We all remember the litany from various math classes we’ve taken, where frustration at a failure to understand a difficult concept bubbles over into the classic, “When am I ever going to need to know this in real life?” But as we all know, even the most esoteric mathematical concepts have applications in the real world, and failure to master them can come back to haunt you.
Take Voronoi diagrams, for example. While we don’t recall being exposed to these in any math class, it turns out that they can be quite useful in a seemingly unrelated area: converting PCB designs into easy-to-etch tessellated patterns. Voronoi diagrams are in effect a plane divided into different regions, or “cells”, each centered on a “seed” object. Each cell is the set of points that are closer to a particular seed than they are to any other seed. For PCBs the seeds can be represented by the traces; dividing the plane up into cells around those traces results in a tessellated pattern that’s easily etched.
This isn’t the first time we’ve seen Voronoi diagrams employed for PCB design, but the method looks so easy that we’d love to give it a try. It even looks as though it might work for CNC milling of boards too.
You may be familiar with origami, the Japanese art of paper folding, but chances are you haven’t come across smocking. This technique refers to the way fabric can be bunched by stitches, often made in a grid-like pattern to create more organized designs. Often, smocking is done with soft fabrics, and you may have even noticed it done on silk blouses and cotton shirts. There are plenty of examples of 18th and 19th century paintings depicting smocking in fashion.
[Madonna Yoder], an origami enthusiast, has documented her explorations in origami tessellations and smocking, including geometric shapes folded from a single sheet of paper and fabric smocked weave patterns. Apart from flat patterns, she has also made chain-linked smocked scarves stitched into a circular pattern and several examples of origami tessellations transferred to fabric smocking. Similar to folds in origami, the stitches used aren’t complex. Rather, the crease pattern defines the final shape once the stitches and fabric are properly gathered together.
Continue reading “Tessellations And Modular Origami From Fabric And Paper”
A breadboard is a great prototyping tool for verifying the sanity of a circuit design before taking the painstaking effort of soldering it all together permanently. After all, a mistake in this stage can cost a lot of time and possibly material, so it’s important to get it right. [daverowntree] wasn’t fully satisfied with the standard breadboard layout though, with fixed rows and columns. While this might work for most applications, he tried out a new type of prototyping board based on hexagons instead.
The design philosophy here revolves around tessellations, a tiling method for connecting the various components on this unique breadboard rather than using simple rows. The hexagons are tessellated across the board, allowing for some unique combinations that might make it slightly more complicated, but can have some benefits for other types of circuits such as anything involving the use of a three-wire device like a transistor.
The post is definitely worth a read, as [daverowntree] goes through several examples of this method of prototyping where the advantages are shown, like a voltage follower circuit and some other circuits involving transistor biasing. If you’re OK with the general design of breadboards, though, and just wished you didn’t have to do anything after the prototyping stage, we’ve got some help for you there as well.