How to create a curved line vector plot of a triangle in Python?

Question

Question

Suppose one has 3 random coordinates with 3 random functions that describe the continuous lines between them*, how would one create a vector plot in Python that allows for smooth lines after infinite zooming in?

Example

The functions should be rotated and translated from their specification to map onto the edge/line in the geometry. For example, one curved line may be specified as -x(x-5)=0 which describes the line from (x,y) coordinates:(2,6) to (5,2) (which has length 5). Another curved line from (x,y) coordinates:(2,2) to (2,6) may be specified as sin(x/4*pi)=0. One can assume all bulges point outward (of the triangle in this case).

Approach

I can perform a translation and rotation of the respective functions to the lines of the coordinates, and then save the plt as a .eps or .pdf, however before doing that, I thought it would be wise to ask how these functions are represented and how these plots are generated, as I expect the dpi setting may simply turn it into a (very) high resolution plot, instead of something that still provides smooth lines after infinite scrolling.

Doubt

I can imagine using a sinusoid does not allow for infinite smooth scrolling as they may be stored numerically. If the representation is finite for sinusoids but analytical/symbolic for polynomials, I would be happy to constraint this question to polynomials only to get smooth infinitely scrollable images (like fractals).