One of the disadvantages about not working at an office anymore is that there is no air-conditioning. So, when it is in the upper twenties, I have to sweat it out. In other words, I’m not that productive these days.
But, if I ignore the 9-5 schedule, I can do better. It is nice and cool right now. (At least it is outside. The outside temperature hasn’t migrated to the indoors yet. But it is not baking.) In other words, take a siesta during the day and work late at night.
My contract job has been oddly silent and not giving me anything to do, so I’ve been working on my own program. There I’ve been struggling.
On Friday I talked to a gaggle of mathematicians and I got a good perspective on what I’m trying to do. The goal is for every map to allow a rectangle to be selected as either a new map or a sub-map. The problem I’ve been faced with is that spheres aren’t that happy about having squares on them. I’ve been using a Rubik’s puzzle of a sphere/globe to organize my thoughts. (Which I cannot find mentioned anywhere on the internet, so I have no way to easily solve it.) There is a sort-of-square on it, and so that is what I’m trying to replicate. The mathematicians were able to point out that the “square” is bounded by great circles. With that, I had a direction to go.
I started doing research with the graphing calculator that comes with every Mac. It’s been invaluable as a testing platform. I don’t think it is happy with me though; I’ve been bringing it to its knees.
Just now I finally got the math working and entered it into my program. It is correctly displaying a great circle going west to east that goes through the two points I wanted.
This whole project would probably have been easier if I had done it in second year university when I was taught about planes, dot products and cross products. I still have my text book from then, but it was a used one and has been very marked up. I’m also not that happy with the production value. It was published in, let me check…1976! Okay, updated in 1988, but still… That might explain why I had so much trouble finding out about dot products and cross products. I don’t think they were invented back then, at least not by those names.
Basically, the internet has saved me a lot of trouble.