Friday, June 5, 2015

More colours

I got some help from a japanese friend of mine and he corrected my previous drawing. I was missing the signature, a proper tang, and the filed holes on the blade.

And a more realistic configuration. 

So, how did I make that?

Easy, you just take (uniform) random "kicks" in either direction with a random (Poisson distribution) size and you see what happens. Again, blue means going inside the screen and red going outside it.
The simple, yet perhaps important lesson, is that the red kink in the lower part of the blade is the sum of several other smaller kinks that interact with each other. This is not a local problem thus you cannot focus on the kink to fix the kink. Zeny-zen isn't it? well, that's the way the world is. To make the red kink disappear, you need to take care of all the red and blue circles, otherwise the kinks will just move around your blade.

Maybe tomorrow I make a video but I'm not sure, I don't think anybody is actually following this rambles. Should do Roubo benches instead.

Ok, sorry for that. I know I'm an awful teacher (that's why I don't give lectures) so when something is clear for me I don't see the point of explaining it further unless somebody asks me specific questions. So go ahead and ask if something is not clear.

For the sake of open source full disclosure and all that, this is the code for making the plots, runs in mathematica, which albeit not open source, comes in raspberry pi's linux dist:

nH = 20;
x0 = RandomReal[{-1, 3}, nH] // N;
y0 = RandomReal[{-1, 1}, nH] // N;
\[Sigma] = -Log[RandomReal[{0, 1}, nH]]/8 // N;
sign = If[# > 0.5, 1., -1.] & /@ RandomReal[{0, 1}, nH] // N;

surface = 
    sign[[i]] Exp[-((x - x0[[i]])^2 + (y + 
              y0[[i]])^2)^2/\[Sigma][[i]]], {i, nH}]];

DensityPlot[surface, {x, -3, 3}, {y, -3, 3}, 
 ColorFunction -> GrayLevel,
 PlotRange -> {{-4, 4}, {-4, 4}, Full}, PlotPoints -> 50, 
 RegionFunction -> 
  Function[{x, y, z}, x + 10 > 30 Abs[y/2] && x > -1], 
 Epilog -> {{White, Disk[{-1, .1975}, .07], Disk[{-1, -.1975}, .07]}, 
   Triangle[{{-2.5, -.125}, {-3.5, 0}, {-2.5, .125}}], 
   Rectangle[{-2.5, -.125}, {-.99, .125}], 
   Table[{If[sign[[i]] > 0, Red, Blue], 
     Circle[{x0[[i]], -y0[[i]]}, 0 \[Sigma][[i]]]}, {i, nH}]}, 
 FrameTicks -> None]


  1. Yes, and exactly what I was wishing that I could visually explain and describe....nailed it! Perfect!

    Roubo benches, hahahahahaha. Or the Studley tool chest (great book BTW)......

    As you well know, most people see this area as one of the "black arts" and beyond the abilities of anyone not a 4th generation blacksmith. Heck, most people don't even know what's out there, outside the doors of the local Woodcraft store, much less how common these great old saws are.

    Somewhere, sometime, someone will see this work and a light will illuminate.