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Tag Archives: orthogonal
SMT solutions
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
Posted in computation, geometry
Tagged constraint, crossing, orthogonal, orthogons, perimeter, polygon, segments, SMT, solver
Comments Off on SMT solutions
Drawing orthogons with an SMT solver
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
Posted in computation, geometry
Tagged constraint, drawing, global, local, orthobraces, orthogonal, orthogons, polygon, SMT, solver
1 Comment
Why drawing orthogons is hard
We’re nearing the end of this little diversion on orthogons. We now know that orthogons are in 11 correspondence with orthobraces, and we can efficiently generate orthobraces. The only thing left is to find a way to turn orthobraces into … Continue reading
Posted in computation, geometry
Tagged constraint, drawing, global, local, orthobraces, orthogonal, orthogons
3 Comments
Orthogons and orthobraces
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
Properties of orthogons II
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
Properties of orthogons I
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
Posted in combinatorics, geometry, proof
Tagged concave, convex, orthogonal, orthogons, polygons, proof, properties, vertices
10 Comments
Orthogonal polygons
It’s time to say more about PWW #21, in which I exhibited things like this: Quite a few commenters figured out what was going on, and mentioned several nice (equivalent) ways to think about it. Primarily, the idea is to … Continue reading