Some headway to report on the geometric font project. There was an early comment by Willem Derks regarding the need to have control over stencilling. After all the focus of this project is manufacturing, meaning that we do expect people to actually cut holes into sheet material based on our strokes. Without stencilling we can end up with topologically disjoint remains (for example the insides of ‘o’, ‘8’ and ‘g’). However we decided it’s not good enough to supply a secondary typeface which has stencil gaps, as the radius of the gaps very much depends on the size of the cutter, the thickness and even the strength of the material.

Stencil bridges

Stencil bridges to avoid disjoint remains.

On the left you can see the formation of islands when symbol strokes form a closed loop. Adding a single bridge will connect the inside of the g with the rest of the material, but it could be a very weak connection as the bending moment across the bridge can be large if the island is long. If the sheet material is strong though this is not a problem. This is why we decided to cater for both primary and secondary bridges. The font designer merely has to put points on the symbol geometry to specify where primary and secondary bridges can be made and the end-user can specify what radii to assign to each category:


Some text without any bridges. This will work fine if the text is burned or milled onto the material without cutting all the way through.


The same text with only primary stencil bridges. Strong material like thick metal sheeting should be able to handle these connections. Of course the user can specify larger bridge widths depending on the milling radius.


Both primary and secondary stencil bridges are now made. There could still be a large bending moment if the ‘islands’ have a large maximum distance to the axis between two stencil bridges.

Although stencilling is finished enough for an initial beta release, there are still problems with the kerning engine. On the whole it works reasonably well and there’s plenty of settings to control the distance between adjacent characters:


Some settings for the layout/kerning engine. Click to embiggen.

Characters can be positioned at fixed intervals (mono-spacing), based on their bounding boxes or based on their actual shapes. The kerning distance between two adjacent symbols is computed iteratively to a high degree of accuracy (which doesn’t usually take more than 3 or 4 iterations). Note that characters consist both of visible and invisible geometry.

I did find that positioning symbols based on a fixed minimum distance did not always visually please. As a result I decided to add a friction curve to the kerning engine. Friction retards the intrusion of one symbol into the bounding box of another. For example two adjacent symbols can be positioned very much ‘inside each other':


Kerning may push a symbol so far leftwards that its bounding box intersect with the box of the previous symbol. In rare cases a symbol may even be placed entirely within the previous symbols’s bounding box. For example the combination ‘C-‘ could result in very strong kerning.

A kerning friction curve lessens motion due to kerning by simulating increasing friction. The further one bounding box is pushed into another, the harder it gets to push it further. I provided both linear and non-linear friction curves, mostly because I have no idea yet what works well.

The last serious (known) bug to solve is to do with intersecting symbols. The example above shows that the text ‘3,4’ results in intersecting symbols as the comma is kerned underneath the ‘3’ and the ‘4’ is kerned over the comma. Kerning is at present purely a two symbol algorithm, which is clearly insufficient. I’ll either have to maintain a spacing front which moves from left to right as individual symbols are positioned, or I simply need to take all existing symbols into account when positioning the next one.

I can certainly see why professional typefaces often come with manually designed kerning offsets…

Oh and of course there’s now also proper file icons for fonts and symbols:


*.font files are just zip archives containing any amount of *.symbol files. Makes sharing easier without closing the format.

As part of Grasshopper 2.0 development I’m trying to read up on good and modern coding practices. Since multi-threading is a design goal for GH2, I need to make sure that the foundations of the new code are thread-safe. There’s more than one way to make code thread-safe of course, but I’ve become exceedingly fond of the immutable types approach. It helps that Eric Lippert is advocating immutability, he typically knows what he’s on about.

There are more than one ways to think about immutability, but here I’m concerned with write-once immutability, meaning that fields get assigned from within constructors and then are never allowed to be replaced with another value. The problem is that C# has no fundamental game plan when it comes to immutability and thus trying to use the concept in your own code means treading very, very carefully.

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Fonts are great. Seriously. They occupy precious real-estate on that narrow overlap between the magistera of Art and Geekdom. Most fonts are defined as closed outlines, the interior of which is what you see. It’s this interior which gets assigned different pixel values on screens or which gets filled with ink on paper. By and large this works really well. The outline approach gives font designers full control over every single geometric aspect of their creations, thus making it possible to design fonts that are a pleasure to read.


But not all text is meant for leisurely consumption, quite often text is engraved or printed onto objects merely as an identifier; ‘Part #576′, ‘Assembly A2′, ‘This side up’. Especially with the advent of computational/algorithmic design and programmable manufacturing, it’s not uncommon to have an assembly featuring hundreds or even thousands of slightly different shapes, which have to be screwed together in the right order. In this case you probably want to include some sort of identifier on each part, and you’ll want to add them without the intervention of a human being who will undoubtedly c*ck it up. Regular fonts that were designed to define the outlines of symbols are not ideal if you’re using a milling machine or a laser cutter to engrave them.


The total length of all symbol outlines is nearly 590 units. Thus the ratio of horizontal text length to text outline length is almost 1:6. Not only is a font like Times New Roman difficult to read when rendered as outlines instead of fills, it also takes a long time to steer the laser or milling bit over all the curves.

There do of course exist single line fonts that describe their geometry in terms of central splines instead of outlines. A quick Google image search yields a large number of potentially halfway decent fonts.


So why don’t we just install one or more of these and select them as the font of choice when generating tags for automated manufacturing? Well, the answer of course is that we do, because it is the single best option available at the moment. But this solutions suffers from and even causes new problems. First of all, fonts were not meant to be single lines, and installing such fonts as system resources may confuse (and sometimes even crash) other programs that attempt to interpret them as outline fonts. Since single-line fonts have a very narrow purpose, it seems like overkill to install them at the OS level. Secondly these fonts often lack characters such as Æ, Ñ, ð, Þ and ß, which may be non-standard in English but are nevertheless commonplace in Iceland, Germany, Turkey, Greece, Russia, France, Estonia, Denmark, Albania, Hungary, Romania, Spain, … enfin, you get the point. Lastly, this geometry is still stored inside TrueType or OpenType font formats, which makes them hard to get at. It’s difficult for programmers to access the clean geometry without referencing 3rd party dlls, and it’s difficult for users to modify or extend a font. First you need to find a font editor that is affordable and modern enough. Then you need to get accustomed to a workflow which can most likely be picked on a scale somewhere between arcane and atrocious.

So in this light I’d like to propose an alternative. I’m not a professional typographer so I may well be underestimating the difficulty of the task ahead, but on the other hand all the worlds professional typographers haven’t managed to solve my problems after trying really hard for 50 years so I’m not convinced we should be listening to them. Instead of making yet another single line font, or writing some software which is really good at interpreting existing single-line font definitions, let us take a step back and re-evaluate what sort of solution would actually solve the problem.

We need to:

  • etch, burn, mill or engrave small amounts of symbols onto a wide range of materials which come in a wide range of shapes,
  • automatically generate and place these symbols using algorithms.

We’d like to:

  • have a good grasp on the geometry of the symbols,
  • be able to modify, extend or replace the pool of symbols ourselves, using graphics software we know well,
  • not spend too much time etching the symbols, time is money.

We don’t care about:

  • performance much. We’re not typesetting books here, just putting a few scratches on a piece of wood.
  • Pleasingness to the eye. Fine-tuned kerning, ligatures, good italic and bold styles are not sought after properties.


It is reasonably easy to use Rhino (or any other drafting software you may be familiar with) to design a single line font. The plethora of drawing tools Rhino provides (snaps, accurate transformations, measuring tools, etc) make the design portion of the problem very tractable. But where to go from here? How does one convert hand-drawn curves into a usable font? I spend the last two days writing a small plugin for Rhino which consumes curves and points (more on points later) and generates very easy to access font data from them. Instead of putting the entire font into a single file, I decided to store each character in its own textfile:


The name of the folder which contains them all equals the font name, and each filename represents the unicode identifier of the character in question. Hashes can be used for comments and in the example above the first two lines are auto-generated comments. The body of the file contains one Codepoint line which identifies the file content. It should be the same as the file name. The geometry of the symbol is a collection of lines, circles and arcs (no bezier/nurbs curves allowed yet), each represented by a sequence of numbers, [center.x, center.y, radius] for circles, [start.x, start.y, end.x, end.y] for lines and [start.x, start.y, end.x, end.y, tangent.x, tangent.y] for arcs.

To ease the process of writing these files, the plugin I’m working on overlays a bunch of unicode pages onto the Rhino model space, so all you have to do is make sure your curves are inside the correct square:


Any lines, arcs, circles and points found inside the appropriate square will automatically be combined into a single symbol file. Each symbol cell shows common font metrics (adjustable using commands) as well as a character preview and the unicode codepoint. Since the unicode space is huge, I also draw a small grid inside each cell as the Rhino grid tends to peter out pretty quick once you’re away from the origin:


The above image shows not just the symbol cells, but also the font preview. After exporting the Rhino curves to a collection of *.char files, those files can be read back in and displayed in the correct cells. This makes it easy to visually check the correctness of the symbol files. Different types of symbol fragments are drawn in different colours (lines in magenta, arcs in red, circles in orange and points in teal).

Incidentally this font definition does not (yet) allow for customized kerning offsets, so the plan is to write an automatic kerning engine for the font interpreter. This work hasn’t been done yet but since I’m not aiming to write the worlds best kerning algorithm it shouldn’t be too difficult. The aforementioned point geometry which can be part of symbol files is never included as part of the visible font, but it allows the designer to increase the ‘size’ of the symbol visible to the kerning engine.

This project is only two days old at this point in time and there’s a lot of work left to do, most notably combining the symbols to make actual text. You can see a YouTube video of what’s working so far here:



ICGG2014 paper

August 22, 2014

The 16th International Conference on Geometry and Graphics has come and gone. I had a lot of fun, it was certainly very different from the usual software gigs I attend. This was a congregation of mathematicians and educators from all over the world (though mostly Central and Eastern Europe and the Far East) where most attendees were also presenting a paper or poster. The conferences I usually attend have at least a 1:20 ratio of speakers to audience. That hierarchy was entirely absent at ICGG, which was probably at least in part responsible for extreme levels of conviviality. At the conference dinner a lot of national groups sang songs from the homeland, and we even had the pleasure of hearing the Russian and Ukrainian delegates perform Moscow Nights together.

As promised and agreed with the conference organisers, I’m now making my paper available for download here. The paper is much more technical than the plenary lecture, dealing with the mathematical and algorithmic characteristics of generic solvers and fitness landscapes. During the talk I focused mostly on the graphical aspect of landscapes and how specific problem definitions result in specific landscape geometries/topologies. The Prezi for the lecture is of course also available, as are the files I used for the live demonstrations.

I’ve written a paper for the ICGG2014 conference to go with my talk. It mostly talks about the theoretical side of things, whereas the talk is going to focus on the pragmatic. In case they won’t accept it I’ll post it here soon, but if they do then it will be available online sometime after the conference.

Over the past few years I’ve grown increasingly tired of slick computer generated graphics. They all too often fail to draw attention to salient details and convey meaning. It’s rare these days that I get to make large illustrations, most of my graphic work is for icons, so I do try and savour it when I get the chance. I’ve put the 10 images I drew for this publication below the fold (with LaTeX overlays and captions).

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My first LaTeX document

February 6, 2014

Donald Knuth is one of the people who got a Grasshopper banner animation (january 10th), but until last week I’d never seriously looked into(La)TeX, probably his most famous contribution to humanity. I’ve been invited to give a lecture at ICGG2014 come August and the abstracts and papers are to be submitted in either tex or doc format. Since I don’t own and can’t stand Word® and pretty much every other word processing software I’ve ever seen*, it seemed like a good opportunity to dive into TeX. It’s a curious mixture of pure awesomeness and horrific muck. One the one hand it’s extremely liberating to be able to program a document rather than write one. It seems that no matter what you want to do, there’s always a way to get there. I’m also very pleased about being able to write in pure text and compiling the final document, as opposed to trying to tell a GUI what it is I want and never quite knowing what monstrously nested makeup and layout tags are silently ganging up on me in the background.

But the implementations of TeX seem to suffer badly from softwareforprogrammersitis. TexWorks (which comes installed with MikTex for Windows) was clearly made by someone who has heard about that thing called UX but wants no truck with it. Once I have some time to do some more research I’ll definitely be looking at a lot of alternative editors, but the dozen or so I’ve seen so far do not fill me with hope. With a bit of luck the LaTeX for Sublime Text will work better.

Anyone has any suggestions?


* TechWriter for RiscOs was ok, but I no longer own an Acorn machine and this was 20 years ago.

An ethical dilemma

January 7, 2014

I can’t quite remember where and when, but a long time ago I heard about or read about an ethical dilemma regarding responsibility and guilt. I think it was in the wake of a Dutch trial in ’94 where a man was charged[dutch newspaper article] with murder and assault by injecting his ex-girlfriend with HIV tainted blood. Although undoubtedly a heinous act, does it qualify as murder before the victim dies? And does it qualify as murder right away if the victim will not die for several years from AIDS complications? At any rate, the ethical dilemma is happily fictional and goes like this:

Three students share a dorm apartment in Albequerque. Alec, Basil and Callum. Alec is a bit of a health-nut and goes hiking —alone— in the desert every weekend. He packs his bag on Friday evening, making sure to include two bottles of water. Basil and Callum both hate Alec to the point of murder and they’ve both decided to try and kill him. However they are not aware of each others feelings and plans. At 11pm Basil sneaks into Alec’s room and pours a small amount of lethal poison into the second water bottle, lest Alec drink it while he’s still close to civilisation. Half an hour later Callum sneaks into Alec’s room, takes the second bottle and empties it before putting it back.

Alec’s mortal remains were found by hikers 3 months later about half a day’s hike from the nearest water source. Who killed him?

The reason this is a dilemma of course is that it’s not obvious who’s ultimately to blame for Alec’s death. It’s clear that both Basil and Callum tried to kill him, so they can at least be charged for attempted murder, but the ultimate responsibility is vague.

We can’t say that Basil killed Alec as the poison was never ingested. It never even came close to Alec as it was poured down the sink while he slept. If Basil had done nothing, the outcome would have been exactly the same.

However it’s also not clear that Callum killed Alec. If Callum hadn’t emptied the bottle then Alec would have died much sooner through poisoning rather than dehydration, a far more definitive death. In fact, one could make the point that Callum’s actions postponed death for several hours, not only —briefly— saving Alec’s life but also giving him a real chance of survival.

If Basil wasn’t involved at all, this would be a clear-cut case. However by doing something which ultimately had no physical effect Basil effectively removed a large portion of responsibility from Callum, and I’m not at all sure where it went. Is there such a thing as conservation of responsibility?


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