Unity-UI-Polygon | Polygon renderer for the new Unity UI | Graphics library

You want to fit your points onto a unit circle, and then scale if desired.

Given a number of vertices >= 3, the angle between each vertex is 360/(number of vertices)

e.g., for 5 vertices, each vertex must be 72 degrees apart.

Now, with a starting angle of 0 degrees, for each vertex, your x-coordinate is the cosine of your starting angle, and your y-coordinate is the sine of your starting angle. After each vertex, increment your starting angle by the above-calculated angle.

Here's some Matlab code which demonstrates what I'm saying for a polygon containing 13 vertices: