So you're think you're good at math?

[KrazyHorse]

If I were given that problem spec I'd just pretend that the world was flat - the user's polygon is imprecise so we can fudge on expanding it

I agree with this. Given that it's impossible to actually do distance-preserving conformal scalings, pretty much anything which gives a reasonable answer would be acceptable.

[KrazyHorse]

Should I click on any of Ben's posts in this thread, or are his spherical geometry skills as poor as I would assume?

[Drake Tungsten]

Do you want to expand by all three directions?

Asher, what Polars do for you is rather than getting into a messy coordinate as cartesians, they let you find a number that you are very interested in, the 'radii' of the object from the com.

Instead of XYZ, you have inside, outside and edge.

Do you want it for n-sided polygons, or do have restricted cases?

Edit, this is probably what you want Asher. They've got the functions here.

http://web2.uwindsor.ca/math/hlynka/Ngon.pdf

You only need 2-d rather than 3 d? That makes it quite a bit easier.

You could say thank you.

Check the link. They should have what you need. Searching for n-polygon functions polar coordinates should get you what you need.

[r1r2sin(theta2-theta1) + r2r3sin(theta3-theta2) + r3r1sin(theta1-theta3)]/2.

For triangles at arbitrary points P1,P2,P3.

http://www-math.mit.edu/~gs/papers/P...igenvalues.pdf

This may also be helpful.

http://maven.smith.edu/~orourke/books/compgeom.html

This may also help too.

Cool, I'm glad I was on the right track.

This is actually similar to some stuff we had to do in Astro way back when. We were always working in Polars (RA + Dec).

[KrazyHorse]

[MikeH]

I agree with this. Given that it's impossible to actually do distance-preserving conformal scalings, pretty much anything which gives a reasonable answer would be acceptable.

Totally. Ignore the sphere.

Also, the person who defined how it should work is a moron.

[Asher]

New problem, related to the original and also related to my thread ranting about the idiot I had yesterday.

The server-side idiots are sending me a randomly-ordered array of points that forms the polygon. All of my code is dependent on a coherent order, clockwise (CW) or counterclockwise (CCW).

Spent a bit of this morning trying to solve this myself. It involved computing surface normals and the midpoint. That'd give me an orthonormal basis for creating angles and sorting them. Using the midpoint and the array of angles, I could probably figure out the ordering. But this started making my head hurt, and I figured this problem must've been solved before in computer graphics.

I ran across the Graham Scan algorithm which I think suits my purposes: http://en.wikipedia.org/wiki/Graham_scan . It'll give me the convex hull of a set of points.

Again, lucky me gets to do this in Javascript client-side because the server-side guys -- where this should be done -- are epicly ****ing stupid.

[Kuciwalker]

Couldn't you just average the points, then order the other points by their angle wrt that point?

[Asher]

I thought of trying that a first but I don't think it'd work well because the polygons can be any obscure shape at all. Imagine a thick-shaped "U" with the midpoint in the center.

[Asher]

I'm trying to explain this to the idiot doing the backend. I sent a lengthy email explaining how and why this is happening.

He responded with "What do you mean by clockwise and counterclockwise?"

Holy ****ing ****. If I wasn't working from home today I'd probably smack him. I can't take much more of tihs.

[KrazyHorse]

How can you even tell what the polygon is if it's given to you as a randomly-ordered series of point? It's not unique.

[Asher]

That's a good point. It may just be bad data.

[KrazyHorse]

As an example, take 5 points, 4 at the corners of a square, one in the middle of the square. There are 4 "reasonable" distinct polygons you can make out of these points.

[Asher]

This is the polygon data they're sending me.

[KrazyHorse]

[KrazyHorse]

There are so many less obtuse ways of doing what you originally stated the problem was that I just can't stop laughing about this.

FWIW, I'm pretty sure thy don't actually want the area you've shown on that pic