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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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I’m in Seattle at RMA headquarters for three weeks discussing the future of Grasshopper (don’t worry, not whether there is a future, but what it might look like). Although there is a great apartment for me to stay in, I’m separated from my books and my music. I don’t hold with Kindle or some such nonsense —paper for me thank you very much— and my laptop speakers can theoretically play my music but what they mostly do is repeatedly stab it in the kidneys until it’s lying as a bleeding and broken corpse on the floor.

However it did get me thinking about music categorization and I thought it would be fun to put up two blog posts with the best humanity has to offer from two opposing groups. Today, my six favourite religiously[1] inspired masterpieces, tomorrow my six favourite pieces making light of religion.

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Curve parameters, an analogy

September 28, 2013

While trying to explain curve parameters to my girlfriend (she was proofreading my previous blog post) we hit upon an apt analogy. Imagine you’re taking a car-trip from home to the nearest Hooters book-shop. It’s a good half-hour drive which takes you over two local roads and a motorway.

Road trip parameters

Road trip parameters

If the shape of the road you travel along equals the shape of a curve, then the curve parameters are analogous to the travel times. If you take this trip once every week, then you travel along the same roads every time. Thus the shape of the curve never changes. However some weeks you run into roadworks or thick fog or a traffic jam and then your travel times start to differ. Some parts of the trip may go faster than usual, others may go slower.

The point is that once you have the entire trip data (i.e. the entire curve data, not just the shape) you can then work out your location at 12:15. And you can work out in what direction you were travelling at 12:15. And you can work out your acceleration at 12:15. And you can work out the centrifugal force you were experiencing due to turning at 12:15. All of these properties can be computed as long as you have the curve (the route) and the correct curve parameter (the time).

It’s now also easy to see that parameters can have different densities in different portions of a curve, and how parameter density can be thought of as the ‘speed’ of a curve.

It even allows us to get a feeling for curve derivatives and why parameterization matters. Derivatives are used to compute the tangency and curvature and torsion of curves. A parallel can be drawn between those properties and the forces that push you into your car-seat due to acceleration. Or the forces that pull you out of your seat sideways because you’re turning too sharply. These forces don’t just depend on the shape of the road, they also depend on your travelling speed.

Another Galapagos Tutorial

September 17, 2013

I’ve been thinking about Grasshopper 2.0 for a while now and there are a lot of facets to the project where I’d like to see improvement. One of the things I’m looking into is incorporating 3rd party code libraries that would provide advanced statistical and algorithmic functionality. One of the libraries I’ve been browsing is the Microsoft Solver Foundation whose main purpose is to solve optimization problems.

Looking for examples on how to use MSF I came across this blog post which poses a hypothetical (but not unrealistic) problem which can be cracked using an algorithmic solver. The post itself has some inconsistencies in the numbers it uses to describe the problem, so I’ll outline it briefly here as well:

  • You own a trading company and you’re looking to import some cheap-ass furniture from China and sell it to gullible Europeans for cut-throat prices. So the goal here is profit maximization.
  • We hire individual containers from a shipping company, and these containers have limits on how much weight you can put in. We’ll use a 500 kilogram limit in this tutorial. We are not concerned with volume limitations.
  • There are three types of furniture we can import; chairs, tables and bookcases (the original article uses cupboards instead of bookcases, but I wanted three items that start with different letters). Each has its own specific purchasing cost, profit margin and weight.
  • There is one additional constraint concerning purchasing cost; your company can only afford to spend 5000 Euros per container.

That’s it, simple enough. A profit function with three variables (amount of chairs, tables and bookcases respectively) and two hard constraints limiting the weight and purchasing costs.

Because of the weight and purchasing constraints this problem becomes non-trivial and an algorithmic approach would be good to have, if only to check your intuitions in case you’re doing the purchasing by hand.

This is a three-variable problem which means the phase space of all possible states is three-dimensional and the fitness landcape is a four-dimensional surface (if you don’t know what a fitness function/landscape is, please see this blog post or buy the Architectural Design publication with my article). I cannot draw a four-dimensional surface on a two-dimensional screen so instead I decided to just make sh*t up and hope it gets the point across regardless of being utter humbug:

Fitness Function with Constraints

Fitness Function with Constraints

Here you see a two-dimensional phase-space (let’s ignore bookcases for the time being and assume we only have to pick chairs and tables) with the resulting three-dimensional fitness landscape. From left to right we go from zero chairs to some arbitrary upper limit. From front to back we go from zero tables to some arbitrary upper limit. Every two-dimensional point is some combination (i.e. state) of chairs and tables. For every combination we can compute the profit that combination would generate, and this has been represented by the height of the landscape. The higher the surface, the more money we’re going to make. Find the highest point on the landscape and you know how many chairs and tables hit the sweet spot.

So far so good. But what about our constraints? Some combinations of chairs and tables are impossible either because they weigh too much or because they cost too much. So our landscape shouldn’t in fact exist at all when this is the case. This is known as a hard constraint and unfortunately in Galapagos it is impossible to add a hard constraint (at least for now).

Luckily we can mimic this effect with penalty clauses. We’re looking to maximize our profit, so what we’ll do is subtract a large amount of money if any of these constraints are overstepped. As long as we subtract enough, the solver will automatically avoid those areas. Enough theorizing, lets hook up some wires!

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This is going to be a difficult post to write on several levels. I’m about to lay heavy blame on a number of people and organisations who are part of my loyal customer base. I am also going to incriminate the industry I work for, which includes my direct employer and —of course— myself.

At the same time I have to marshal my arguments very carefully so as not to belittle a specific individual whose work I am about to dissect and critique in a harsh tone. I firmly believe —although he probably doesn’t agree with me— he is the victim of the twin evils of underinformed educators and overeager, heedless software companies. I wish neither to patronise nor scapegoat him and I know that cushioning language is not my strong suit. Please remember this while reading the text below. This is not about ridicule, but rather about a pervasive and alarming world-wide trend in academic architecture.

I’d like to thank ███████████ for sending me his work and having the courage to allow me to publicly critique it, knowing I’d focus only on the bad and not the good.

Also my sincere thanks goes out to K. who —unlike me— did receive proper academic training during her time at University (Turku University, Department of English) and was able to comment comprehensively on the scholarly and academic aspects of this critique.

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