Stereographic Projection take 2

The first time we took on stereographic projection, I discussed how it reminded me of the little kid night lights that projected starry nights onto the ceiling. When attempting to replicate the starry night, I failed and turned it into a cloudy night projection. Because I was annoyed I couldn't make it work and because right after I finished my project last time, I came up with new ideas, I decided to repeat the stereographic projection example and make it better.

Last time, I used an array of clouds out of frustration because I could not get stars to work. My clouds were each made up of four circles and then I just multiplied them across an array. Well, that was boring. And while I still haven't been able to create the perfect star, I have decided to create a recognizable constellation rather than an array. Since I still couldn't figure out how to use the hull function properly with stars, I decided to create my constellation using lines. I thought this was a genius idea but when I was finished, I realized a piece of my final sphere would be missing, so I scratched that idea too. Eventually, I decided to plot the points where a star would be and hull them to a single point above.

The constellation I chose to replicate is the big dipper because it is a fairly recognizable constellation in my opinion but for those who don't know what it looks like, you can see a picture from azcentral.com below:

I was able to make improvements from my last example by plotting individual points in specific places on the grid to form a constellation rather than just forming an array of identical shapes. I couldn't find actual points of the stars in the constellation, so I just maneuvered the location of the points until it resembled the big dipper. The image below shows the constellation I created.

While the points are pentagons and not quite stars, you are still able to see the constellation form between all of the points! My final object will be a sphere and when a flashlight is shown through the top hole, a projection of the big dipper will appear on the wall. This design was more challenging than my first example and although there was probably a simpler way to code it, my example still runs and I think the print will turn out well.