X-Git-Url: https://git.gag.com/?p=fw%2Faltos;a=blobdiff_plain;f=src%2Fcore%2Fao_quaternion.h;h=044f1607d8b4a8aabba54841aaae7da47ec6434a;hp=f4b8aaa49a40f99ea572521722c523e7055096f7;hb=bb9fdef607728cc326a82aa632e59724f272e53b;hpb=08143a922fe27bc50a19924f46538f9476ab5fd1

diff --git a/src/core/ao_quaternion.h b/src/core/ao_quaternion.h
index f4b8aaa4..044f1607 100644
--- a/src/core/ao_quaternion.h
+++ b/src/core/ao_quaternion.h
@@ -26,11 +26,44 @@ struct ao_quaternion {
 };
 
 static inline void ao_quaternion_multiply(struct ao_quaternion *r,
-					  struct ao_quaternion *a,
-					  struct ao_quaternion *b)
+					  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);
@@ -40,7 +73,7 @@ static inline void ao_quaternion_multiply(struct ao_quaternion *r,
 }
 
 static inline void ao_quaternion_conjugate(struct ao_quaternion *r,
-					   struct ao_quaternion *a)
+					   const struct ao_quaternion *a)
 {
 	r->r = a->r;
 	r->x = -a->x;
@@ -48,7 +81,7 @@ static inline void ao_quaternion_conjugate(struct ao_quaternion *r,
 	r->z = -a->z;
 }
 
-static inline float ao_quaternion_normal(struct ao_quaternion *a)
+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);
@@ -56,7 +89,7 @@ static inline float ao_quaternion_normal(struct ao_quaternion *a)
 }
 
 static inline void ao_quaternion_scale(struct ao_quaternion *r,
-				       struct ao_quaternion *a,
+				       const struct ao_quaternion *a,
 				       float b)
 {
 	r->r = a->r * b;
@@ -66,7 +99,7 @@ static inline void ao_quaternion_scale(struct ao_quaternion *r,
 }
 
 static inline void ao_quaternion_normalize(struct ao_quaternion *r,
-					   struct ao_quaternion *a)
+					   const struct ao_quaternion *a)
 {
 	float	n = ao_quaternion_normal(a);
 
@@ -76,18 +109,78 @@ static inline void ao_quaternion_normalize(struct ao_quaternion *r,
 		*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,
-					struct ao_quaternion *a,
-					struct ao_quaternion *b)
+					const struct ao_quaternion *a,
+					const 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_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)
 {
@@ -113,4 +206,44 @@ static inline void ao_quaternion_init_zero_rotation(struct ao_quaternion *r)
 	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_ */