Mapthematics Forums

Milo wrote: ↑Sun Nov 21, 2021 11:41 am This is a conformal projection. Honest.

The boundary looks like the Cantor function: is that a coincidence?

This seems like it's identical to the usual definition in terms of Tissot indicatrices: "max a" is the largest semimajor of any Tissot indicatrix, "min b" is the smallest semiminor of any Tissot indicatrix. (At least, those are the terms I'm used to thinking in.) It's more gener...

Milnor, J. (1969). A Problem in Cartography. The American Mathematical Monthly, 76(10), 1101–1112 includes this statement. For a map projection whose domain is a circle of radius alpha, this inequality holds: alpha/sin alpha <= max a/min b where max a is the maximum scale across the domain, and min...

I read your paper a while ago; sorry that I did not get back to you about it. It’s a good paper. Do you intend to publish? I had a busy spring, but I'm finally getting back around to submitting it. It's published now: A variation on the Chamberlin trimetric map projection . If anyone doesn't have i...

A couple of comments on the non-differentiable lines in Snyder's projection. One is that the Shirley-Chiu transformation from the disk to the square has those same non-differentiable lines from the vertices to the center. If you want to find a differentiable equal-area polygon projection (or prove t...

Are there any shapes that are easy to project? All of the hemisphere-to-polygon conformal maps can be expressed like this: Sterographic projection from hemisphere to disk Mobius transformation from disk to upper half-plane Schwarz–Christoffel mapping from upper half-plane to polygon When the polygo...

I'm okay with trying to figure out how to use special functions, so long as I know which special functions, and I don't need to stack too many of them in a row. The Schwarz triangle function is in theory sufficient to map any spherical or Euclidean (or hyperbolic) polygon onto any other spherical o...

I think a reasonable minimum requirement of any polyhedral projection should be that it's continuously-differentiable everywhere except the vertices. Are there any examples of such a projection other than the conformal ones? Conformal projections are theoretically simple by comparison. By the Riema...

New blog post, showing that the Collignon projection and the COBE Sky Cube projection are special cases of Snyder's equal-area projection: https://brsr.github.io/2021/08/31/snyder-equal-area.html . Also gives a closed-form formula for the inverse. Also the paper I mentioned in the Experimental Proje...

I read your paper a while ago; sorry that I did not get back to you about it. It’s a good paper. Do you intend to publish? I had a busy spring, but I'm finally getting back around to submitting it. I might implement this in Geocart if you don’t mind. It probably won’t be soon; I’ve been completely ...