# Day 21: 23 February 2013

**7:58:** I’m hoping to get lots done today and this weekend. Like I said yesterday, suddenly seeing a ‘2’ in the day number is a little scary.

Yesterday, I stated that I wanted to get this transformation stuff knocked out today, or at least this weekend. That’s still the hope, but I think I need to be realistic. A day completely packed with hard math like these transformation matrices is almost a guarantee to fry me.

So I’m trying to find some alternative things that are a bit lighter to do during the day as well. That will help break up the monotony. I don’t know exactly what those things are yet, though.

**14:55:** Geez. How many times to I need to learn this? **The cross product of two unit vectors is not necessarily a unit vector! Only the cross product of two perpendicular unit vectors is a unit vector.**

**17:19:** Perhaps you already saw, but I just posted a different post explaining my basis transformation code. This is what I’ve been working on all day, and takes what I’ve been working on all week and pushes it to the next level.

I also wrote the inverse of this, to transfer back out of a basis to the original coordinate system.

Now I need to make sure that they “stack” appropriately. That is, if I have a piece attached to another piece attached to another piece, they should all get transformed correctly. I *think* they will, since that’s how matrices are supposed to work, but if not… I may still have a long way to go.

**19:34:** I’ve got to stop. My mind is pretty worn out. But I think it’s working, for the most part. In order to really wrap this up, I’m going to need to make sure I can transform rays and points from one coordinate space to another. I think that should be pretty easy to do, considering that that’s technically what’s being done as it’s being drawn.

I think, though, that tomorrow is going to be a bit of a lighter day. I’ll find some less complicated things to work on for most of my time tomorrow.

Anyway, below is a picture of what I’ve got right now. Yes, it looks like some sort of creepy virus that grew guns on it.