a simple idea is to first calculate total width of the curve then divide with number of steps or segments whatever we say, this is avg. for all those steps or if i predefined space i.e 20px on each then i have to increase steps as there will be shortage of steps on predefined space.
You can have infinite points, but a quick way is to get the distance of the line, and divide that by a certain amount that will make up the segments of that curve.
The divisor is what you would call the resolution. How smooth it is.
You can use log or ^ if you think you will need to scale a lot.