How to use custom (user specified) quadrature for different mesh elements?


My application requires using custom quadrature points and weights for mesh elements. Note that the user-specified quadrature points change from one element to another (even if element shape is not changing), so it’s not a consistent scheme. From searching, it seems the place to look at is FIAT/ Is it possible to pass the element id to the quadrature scheme somehow so that the appropriate quadrature rule is returned (say from a look-up table)? Another approach could be to create a mesh with custom elements with user defined quadrature rule.
Any help will be appreciated. Thank you.