The basal triangle

This post is not related to any of my previous girlfriends.

I got a mail from one of our loyal readers making me notice two things. First, I confused rake and slope  and fleam in the previous post, now it's fixed.

Second, our attentive reader said something along the lines of, "ok mister physics. you think you are so smart no? Then why I cannot see in your model the little triangle on the base of the teeth that is so typical of Japanese saws? Regards, Mirijam."

What triangle? I replied. Then she sent me a picture.

I think she hacked my iCloud account, because that saw looks uncanny similar to my cross cut dozuki. And also this one.

Which again, looks like my Azebiki. I should stop using my mail address as the password for all my accounts. 

I think she meant the the triangle that one can see on the front of the teeth. (The back of the teeth is where you don't file. They looks completely flat from behind. This reminds me of someone... maybe an ex-gf?)

You can see that the basal triangle (anyone knows the japanese term for it?) is smaller on the cross cut dozuki, which also has finer teeth and cuts way nicer than the azebiki.

So, puzzled with this basal triangle and how it comes to being, I called a scientist. A real one, that is. Enters @elnicorivas

I was modelling the file as 2 planes, but when I wanted to model the cutting from 2 different sides, at 2 different rake, slope and fleam, I needed matrices. Not that I don't like them, but I failed Quatum Mechanics once because of them. But nico didn't. So he wrote the code to rotate the "file" in any angle you want to and I made the gif. 

Look mom, I made a gif without a cat on it. 

The yellow square is a piece of steel. Each snapshot shows the result of filing once on each side of the tooth. 

Yes indeed. That looks like a triangle.  

You still need to file to top eye, or third facet, but you catch my drift, don't ya?

Thanks a lot Mirijam for your insightful input, but it's really not cool steal other people's iCloud photos, don't do it again. Promise? 

When I did this, I realised something else...  you need to file at a constant position, the file only moves on the vertical direction, so to say, it only goes "down" when you file. I had trouble understanding how to do this, and the 3D model opened my eyes. Now I try it in the real world.

Thanks for rotating the planes nico!