Confusing tf transforms

edit

I think what is missing here is a concrete math proof.

I came across this on the coursera website, see this link. Watch from 10:40 till the end.

Read this after watching the above video once -

The video explains how to get source datapoint using the Rotation Matrix. The opposite ( by taking a simple transpose of Rotation matrix ) is true for getting the target data point in the source frame, you have to use the inverse of the Rotation matrix ( Rotation required to convert source to target basis vectors )

Hence it also explains ( taken from the above answer by @tbh )

"When referring to transform between coordinate frames (transforming the frames, it is the inverse of the transform of data between the two frames)"

Hmm, that is weird. Looking at the python documentation it looks like you're correct:

lookupTransform(target_frame, source_frame, time) -> (position, quaternion)

Then, looking at the cpp documentation, the order is the same:

void Transformer::lookupTransform  ( const std::string &  target_frame,  
                                     const std::string &  source_frame,  
                                     const ros::Time &  time,  
                                     StampedTransform &  transform  
                                     )  const 

Get the transform between two frames by frame ID. 
Parameters:
target_frame The frame to which data should be transformed  
source_frame The frame where the data originated  
time The time at which the value of the transform is desired. (0 will get the latest)  
transform The transform reference to fill.

I read that to mean it returns the source_frame described with respect to the target_frame.

But for some reason, the code for the tf_echo tool has this:

echoListener.tf.lookupTransform(source_frameid, target_frameid, ros::Time(), echo_transform);

So it looks like that will definitely provide the inverse of what your python function is providing.

And the documentation for the tf_echo tool says:

tf_echo <source_frame> <target_frame>- Print information about a particular transformation between a source_frame and a target_frame. For example, to echo the transform between /map and /odom: rosrun tf tf_echo /map /odom

This is worded vaguely, the word "between" doesn't indicate direction. If this is the way tf_echo is suppose to work, it should really say something like "this prints the target_frame described with respect to the source_frame". I wonder if this is an error. At a minimum the description should be made more clear.