h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Entry: Thiessen polygons - A794117
Author: Gordon the Scout, Keeper of Postal Codes and Maps No One Can Re-fold Properly - U198614

I wrote this entry for a University Project, but I'm not going to be able to work on the project for a while so I'm tossing this in PR. Enjoy!

I looked choropleth up by Google, and most definitions of it presume you know what you are doing, and are pretty abstruse. Can it truly be explained in a short paragraph?

Looks sound to me. Diagrams would help a huge amount, even just one picture. Everything makes so much more sense with an example. The libraries example somehow seems a little clumsy. Its not really clear what the Voronoi cell diagram will do for you, and of course no diagrams doesn't help. Maybe talking about catchment areas for lakes or something would be clearer, dunno.

There was a really cool exhibit at the Exploratorium, a science museum in San Francisco. There's a big square on the floor, and somewhere up above you is a camera and a projector. It works out where people are standing in the square and then projects the Voronoi diagram for the positions of the people standing on the square. So as you walk around you're surrounded by a constantly changing cell, separating you from the other people.

Now that *IS* cool. Clearly, I'm going to have to visit the Exploratorium.

Diagrams would definitely help this and I can generate some diagrams if they could be included in the entry.

Good point. This entry was going to be part of a larger collection of entries, so I'll have to tweak that. I'll go write a paragraph about choropleths.

Very interesting! I'd never heard of these before, and from reading this entry, I understand them pretty well, I think. A diagram would be tremendously helpful, I think. That shouldn't be difficult to get attached in the editing process. Now that the community art scheme is running, I think it's easier to have entries illustrated.

On the chloropleth map - is there some common example that you could cite? Like a weather map, where areas of similar temperature are coloured similarly - is that a chloropleth map?

What Thiessen poloygons remind me of, as a first impression, are "basins of attraction", particularly the ones associated with different magnets in James Gliek's (sp?) Chaos - the software. Is there more than a superficial connection there, do you think?



GTB

Oooh I did like this. I think diagrams would be nice, especially to illustrate the library example (which I thought was quite clear btw). And a modified one following the road lines would also be nice.

I tuned out of the maths (I always do).

I wonder if it would be worth actually explaining what a perpendicular bisector is and how you can draw one using a compass and a ruler (we did this at school but only because I was in the top set of maths, the lower sets didn't do anything about it), you could then easily go on to manually constructing the diagram (unless I've got completely the wrong end of the stick you draw pb's for all the adjacent points for each point and then join them up to create polygons)

I'd never heard of these thingies (dispite a degree in geology which included some GIS and a career in statistics (including geographical stats)) *planning ways to wow boss with shiney new diagrams...now I just have to figure out how to draw them in excel using ms map...*

ignore comments on manually constructing the diagram - its already there I just missed it somehow

Yet another h2g2 entry subject I've never heard of

Most of the content went way above my head, but the library example helped a lot

If you're going to use the paragraph tag btw, you need before the paragraph, and at the end. Putting in the entry doesn't have any effect.

There are some good comments and suggestions here. I'll try and incorporate them into the entry. A couple of them may take a day or two to incorporate.

Tuning out the math isn't a big problem with this entry. I did my best to describe it in as non-technical language as possible, but I couldn't leave out the theory.

They've been around for a while. I believe the UK Census people are using them to delineate polygons around houses and I used them to code polygons in a product I created at Statistics Canada.

If you figure out how to do them in Excel, please let me know. I'd be interested in seeing it.

Interesting! I'd never heard of these.

The following sentence is slightly confusing:

"The area contained in each polygon is closer to the point the polygon is based on than any other point in the dataset. "

What you really mean is:

"Each point within a Thiessen polygon is closer to the point the polygon is based on than any other point in the dataset."

"Survey's" should be "Surveys"

Thinking about it, I'm a bit unclear on how you make the Triangulated Irregular Network. Your description just says connect each point to its nearest neighbour. Surely there's more to it than that. And isn't there more than one possible TIN? How do you decide which to use? Consider four points which make a diamond shape (rhombus). By joining across the middle, you get two triangles which are roughly equilateral. But if you joined the other way, you'd end up with two long thin triangles.

Gnomon's right, it is a little vague. Perhaps you should describe the desired result (that each point in the selection has a polygon around it showing which points are closer to it than they are to any other selected point) and then give a more detailed algorithm for construction.

I think this should make it into the edited guide, hopefully with a couple of diagrams. A few things, though:

Isn't the footnote for "Voronoi networks" merely a short description of a division into Thiessen polygons? Also is there a difference between a Delauny triangulation and a triangulated irregular network?

Also, when you talk about imposing the road network, do you mean you define distance as via roads rather than as the crow flies? If so, doesn't this make the construction harder?

Finally, your "p1,p2,p3" doesn't look too good - the subscript runs into the comma. I think putting "p1 ," etc might work better, but I haven't tried it.

Not quite.

Points are discrete entities. In a set of Thiessen polygons, the area in a given polygon is closer to the point the polygon was based on than it is to any other point used to create a polygon. Technically speaking, there aren't any points in a set of Thiessen polygons.

If you take another set of points and perform a point-in-polygon operation (PIPA) on them, you'll be able to find out which point in the original set of points they are closest to based on which polygon they fall in.

Hmm... maybe that's a better way to say it.

I agree that the sentence is awkward and I'll try to find a better wording without using a more technical vocabulary.

Hi all,

A Scout has recommended this entry for the Edited Guide, but before we press the magic 'ACCEPT' button, I just thought I'd check it's okay with everyone first.

So, what gives?

Jimster

though it needs just one good picture at the start so people have some idea of what they look like.

I'd rather the author had replied to more of the points Gnomon and I made - specifically the non-technical description could do with being clearer (not an easy task I'll admit; I've tried writing mathematical stuff without resorting to mathematical terminology and it ends up with really bloated sentences). Can we wait and see what Gordon thinks?

Could we hold off clicking ACCEPT until I can re-review the comments to make sure I've properly addressed things?

I don't think anything we pointed out was a fatal error, I would have said "go ahead" but I wasn't sure if you were still up to anything with it.

I'm taking a final look at it and the comments. I don't think I'm going to make any changes to the entry, other than minor typos.

In simplest terms, you connect each point to its neighbours to create triangles. There's a bit more to TINs than that, but a more detailed description really deserves an entry of its own.

Simplifying the non-technical description is not an easy task and I'm not sure it's overly technical. I tried to define the technical terms that I did have to use, such as bisect, with footnotes.

The image will be ready tomorrow. Jimster, should I create a separate entry with references to them or submit then via email?