaternion
* @b: 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
*/
gboolean
cogl_quaternion_equal (gconstpointer v1, gconstpointer 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
*
*
* Since: 2.0
*/
void
cogl_quaternion_get_rotation_axis (const CoglQuaternion *quaternion,
CoglVector3 *vector);
/**
* cogl_quaternion_normalize:
* @quaternion: A #CoglQuaternion
*
*
* Since: 2.0
*/
void
cogl_quaternion_normalize (CoglQuaternion *quaternion);
/**
* cogl_quaternion_dot_product:
* @quaternion: 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.
*
* Since: 2.0
*/
void
cogl_quaternion_multiply (CoglQuaternion *result,
const CoglQuaternion *left,
const CoglQuaternion *right);
/**
* cogl_quaternion_pow:
* @quaternion: A #CoglQuaternion
*
*
* Since: 2.0
*/
void
cogl_quaternion_pow (CoglQuaternion *quaternion, float exponent);
/**
* cogl_quaternion_slerp:
*
* 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:
*
*
* 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);
G_END_DECLS
#endif /* __COGL_QUATERNION_H__ */

4
cogl/cogl-types.h
View File

@ -118,6 +118,10 @@ cogl_object_unref (void *object);
*/
typedef void (* CoglFuncPtr) (void);
/* We forward declare this in cogl-types to avoid circular dependencies
* between cogl-matrix.h, cogl-euler.h and cogl-quaterion.h */
typedef struct _CoglMatrix CoglMatrix;
/**
* CoglFixed:
*

1
cogl/cogl.h
View File

@ -77,6 +77,7 @@ typedef struct _CoglFramebuffer CoglFramebuffer;
#include <cogl/cogl-buffer.h>
#include <cogl/cogl-pixel-array.h>
#include <cogl/cogl-vector.h>
#include <cogl/cogl-quaternion.h>
#include <cogl/cogl-texture-3d.h>
#include <cogl/cogl-index-array.h>
#include <cogl/cogl-vertex-array.h>

1
doc/reference/cogl-2.0/cogl-docs.xml.in
View File

@ -112,6 +112,7 @@
<xi:include href="xml/cogl-color.xml"/>
<xi:include href="xml/cogl-matrix.xml"/>
<xi:include href="xml/cogl-vector.xml"/>
<xi:include href="xml/cogl-quaternion.xml"/>
<xi:include href="xml/cogl-types.xml"/>
</section>

28
doc/reference/cogl-2.0/cogl-sections.txt
View File

@ -355,6 +355,34 @@ cogl_matrix_get_array
cogl_matrix_get_inverse
</SECTION>
<SECTION>
<FILE>cogl-quaternion</FILE>
<TITLE>Quaternions (Rotations)</TITLE>
CoglQuaternion
cogl_quaternion_init_identity
cogl_quaternion_init
cogl_quaternion_init_from_angle_vector
cogl_quaternion_init_from_array
cogl_quaternion_init_from_x_rotation
cogl_quaternion_init_from_y_rotation
cogl_quaternion_init_from_z_rotation
cogl_quaternion_equal
cogl_quaternion_copy
cogl_quaternion_free
cogl_quaternion_get_rotation_angle
cogl_quaternion_get_rotation_axis
cogl_quaternion_normalize
cogl_quaternion_dot_product
cogl_quaternion_invert
cogl_quaternion_multiply
cogl_quaternion_pow
cogl_quaternion_slerp
cogl_quaternion_nlerp
cogl_quaternion_squad
cogl_get_static_identity_quaternion
cogl_get_static_zero_quaternion
</SECTION>
<SECTION>
<FILE>cogl-pipeline</FILE>
<TITLE>Pipeline</TITLE>

1
doc/reference/cogl/cogl-docs.xml.in
View File

@ -97,6 +97,7 @@
<xi:include href="xml/cogl-buffer.xml"/>
<xi:include href="xml/cogl-vector.xml"/>
<xi:include href="xml/cogl-texture-3d.xml"/>
<xi:include href="xml/cogl-quaternion.xml"/>
</chapter>

28
doc/reference/cogl/cogl-sections.txt
View File

@ -658,3 +658,31 @@ cogl_program_uniform_matrix
cogl_offscreen_ref
cogl_offscreen_unref
</SECTION>
<SECTION>
<FILE>cogl-quaternion</FILE>
<TITLE>Quaternions (Rotations)</TITLE>
CoglQuaternion
cogl_quaternion_init_identity
cogl_quaternion_init
cogl_quaternion_init_from_angle_vector
cogl_quaternion_init_from_array
cogl_quaternion_init_from_x_rotation
cogl_quaternion_init_from_y_rotation
cogl_quaternion_init_from_z_rotation
cogl_quaternion_equal
cogl_quaternion_copy
cogl_quaternion_free
cogl_quaternion_get_rotation_angle
cogl_quaternion_get_rotation_axis
cogl_quaternion_normalize
cogl_quaternion_dot_product
cogl_quaternion_invert
cogl_quaternion_multiply
cogl_quaternion_pow
cogl_quaternion_slerp
cogl_quaternion_nlerp
cogl_quaternion_squad
cogl_get_static_identity_quaternion
cogl_get_static_zero_quaternion
</SECTION>