+++ /dev/null
-/*
- * 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 float ao_quaternion_dot(const struct ao_quaternion *a,
- const struct ao_quaternion *b)
-{
-#define T(_a) (((a)->_a) * ((b)->_a))
- return T(r) + T(x) + T(y) + T(z);
-#undef T
-}
-
-
-static inline void ao_quaternion_rotate(struct ao_quaternion *r,
- const struct ao_quaternion *a,
- const struct ao_quaternion *b)
-{
- struct ao_quaternion c;
- struct ao_quaternion t;
-
- ao_quaternion_multiply(&t, b, a);
- ao_quaternion_conjugate(&c, b);
- ao_quaternion_multiply(r, &t, &c);
-}
-
-/*
- * Compute a rotation quaternion between two vectors
- *
- * cos(θ) + u * sin(θ)
- *
- * where θ is the angle between the two vectors and u
- * is a unit vector axis of rotation
- */
-
-static inline void ao_quaternion_vectors_to_rotation(struct ao_quaternion *r,
- const struct ao_quaternion *a,
- const struct ao_quaternion *b)
-{
- /*
- * The cross product will point orthogonally to the two
- * vectors, forming our rotation axis. The length will be
- * sin(θ), so these values are already multiplied by that.
- */
-
- float x = a->y * b->z - a->z * b->y;
- float y = a->z * b->x - a->x * b->z;
- float z = a->x * b->y - a->y * b->x;
-
- float s_2 = x*x + y*y + z*z;
- float s = sqrtf(s_2);
-
- /* cos(θ) = a · b / (|a| |b|).
- *
- * a and b are both unit vectors, so the divisor is one
- */
- float c = a->x*b->x + a->y*b->y + a->z*b->z;
-
- float c_half = sqrtf ((1 + c) / 2);
- float s_half = sqrtf ((1 - c) / 2);
-
- /*
- * Divide out the sine factor from the
- * cross product, then multiply in the
- * half sine factor needed for the quaternion
- */
- float s_scale = s_half / s;
-
- r->x = x * s_scale;
- r->y = y * s_scale;
- r->z = z * s_scale;
-
- r->r = c_half;
-
- ao_quaternion_normalize(r, r);
-}
-
-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;
-}
-
-/*
- * The sincosf from newlib just calls sinf and cosf. This is a bit
- * faster, if slightly less precise
- */
-
-static inline void
-ao_sincosf(float a, float *s, float *c) {
- float _s = sinf(a);
- *s = _s;
- *c = sqrtf(1 - _s*_s);
-}
-
-/*
- * Initialize a quaternion from 1/2 euler rotation angles (in radians).
- *
- * Yes, it would be nicer if there were a faster way, but because we
- * sample the gyros at only 100Hz, we end up getting angles too large
- * to take advantage of sin(x) ≃ x.
- *
- * We might be able to use just a couple of elements of the sin taylor
- * series though, instead of the whole sin function?
- */
-
-static inline void ao_quaternion_init_half_euler(struct ao_quaternion *r,
- float x, float y, float z)
-{
- float s_x, c_x;
- float s_y, c_y;
- float s_z, c_z;
-
- ao_sincosf(x, &s_x, &c_x);
- ao_sincosf(y, &s_y, &c_y);
- ao_sincosf(z, &s_z, &c_z);
-
- r->r = c_x * c_y * c_z + s_x * s_y * s_z;
- r->x = s_x * c_y * c_z - c_x * s_y * s_z;
- r->y = c_x * s_y * c_z + s_x * c_y * s_z;
- r->z = c_x * c_y * s_z - s_x * s_y * c_z;
-}
-
-#endif /* _AO_QUATERNION_H_ */