Get vector representation of x, y, z axis from geometry_msgs Pose

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Here's a simple Python version:

import numpy as np
import geometry_msgs.msg
import tf
import tf_conversions

p = geometry_msgs.msg.Pose()
# let's define a positive rotation of pi/4 rad about the reference frame's z-axis:
q = tf.transformations.quaternion_from_euler(np.pi/4, 0, 0, 'szyx')
p.orientation = geometry_msgs.msg.Quaternion(*q)

# now let's compute the desired x-axis components in a few ways:
print "x1 =",tf_conversions.fromMsg(p).M.UnitX()
print "x2 =",(tf.transformations.quaternion_matrix(q))[0:3,0]

It sounds like you're using C++ and looking for a vector in the parent frame with the same direction as the x axis of the child frame, or vector D in this picture.

You've got the geometry_msgs/Pose expressed as a tf::Transform, that's great! The basis of the transform is the rotation matrix to go from the child frame to the parent frame. An x axis vector is (1,0,0). To transform an x axis vector from the child frame to the parent frame you can use operator*(Matrix3x3, Vector3) from the following link

http://docs.ros.org/jade/api/tf2/html...

tf::Transform my_pose = ... //You already have this
tf::Vector3 x_axis(1,0,0);
tf::Vector3 D = myPose.getBasis() * x_axis;

Make sure to do matrix * vector and not vector * matrix. The latter will return the parent x axis expressed in the child frame.