# Questions tagged [map-projections]

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### Finding metric projection mapping [closed]

Let $X$ = $c_0$, with supremum norm and $W$ = $\{ \{x_n\}_{n \geq 1} \in X$ $|$ $x_1=0\}$. Then how to find $P_W(x)$. Note that, $P_W(x)$ = $\{y_0 \in W : ||x-y_0|| = \inf ||x-y||,$ $y \in W \}$. In ...
1 vote
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### Projection operator fixed up to a constant

Let $\Omega$ be a polygonal domain in $\mathbb{R}^2$, $V$ a closed and finite dimensional subspace of $H^1(\Omega)$ and $\mathbb{P}_k(\Omega)$ the usual space of polynomials of maximum degree $k$. I'...
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### Transform distances in North and East to distances on Lambert projection

I think I read somewhere about a transformation between distances in North and East and distances on a Lambert conformal conic projection based on a series expansion. The goal was to get distances ...
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### In Spherical Mercator Tile coordinates, how to go one zoom-level deeper but span the same area?

For an arbitrary tile region defined by (z1, x1, y1) in Standard Web Mercator Tile format (Spherical Mercator) , how can we increase ...
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### Is there an easy way to convert a partial arc length or movement along an elliptic curve into an X,Y position?

I had this idea to project the Earth onto a 2D map using elliptical cylinders that could be unrolled. (The Earth can be well approximated by rotating an ellipse on its axis to create an oblate ...
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### If $U \subset Y \subset \mathbb{R}^n$, and $U$ is open relative to $Y$, then is $\Pi_k(U)$ open relative to $\Pi_k(Y)$? ($\Pi_k$ is a projection map)

Here, $\Pi_k: \mathbb{R}^n \to \mathbb{R}^k$ denotes the projection map, mapping an element of $\mathbb{R}^n$ to its first $k$ coordinates. If $x = (x_1,\ldots,x_n)$, then $\Pi_k(x) = (x_1,\ldots,x_k)$...
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### Proof of integral substitution rule

I have the proof of the integral substitution rule at the university. In order this rule to use, I must have some conditions. So $f: I\to R$ and $g: I_0 \to I$ and $I,I_0$ are not trivial intervals ...
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### How to create a map projection

Theoretically, there are infinitely many map projections. They are usually defined by precise mathematical formulae, although so-called comprise maps (most notably the Robinson projection) also exist, ...
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### Norm convergence of a series of operators.

Let $\mathcal H$ be a infinite dimensional Hilbert space and $T \in \mathcal L (\mathcal H)$ be a compact normal operator. Let $\sigma (T) = \{\lambda_1,\lambda_2, \cdots\} \cup \{0\}$ be the spectrum ...
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### What is the image of the circle $z=2n\pi e^{i\theta}$ under the map $w=1+e^z$

What is the image of the circle $z=2n\pi e^{i\theta}$ under the map $w=1+e^z$ Can somebody help me with this problem? In the book, it says that ${(i)}$ the region $0 \le x\le x_0$ and $z$ on the ...
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### Pythagoras on Mercator's Map

Very stupid question, but I cannot help but wonder whether measuring (and finding true distance after correcting scale distortion) of the horizontal and vertical displacement, and using the Pythagoras ...
1 vote
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### Projecting Sphere to Rectangle/Square using Mercerator Projection

I am learning some projection technique where we can project a 3d object like globe to a 2d. I have the 3d coordinates of points on the surface of sphere same as globe. Here is a reference where a ...
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1 vote
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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 $\mathbb{R}^d$....
1 vote
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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 ...
1 vote
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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 $S=\{(x,y)\in \mathbb{R}^2|x^2+(y-1)^2=1\}$ (...
1 vote
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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 ...
1 vote
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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 $P^2 = P$.
1 vote
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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 ...
1 vote
Let $V$ be a Banach space, $W$ a (strict) subspace of $V$, and $U$ a dense proper subset of $V$. When is does there exist a (linear) projection $P^V_W:V\twoheadrightarrow W$, such that $$P_W^V(U)=W .... 1 vote 1 answer 68 views ### How to show that a map is linear in C^n? Could someone tell me if I am on right way solving Problem b)? Problem: Let U,V\subset\mathbb C^n be two subspaces, such that \mathbb C^n = U+V and further assume U\cap V = \{0\}. a) Show that ... 1 vote 1 answer 741 views ### How to draw a globe in 2D? [duplicate] I want to draw such globe: Let's say my input params are: center (x,y) radius number of meridians number of parallels. I know such concepts as: 2D ellipse equation 4x4 projection ... 0 votes 1 answer 132 views ### Howto calculate the latitude of a given y coordinate from a mercator projected map Say I have a mercator projection map: I would like to calculation the latitude for different points with one formula. I have already resaerched several sites and wikipedia, where the hole math is ... 4 votes 1 answer 255 views ### Equal-area projection from sphere to tangent plane I'm running into a problem trying to understand the work in the two following papers: Feasibility Study of a Quadrilateralized Spherical Cube Earth Data Base. and An Icosahedron-based Method for ... 0 votes 1 answer 411 views ### Non orthogonal projection of a point onto a plane I have multiple points in a circle and I need to project them onto a finite plane that is angled in respect to the circle. This is actually a light cone, that originates some millimetres behind the ... 3 votes 2 answers 61 views ### Bounded linear operator Linear bounded operator T on l^2 is given by : T(x_1,x_2,x_3,..) := (x_1,x_1,x_1,x_2,x_2,x_2,x_3,x_3,x_3,..). Prove that \frac{T^*T}{3} and \frac{TT^*}{3} are orthogonal projections. Thanks ... 1 vote 0 answers 55 views ### Correcting for arbitrary distortion in experimental CNC Router I have an issue which I would love any guidance at all with. The Background: I have been working on an experimental CNC router which looks like this: The X and Y position is controlled by ... 1 vote 2 answers 74 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/... 0 votes 2 answers 1k views ### The inverse of projection function is a closed map? I have this questione about the projection, be:$$\pi :X \times Y \to X if we consider $\pi^{-1}(x): x \to x \times Y$ I want to know if this is a closed map, is easy to see that $\pi$ is not, ...
I would to learn what happens in a projection about universality. I searched in google and i found this: https://en.wikipedia.org/wiki/Projection_(mathematics) Let's conside that we refer in $Set$ ...