Then I thought that maybe the best option is to ass points that are on the curve.

What you need is:
– 4 points of a Bezier curve
– 2 equations to yield values for x and y
– number of points you want to “rasterize” your curve

Take this example :
M0,0
c35,0,50-50,100-50
The four points are 0,0; 35,0; 50,-50 ; 100,-50; (0,0 because it’s relative coordinates).

This link http://www.moshplant.com/direct-or/bezier/math.html gives you the explanation to calculate 6 values and create the two equations (one for x one for y).

Because the Bezier curve is defined in [0,1], it’s easy to pick up values:
– to have one extra point, take 1/2
– to have 3 extra points, take 1/4, 1/2 and 3/4

In my example, I want to add 3 points. The equations give me this:
v=0.25
x=23.359375
y=-7.8125

v=0.5
x=44.375
y=-25

v=0.75
x=68.203125
y=-42.1875

Now, you have to change your path.
It was: c35,0,50-50,100-50
Meaning: a curve from 0,0 (current point) to 100,-50

Now you have to draw 4 lines.
You need to calculate relative coordinates for each new point and the new coordinates of the final point (100,-50).

you start at 0,0
then 23.359375,-7.8125
then you need to subtract the x and the y with the previous

Then you create 4 lines:

l23.359375-7.8125
l21.015625,-17.1875
l23.828125,-17.1875
l31.796875,-7.8125

And voilà! You have 4 segments instead of a Bezier curve.

Tip: add all x and all y and you find the final point.