Voronoi Partition

now that you're comfortable reading shading packets let's get to work to begin let's step back and simplify the problem a dino leg is essentially a cylinder with claws at the bottom let's ignore the claws for the moment and if we unwrap the cylinder we get a flat rectangle or a 2d plane we can do all the work like this in a flat plane and then wrap it up whenever we want to test it out let's first think about the geometry of our dino scales each scale is an irregular shape and all of these different scales need to fit together like a puzzle at Pixar we use a really cool trick to generate these kinds of patterns it's known as a Voronoi diagram it's based on a pattern we see all over the place in the natural world from the spots on a giraffe to the cracks that form when mud dries and I love that we can explain the math behind boring patterns with bubbles if we fill a container with bubbles like this they squish together and we get the same pattern based on where the bubbles touch let's think about the geometry of what's going on here we start by placing a few points somewhere on the plane doesn't matter where imagine they are tiny bubbles let's call these sites and then we blow them up into larger bubbles eventually the neighboring bubbles collide at a single point as they expand this grows into a line where they squish together these bubble boundaries is where we draw our lines and watch what happens when we do this with many sites scattered about we get this irregular puzzle pattern and that's it a Voronoi pattern or Voronoi partition if you really want to show off we'll call each of these bubble regions as cell so we have sites and cells and there are some really interesting properties here the border of each cell is always the same distance to the two nearest sites and wherever three lines meet we get a point or a vertex right here and this is equally distant to the 3-years sites all thanks to the awesome power of math let's stop here and make sure that you understand how to draw these Voronoi patterns the following exercise will get you thinking about how these work it's also a great time to grab a pencil and paper remember dueling is your friend do you have a good story about Voronoi patterns I do when we were working on the Incredibles we had this cake that was absolutely beautiful and it was made for Bob Parr was going to take a big bite out of it and it was full of these beautiful bubbles and the craft was shiny and it was moist and it was really really gorgeous and then the story changed a little bit and the shot ended up being filmed all at night so you can never see all those beautiful Borno bubbles sounds delicious