I built this diagonal kitchen sink cabinet about 40 years ago.  The hinges are shot.  They are very old school and I can't find a model number on them.  The hinges do not clip to the mounting plate, there is a screw that holds the hinge to the plate.

Looking at the Blum catalog, the 79B3598 is a modern replacement (see PDF).  I realize I will need to redrill the doors for the Inserta mounting system.  There is another version with screw mount that should bolt right in, but I prefer to upgrade to the Blumotion. so I will deal with any plugging and redrilling.

When I purchased the original hinges they came packaged with the mounting plates.  As far as I can tell the hinges and mounting plates are now sold separately, and the Blum catalog page does not specify which plate is compatible.

I can see that I need H=0mm mounting plates, and the construction is frameless, but I cant figure out which mounting plate to order.  With wood screw attachment, there is

Std 1 piece wing 173L6100
Cam adjust wing 173H7100
Std 2 piece wing 175H7100
Cam adjust in line 175H3100

The standard 2 piece wing style is similar to what I have worked with in the past.  I am not familiar with the cam adjust syle.

Thanks for your help

79B355180 or 79B3558 for the screw version IIRC (don't have the catalog in front of me)

Cam adjustment range is smaller, but it's useful for inset.  Mostly a nice to have though, using only one of your hinges cam.

The reason they don't come with the mounting plates is because they are "modular".
The exact same hinge can be use in several different configurations. The thinnest one is for a "full overlay" door, then there is one that is intended for "half overlay", and also "inset" which are the thickest. 
There are hinges made specifically for each of those situations too, and they all use the thin plate.
Most of the Blum hardware is like that. Drawer guides don't come with the clips to hold them to the drawer either.