flow or morph a spiral

i am trying to reproduce the rhino flow command in grasshopper.

the attached definition contains:

- a spiral that should be deformed

- a line, the base curve for the flow

- an arc, the target curve for the flow

any ideas how to perform the flow-like command?

is one of the morph/box components usefull in this case? i never used them, so have no experience ...

thanks in advance for any help