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Questions tagged [cartography]

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

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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 ...
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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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122 views

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 ...
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1answer
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 ...
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1answer
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 ...
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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: ...
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1answer
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 ...
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2answers
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/...
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1answer
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 ...
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1answer
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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1answer
88 views

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-...
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1answer
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,...
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1answer
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?
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1answer
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. ("...
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1answer
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 ...
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1answer
504 views

How do great circles project on the mercator projection?

Given a great circle connecting two points on a sphere, what is the function describing it's Mercator projection? In other words, given two longitudes and latitudes $(\phi_1, \theta_1)$ and $(\phi_2, \...
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2answers
51 views

coordinates format to GPS

I was wondering if someone could help me figure out how to go about converting the coordinates on a map I was sent from abroad from the format I see to the usual latitude/longitude I'm used to. (I'm ...
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70 views

How to get parallels of tilted Equator?

I have a Great Circle on Earth, which is not an Equator nor Meridian, and it's not parallel to these. I have four geographical coordinate pairs for it, separated by 90 degrees, so I can use these in ...
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371 views

Latitude/Longitude Dimension Reduction - 2D to 1D and back again

I have a 2D array (latitude, longitude) which I would like to convert/map to a 1D integer (i.e. for machine learning regression purposes). I would then like be ...
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0answers
61 views

What happens to a line/curve from a flat map to a spherical map?

The scenario starts from the Earth (assumed as a sphere with radius $r$). The sphere is turned into a square map (cartography) and now I measure a curve on that map (gaining a polynomial function to ...
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1answer
2k views

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 ...
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1answer
126 views

Reference request: stereographic images of loxodromes

The north and south poles are antipodal points on a sphere and definitions of parallels of latitude and meridians of longitude are well known. A curve that meets every parallel of latitude at the ...
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1answer
830 views

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 ...
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696 views

Convert Bearing Degrees to Slope

I'm working on a mapping application that sketches a graphic on the map. The user will input the distance of a line segment and provide a bearing for the line segment. For example, a line segment is ...
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2answers
4k views

Conformal mapping circle onto square (and back)

I'm programming an implementation of the Peirce quincuncial map projection. The projection involves a stereographic projection of a hemisphere of the globe onto a circle (I've got that part), then ...
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1answer
469 views

What is a “Face Graph” in Graph Theory?

I am reading the following paper on Rectangular Cartograms - http://ac.els-cdn.com/S0925772106000770/1-s2.0-S0925772106000770-main.pdf?_tid=ce3aa43e-cef1-11e3-b342-00000aacb361&acdnat=...
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2answers
144 views

Why are rectangular cartograms hard to generate?

I was reading this paper on rectangular cartograms - http://ac.els-cdn.com/S0925772106000770/1-s2.0-S0925772106000770-main.pdf?_tid=1ecf274e-cb1e-11e3-b916-00000aacb361&acdnat=...
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1answer
66 views
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1answer
70 views

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 ...
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2answers
567 views

How can I know the time difference between two cities almost at the same latitude?

Well I know that's the earth rotation speed is: $v=1669.756481\frac{km}{h}$ I have two cities New York, Madrid almost at the same latitude and the distance between them is: $d=5774.39$ $km$ I ...
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2answers
892 views

How can I know the time difference between two cities by knowing the distance between them and earth speed?

Well I know that's the earth speed is: $v=1669.756481\frac{km}{h}$ and I have two cities Moscow and NewYork the distance between them is: $d=7518.92$ $km$ Actually I know that's : $\Delta t=...
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1answer
289 views

Area projection from cube to sphere

I have a regular cube of edge length = 2, and a sphere of radius = 1. Each face of the cube has been divided into N*N equal-area squares. How can I compute the projected area of every square on the ...
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1answer
65 views

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. ...