Confusing tf transforms

edit

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.

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)"