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/*
* Copyright © 2013 Keith Packard <keithp@keithp.com>
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; version 2 of the License.
*
* This program 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
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program; if not, write to the Free Software Foundation, Inc.,
* 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA.
*/
#ifndef _AO_QUATERNION_H_
#define _AO_QUATERNION_H_
#include <math.h>
struct ao_quaternion {
float r; /* real bit */
float x, y, z; /* imaginary bits */
};
static inline void ao_quaternion_multiply(struct ao_quaternion *r,
const struct ao_quaternion *a,
const struct ao_quaternion *b)
{
struct ao_quaternion t;
#define T(_a,_b) (((a)->_a) * ((b)->_b))
/*
* Quaternions
*
* ii = jj = kk = ijk = -1;
*
* kji = 1;
*
* ij = k; ji = -k;
* kj = -i; jk = i;
* ik = -j; ki = j;
*
* Multiplication p * q:
*
* (pr + ipx + jpy + kpz) (qr + iqx + jqy + kqz) =
*
* ( pr * qr + pr * iqx + pr * jqy + pr * kqz) +
* (ipx * qr + ipx * iqx + ipx * jqy + ipx * kqz) +
* (jpy * qr + jpy * iqx + jpy * jqy + jpy * kqz) +
* (kpz * qr + kpz * iqx + kpz * jqy + kpz * kqz) =
*
*
* (pr * qr) + i(pr * qx) + j(pr * qy) + k(pr * qz) +
* i(px * qr) - (px * qx) + k(px * qy) - j(px * qz) +
* j(py * qr) - k(py * qx) - (py * qy) + i(py * qz) +
* k(pz * qr) + j(pz * qx) - i(pz * qy) - (pz * qz) =
*
* 1 * ( (pr * qr) - (px * qx) - (py * qy) - (pz * qz) ) +
* i * ( (pr * qx) + (px * qr) + (py * qz) - (pz * qy) ) +
* j * ( (pr * qy) - (px * qz) + (py * qr) + (pz * qx) ) +
* k * ( (pr * qz) + (px * qy) - (py * qx) + (pz * qr);
*/
t.r = T(r,r) - T(x,x) - T(y,y) - T(z,z);
t.x = T(r,x) + T(x,r) + T(y,z) - T(z,y);
t.y = T(r,y) - T(x,z) + T(y,r) + T(z,x);
t.z = T(r,z) + T(x,y) - T(y,x) + T(z,r);
#undef T
*r = t;
}
static inline void ao_quaternion_conjugate(struct ao_quaternion *r,
const struct ao_quaternion *a)
{
r->r = a->r;
r->x = -a->x;
r->y = -a->y;
r->z = -a->z;
}
static inline float ao_quaternion_normal(const struct ao_quaternion *a)
{
#define S(_a) (((a)->_a) * ((a)->_a))
return S(r) + S(x) + S(y) + S(z);
#undef S
}
static inline void ao_quaternion_scale(struct ao_quaternion *r,
const struct ao_quaternion *a,
float b)
{
r->r = a->r * b;
r->x = a->x * b;
r->y = a->y * b;
r->z = a->z * b;
}
static inline void ao_quaternion_normalize(struct ao_quaternion *r,
const struct ao_quaternion *a)
{
float n = ao_quaternion_normal(a);
if (n > 0)
ao_quaternion_scale(r, a, 1/sqrtf(n));
else
*r = *a;
}
static inline void ao_quaternion_rotate(struct ao_quaternion *r,
struct ao_quaternion *a,
struct ao_quaternion *b)
{
struct ao_quaternion c;
struct ao_quaternion t;
ao_quaternion_conjugate(&c, b);
ao_quaternion_multiply(&t, b, a);
ao_quaternion_multiply(r, &t, &c);
}
static inline void ao_quaternion_init_vector(struct ao_quaternion *r,
float x, float y, float z)
{
r->r = 0;
r->x = x;
r->y = y;
r->z = z;
}
static inline void ao_quaternion_init_rotation(struct ao_quaternion *r,
float x, float y, float z,
float s, float c)
{
r->r = c;
r->x = s * x;
r->y = s * y;
r->z = s * z;
}
static inline void ao_quaternion_init_zero_rotation(struct ao_quaternion *r)
{
r->r = 1;
r->x = r->y = r->z = 0;
}
#endif /* _AO_QUATERNION_H_ */
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