Questions related to mathematical procedures and concepts involved with the study and practice of making maps.
Questions tagged [cartography]
57 questions
19
votes
8 answers
Why do I see half of earth’s surface from space but the area of its shadow is only a fourth?
I’m not clear why orthographic projection is different from shadows. If I look at a sphere, I see potentially up to half its surface, yet if the sphere’s shadow is cast onto a plane at the same viewing point, apparently that shadow is only ¼ the…
Svenn
- 428
8
votes
1 answer
Area preserving bijection between square and circle that is conformal on the perimeter?
Is there a bijection between a square and circle that is (1) area-preserving (2) conformal (angle-preserving) on the perimeter (except at the corners)?
This map satisfies (1) but not (2). This theorem constructively proves the existence of map…
Christopher King
- 10,773
7
votes
1 answer
Where is the "thread" of a river?
Lawyers speak of the "thread" of a river. When the boundary between two counties or states is a river, it is usually the "thread" of the river, a path running along the center of the river. (In England, I suspect this has applied primarily to…
5
votes
1 answer
n-by-n degree grid on a sphere?
I've been trying to generate an evenly spaced grid centred at a given point on a sphere, such that the angular separation between any neighbouring pair of points is the same (e.g., 1 degree). The grid should be oriented with the central column of…
Marcin
- 51
- 1
- 4
4
votes
1 answer
How can I geometrically (or geographically) group items together?
I'm a programmer, and I'm working on a project that takes a bunch of photos and separates them into groups by their gps coordinates. I have no experience in things like geometric group theory so I'm not even sure if that's the field that would help…
fivestones
- 43
4
votes
0 answers
What is the best way to tessellate sphere into equal area in any level of detail? HEALPix or Geodesic Grid or another method?
I want to tessellate sphere into a grid in my 3D world map. There was 2 ways that I was consider right now, HEALPix and Geodesic
If I use it specifically for world map that could be zoom into any level of detail; What would be the better method…
Thaina
- 692
4
votes
1 answer
How is the Gastner-Newman equation implemented to create value-by-area cartograms?
There is a paper called "Density-equalizing map projections: Diffusion-based algorithm and applications" by Michael T. Gastner and M. E. J. Newman, which explains their algorithm for generating value-by-area cartograms.
While it explains the…
Frick Steves
- 141
4
votes
1 answer
A name for great circles that pass through both poles
The union of two meridians of longitude separated by $180^\circ$ is a great circle. Is there a particular name for these great circles that pass through both poles?
4
votes
1 answer
How do great circles project on the equirectangular projection?
Given a great circle connecting two points on a sphere, what is the function describing it's equirectangular projection? In other words, given two longitudes and latitudes $(\phi_1, \theta_1)$ and $(\phi_2, \theta_2)$, what is the function…
Nathaniel Bubis
- 33,425
3
votes
1 answer
Which map of the Earth corresponds to the usual parametrization of the sphere?
The unit sphere $S$ in $\mathbb{R}^3$, given by the equation $x^2+y^2+z^2 = 1$, can be parametrized by
$$(u,v)\mapsto (\cos u \cos v, \sin u \cos v, \sin v).$$
Under the above parametrization, points of $S \setminus \{(0,0,1),(0,0,-1)\}$ are in…
Monsieur Periné
- 300
3
votes
2 answers
Stereographic Projection: Cartography Applications
Compared to the Mercator's, which is also conformal, how does the Stereographic projection help in areas such as navigation? Or any application besides simply mapping polar areas, although I would prefer answers on the polar aspect.
Additionally,…
swang
- 65
3
votes
1 answer
Could someone help me calculate the areas in this map?
Map of my book - Please click here to see it
So, I'm writing a book and I'm trying to be really detailed. Right now I'm writing a wiki of it and I want to specify the areas of continents and cities.
But I'm having a lot of trouble doing this. I'm…
andreaweb
- 31
3
votes
1 answer
Characterizations of the stereographic projection
A plane touches the globe at the north pole. A line through the south pole and through another point on the globe intersects that plane. That intersection point is the image, under the stereographic projection, of that other point on the globe than…
3
votes
0 answers
Complex exponentials and the math behind Mercator's projection
I came across this post by David Bau, in which he reproduces the most widespread Mercator projection as the plot of the complex function
$$f(z)=\exp \mathrm i z.$$
The result is familiar:
preserving the shape of the different landmasses, at the…
Antoni Parellada
- 10,239
3
votes
1 answer
Understanding Charles Sanders Peirce's cartography
Charles Sanders Peirce wrote$^\dagger$ about
an orthomorphic or conform projection formed by transforming the stereographic projection, with a pole at infinity, by means of an elliptic function.
("Conform projection" seems to mean what today we…