What is a good way of storing robot paths and access them?

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Hi guys

I am writing a controller for a 6DOF robot arm. I am generating paths for the robot to come from the starting point to a desired pose. To do this I do a piecewise polynomial interpolation. Meaning that I first easily interpolate linearly over time between the two points. And then I attach a 6-degree polynomial in the beginning and the end to smoothen the motion. It looks then as follows:

Now I have the problem, that because of numerical issues (at least I think so) or because of time discretization, I got small jumps between the different polynoms:

My idea is now to just filter the paths to get rid of these jumps. For this I need to store the path somehow that I can filter it but I don't really have an idea what is a good way of doing this. How are paths saved for example in MoveIt? Do they save discrete or continuous paths? Is there a way of connecting my polynoms to make it "filterable"?

Thanks for your help!