Tag Archives: orthogons

SMT solutions

Posted on July 30, 2018 by Brent

In my last post I described the general approach I used to draw orthogons using an SMT solver, but left some of the details as exercises. In this post I’ll explain the solutions I came up with. Forbidding touching edges … Continue reading →

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Drawing orthogons with an SMT solver

Posted on July 12, 2018 by Brent

I’m long overdue to finish up my post series on orthogons as promised. First, a quick recap: An orthogon is a polygon with only right angles. Two orthogons are considered the same if you can turn one into the other … Continue reading →

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Why drawing orthogons is hard

Posted on April 5, 2018 by Brent

We’re nearing the end of this little diversion on orthogons. We now know that orthogons are in 1-1 correspondence with orthobraces, and we can efficiently generate orthobraces. The only thing left is to find a way to turn orthobraces into … Continue reading →

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Efficiently listing orthobraces

Posted on March 26, 2018 by Brent

In my last couple posts, we talked about a simple yet inefficient method for listing all orthobraces of a particular size. So how do we generate them efficiently? It turns out that it can be done: in 2011, Karim, Sawada, … Continue reading →

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Haskell code to naively list orthobraces

Posted on March 21, 2018 by Brent

Let’s see some simple Haskell code to generate orthobraces, by generating all sequences and throwing away ones we’ve already generated. First, some library imports we’ll need. > import Data.List > import qualified Data.Set as S Here’s a function to generate … Continue reading →

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Listing orthobraces

Posted on March 20, 2018 by Brent

I took a bit of a break to finish writing a paper for submission to the International Conference on Functional Programming—which I should write about here! All in good time. (I tend to accumulate things to write about faster than … Continue reading →

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Orthogons and orthobraces

Posted on February 19, 2018 by Brent

One of these days soon I will get back to writing about primality tests, but for now I am having fun getting sidetracked on orthogons! In a previous post I gave rules for when two orthogons will be considered the … Continue reading →

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Properties of orthogons II

Posted on February 10, 2018 by Brent

In my previous post I proved three out of the four properties of orthogons I originally stated. Now let’s prove the final property: Every sequence of an even number of X’s and V’s, with exactly four more X’s than V’s, … Continue reading →

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Properties of orthogons I

Posted on February 5, 2018 by Brent

First things first: from now on, when talking about polygons with only right angles, instead of calling them “orthogonal polygons” I’m going to start calling them “orthogons”, which sounds cool, is much less clunky than “orthogonal polygons”, and doesn’t seem … Continue reading →

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