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Diffstat (limited to 'src/core/ao_quaternion.h')
| -rw-r--r-- | src/core/ao_quaternion.h | 249 | 
1 files changed, 0 insertions, 249 deletions
diff --git a/src/core/ao_quaternion.h b/src/core/ao_quaternion.h deleted file mode 100644 index 044f1607..00000000 --- a/src/core/ao_quaternion.h +++ /dev/null @@ -1,249 +0,0 @@ -/* - * 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_ */  | 
