Deforming Trefoil Knot

Hello world !!

I'm trying to deform a trefoil knot made mathematically but I'm not very proud of the result.

In the equation, like you see in the pictures, t is the domain (-pi and pi), r controls the scale of the curve and e the amplitude (when it's 0 it's a flat trefoil).

I'm trying to deform the first trefoil by mixing him with another one with a bigger amplitude: I obtain the curve on the third picture by cutting parts of the two base curves and joining them with the "blend crv". I'm not very happy with the result.

Like you see in the fourth picture, the nice smoothness of the mathematically done curve is gone and it's just a messy "rafistolage".

Now I'm gonna try a different approach, deform parts of the first curve by attracting them by some points in space. The thing is that I'm not very sure how to proceed next because i want the lowest parts of the curve to remain the same...

I was also wondering if there is a mathematical way to do that by adding variables to the functions... ? Or maybe saying for example that from "this" domain to "this" domain it takes results closer to the function with the smaller amplitude and from "this" domain to "this" domain it takes results closer to the other function... I'm very opened to any advises!

Maybe what i want to achieve can be a done with the spatial deform component or the other scale components... ?

Or with forces using kangaroo ?

I'm not sure if my explanations are very clear, thanks in advance for your help.