projecting a line with the curvature at different points

hi everyone,

I have a random curve with different division points on it, and what I am trying to do is extend a STRAIGHT line from those different points, and I suppose there is a bit of mathematics included because the vector of the line is taken from the vector of the curve from that specific point, I cannot seem to find a way to do it in grasshopper, I would appreciate it if someone would give me a hand with it. here is a screen shot of what I am trying to achieve.