Obviously vector rotation should be done with quaternion multiplication...

utils/space_ops.py

@@ -7,13 +7,46 @@ from constants import TAU
 from functools import reduce
 from utils.iterables import adjacent_pairs
 
-# Matrix operations
-
 
 def get_norm(vect):
     return sum([x**2 for x in vect])**0.5
 
 
+# Quaternions
+# TODO, implement quaternion type
+
+
+def quaternion_mult(q1, q2):
+    w1, x1, y1, z1 = q1
+    w2, x2, y2, z2 = q2
+    return np.array([
+        w1 * w2 - x1 * x2 - y1 * y2 - z1 * z2,
+        w1 * x2 + x1 * w2 + y1 * z2 - z1 * y2,
+        w1 * y2 + y1 * w2 + z1 * x2 - x1 * z2,
+        w1 * z2 + z1 * w2 + x1 * y2 - y1 * x2,
+    ])
+
+
+def quaternion_from_angle_axis(angle, axis):
+    return np.append(
+        np.cos(angle / 2),
+        np.sin(angle / 2) * normalize(axis)
+    )
+
+
+def quaternion_conjugate(quaternion):
+    result = np.array(quaternion)
+    result[1:] *= -1
+    return result
+
+
+def rotate_vector(vector, angle, axis=OUT):
+    quat = quaternion_from_angle_axis(angle, axis)
+    quat_inv = quaternion_conjugate(quat)
+    product = reduce(quaternion_mult, [quat, vector, quat_inv])
+    return product[1:]
+
+
 def thick_diagonal(dim, thickness=2):
     row_indices = np.arange(dim).repeat(dim).reshape((dim, dim))
     col_indices = np.transpose(row_indices)
@@ -64,10 +97,6 @@ def z_to_vector(vector):
     return np.dot(rotation_about_z(theta), phi_down)
 
 
-def rotate_vector(vector, angle, axis=OUT):
-    return np.dot(rotation_matrix(angle, axis), vector)
-
-
 def angle_between(v1, v2):
     return np.arccos(np.dot(
         v1 / get_norm(v1),