I'm not sure if this is on topic, but I can share it.
When I was in college, I had begun to learn how to create 3D models using Renderware for use in ActiveWorlds. I was working with a guy who ran an ActiveWorlds instance and he said if I learned how to use that language, then I could help on his project. So I went about trying to learn it. While 3D UI modelling programs were available, they were out of reach for me financially, and the conversion tools were not as good as I would have liked. So there was no shortcutting the process. I would first draw objects onto graph paper, determine their vertices and connect them. The vertices are all three dimensional coordinates. And this was done only using graph paper and Notepad.exe to create the object file. When I think I am done, I load the file into the renderer and see how it looks.
It was quite difficult for me at first. One wrong coodinate means that the object has one point shooting off into the distance. I remember the day in the computer lab, the day that it just clicked and I figured it out. A literal eureka or lightbulb moment. I then moved away from the complex shape training I was doing and moved into a more complex project. My goal then was to create a 3D model of the Iomega Ditto Max tape drive. It took some weeks but I did finally manage to do it. I remember it being 11 pages of code, which I then printed.
My Technical Math professor at college had said at the beginning of the semester that everyone had to pick a project, and half way through he would meet with everyone to see how the progress was. I didn't really pick anything from his list, but when I had the meeting I brought the printout of the code for the 3D model. I showed him that and the original graph paper drawings and explained how I had determined the vertices in 3D space for each and went through the code to show how those were used to construct polygons. That did end up being related to a chapter in the text book, although it was not in such detail. He understood that connection and said I didn't have to come to class anymore and I got an A for the course.
Fully understanding relationships of vertices and vectors changed how I viewed certain things. I was now able to see angles in real life. The best real world example was from playing pool. I was immediately able to identify the appropriate shot that had to be taken. In the end, I didn't get to do much work in ActiveWorlds, and eventually Renderware became well known starting as the engine used by Rockstar in Grand Theft Auto III and many other games. A couple years later I ended up working on learning creating interactive images using the vector-based SVG language, which was uniquely powerful... Including the creating of a fully text-based website that used zero actual images and was created solely using XML and SVG. Projects of a bygone era, I never do anything like that anymore.
