The first thing is to write a function to draw a bezier curve. I could have used lines, but I feel bezier curves look nicer.

I use a very simple algorithm, which can be visualized with this animation:

• We have point Q0(t) which varies from P0 to P1.
• We have another point Q1(t) which varies from P1 to P2.
• A third point Q2(t) varies from P2 to P3.
• We then compute R0(t) which varies from Q0 to Q1
• We compute R1(t) which varies from Q1 to Q2
• We then get the final point we are interested by varying R0 to R1.