Questions tagged [cartography]

Questions related to mathematical procedures and concepts involved with the study and practice of making maps.

33 questions
12 views

Least possible distance distortion for a map

The background to the question is that I would like to figure out how much a map of Europe must distort distances. Let us try to formulate this mathematically. Say I have a closed subset, $D$, of ...
6 views

connected network of paths on a map, so that every point of the map is not too distant from a path

I saw no references on the very simple cartographic geometric algorithmic problem Given a bounded euclidian plan, find a connected network of paths (lines), so that every point of the plan is not too ...
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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 ...
38 views

How do GPS receivers keep accurate on-board time? [closed]

GPS, or Global Positioning System is a network of satellites in orbit above the surface of the Earth. By the satellites constantly transmitting their exact position and on-board time through radio ...
43 views

Parametrization of a sphere such that distances are separable

Question Is there a parameterization $(u, v)$ of a 2-sphere -- i.e. a map projection -- such that the geodesic (great-circle) distance function $d$ is "separable"? By separable I mean that the ...
51 views

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: ...
151 views

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 ...
64 views

Is it true that you need atleast 350 colors to color-in the boundries of a flat map where all the boundries are clearly defined?

Since a providence may build on a bridge, and since certain bridges may be placed as archways over land: it is an obvious fact that this Earth could be turned into a topological and territoried donut/...
466 views

Triangulation math

I'm trying to do sound triangulation mathematically, and I'm a little lost. I have a list of latitudes, longitudes, heights and precise times, each representing the same sound as heard by a number of ...
345 views

Mathematical methods of map making?

I am in high-school and we have an assignment to be submitted. It's basically choosing a topic that interests you and explore that in a depth way. I am interested in map making and the mathematics ...
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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-...
164 views

How to define the boundary of a set of points clustered on a unit sphere?

I have a set of points assigned to a single cluster on a unit sphere. How do I find the boundary of the points on the surface of the sphere? I'm currently using a built-in boundary algorithm in MATLAB,...
55 views

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?
107 views

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. ("...
645 views

Converting from Mercator Projection to Latitude and Longitude

I have an image of (what I believe to be) a Mercator Projection map of Strangereal, from the Ace Combat game series. I have opened this map in GIMP and am reading pixel measurements for different ...
504 views