Escher Lizard Flooring Project (part 2)

So at the end of the last episode, I had (what I hoped) was the data for a lizard shape that should be perfect for tesselating. Should.

I mean: the principle seems sound, and I’ve spent a fair amount of time copying and rotating the results in an art package to check that there is no obvious error. But that’s not the same thing as dealing with proper laser-cut lumps of wood.

My code that exports DXF data (apparently the standard requirement for laser cutting software) was largely untested. The DXF format is a bit of a pain to handle – there’s lots of bits of information that seem more or less optional – but some software expects it, and some doesn’t. For example, none of my data would load into Inkscape (a mature, open-source vector-art package) but the SolidWorks eDrawings viewer and AutoCAD both accepted it without complaint (thanks to Trevor Johnson for testing my data for me). So without having access to laser cutting software, I was working in faith.

I was also concerned about rounding errors. For those who don’t do computer programming: rounding errors occur when you try and represent a floating-point number (a number that may have a decimal point in it and an arbitrary number of digits after it) in a limited number of bytes. Though it makes a good job for most purposes, you normally find that any calculation rounds up or down after a number of decimal places – so the number that gets stored may be not-quite the number that was calculated.

Compound rounding errors are when you use these rounded-numbers in further calculations – so a resulting number you need to use may be the product of multiple intermediate floating-point numbers, each one possibly subject to a rounding error of its own.

For 99.99998% (see what I did there?) of the time, this degree of precision is acceptable. If I were only dealing with pixels on a screen, for example, it would be no problem. But I have no idea how much accuracy is important when cutting large chunks of wood to millimetre-accuracy. Nor do I know how forgiving wood is – how much it might expand or compress, for example, when you’re thumping pieces together with a mallet.

And I’m about to use this untested data to get a lot of flooring cut, potentially wasting a huge amount of money. Ho boy.

It seemed sensible to get some test pieces cut, to “prove” the data. Test pieces that don’t necessarily have to be “actual” size – as long as I scale both the X and Y axis the same and all the lizards are identical then that should be a good test.

I tried a number of avenues for this. I began with a local acrylic company, who claimed to be able to cut any shape. It seems they’re more used to cutting any shape they design, and are more prepared for the design aspect than for people who approach them with the data ready-done. Next I tried visiting the Nottingham Hackspace (who were lovely, by the way – if you live nearby then they’re worth a visit) but the timescale required to sign-up, get membership sorted, get an induction on the laser-cutter – all made it a bit difficult to work with my timetable. And I have a forty-mile round trip every time I want to visit, and a lot of train fare.

But then I found Martin Raynsford, a designer and hobbyist with his own laser cutter who does a good trade in custom design and precision woodworking jobs. Have a look at his blog or website if you need any hobby inspiration or are just stuck for birthday present ideas for the geek in your life.

He was able to load my created data (proving that my data would be accepted by cutting software) and produce these shapes from 6mm laser-grade plywood:


I received them through the post in a few days, and am incredibly happy with them! To my untrained eye, they look pretty-much perfect. I feel much more confident that an industrial-size laser cutting service should be able to accept my data and cut me the proper floor tiles.

Now I can go ahead and get quotes for the job – at which point I’m sure I’ll discover that the process is far too expensive to cover a whole dining rooom, and kill the project stone dead.

But even if it becomes unfeasible, I’ve enjoyed the project immensely. And makes me consider building my own small laser cutter …

[Part 1] [Part 3] [Part 4] [Part 5] [Part 6] [Part 7] [Part 8]