# Questions tagged [map-projections]

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### What is a good introduction to the math of map projections

I'm interested in learning the math behind map projections but often the explanations (wikipedia one for example) are way beyond my level, so I was wondering if someone know of a good book or internet ...
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### Can argmin act as a “projection”?

My professor is teaching us about a clustering algorithm called K-means clustering. He used the term projection in a way I'm unfamiliar with. Assume all vectors in this example are in $\mathbb{R}^d$....
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### Which map projection should be used for preserving coordinates on a 2D image?

I have coordinates of a city on earth, say latitude: 57.7072326, longitude: 11.9670171. This is city A. I also have coordinates for another city, called city B. I want to place a marker on these 2 ...
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### Mapping $2$ kinds of operators?

So $z$ from complex analysis can be mapped as: $$z \to \hat z = \begin{pmatrix} \Re z \\ \Im z \end{pmatrix}$$ Now the $+$ in complex analysis seems to be the same operation as the $+$ in linear ...
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### If $f:A\to B$ and $g :B\to C$ are 2 mappings then if $g\circ f:A\to C$ is injective then prove that $f$ is injective

My attempt : Let $f(x_1)=f(x_2)$ for some $x_1$ and $x_2$. $g\circ f(x_1)=g\circ f(x_2)$ implies that $x_1=x_2$ holds. Thus $f(x_1)=f(x_2)$ implies that $x_1=x_2$ and therefore $f$ is injective What ...
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### Stereographic Projection - Example

to work with stereographic projections I want to know how to solve this example first: It is it about finding a map $f:\mathbb{R} \rightarrow S$ where $S=\{(x,y)\in \mathbb{R}^2|x^2+(y-1)^2=1\}$ (...
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### Lat long projection to not distort distance

I have many circles which are lat long positions and a radius in meters. I need to check if two circles intersect and I can use this haversine distance function. However, to speed up performance I ...
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### How to map a Cartesian vector into equirectangular coordinates

I am working on a tectonic plate simulation for terrain generation. I have a plate in Cartesian coordinates mapped to an equirectangular and I need to map its drift vector onto the same ...
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### Is the gnomonic projection the only one mapping great circles to straight lines?

The gnomonic projection maps from a hemisphere to the plane, with the equator at infinity. It is noted for having the property that great circles map to straight lines. As a result, any line segment ...
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### Latitude more than 90

I want to calculate mercator projection of points inside of sphere. First, the points are transformed to local system. Then the latitude and longitude are calculated based on following equations ...
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### Conversion of coordinates (longitude ; latitude) to (X;Y)

We have an old mapping system we are needing to convert some data to and from. We need to convert from Lng/lat to XY and from XY to Lng/Lat. We can convert from Lng/Lat to XY Using the following: ...
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### What is the formula for the Collignon projection (diamond form)?

So, I want to project a sphere onto a square with the poles at two opposite corners, preserving areas (long story, but I have a practical application in mind). Wikipedia and other online sources ...
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### How can I project a curved surface onto another curved surface?

I don't really know where to look in the world wide web for this specific problem. So I hope you can point me into the right direction. Here is my specific problem: I have a deformed spherical ...
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### Given a closed linear subspace, is there always a projection that maps onto it?

Given a closed linear subspace, is there always a projection that maps onto it? Here, a projection $P$ should be a linear and continuous mapping and satisfies $P^2 = P$.
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### If projections $P$ and $Q$ are commutative, then $P+Q-PQ$ projects onto $\text{im}P+\text{im}Q$

Projection: Suppose $X$ is a normed vector space, we define a projection $P$ as a linear and continuous mapping from X to X, such that $P^2 = P$. im$P$: the image of $P$ commutative: $PQ=QP$ The ...