Pass data to front end with REST api

This is probably simple but I cant seem to understand changing a front end on back end data changes.

So I have a front end that is plotting 3d points. I also have a separate program that is getting and processing the points. When I finish processing I want to send them to my front end and tell it to draw them. How do I do this?? What tells the front end to wait and listen to receive data?

I have tried making my backed send a PUT request when it is finished but I dont understand how to connect the two...