# Questions tagged [map-projections]

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### How do I describe what I want to do with a planar graph?

The image shows a planar graph, the points of which are calculated by Python's NetworkX. (While, in this example, the graph also happens to be a triangulation, that is not always the case). What I ...
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### The range projection and monotone complete C*-algebra.

Let $A$ be a monotone complete C- algebra (i.e every increasing , norm bounded net in A has a supermum in A), this kind generlises many types of C-algebra (Von nuemann algebra...). Also, it generetes ...
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### Defining an injective map from the algebraic numbers to the set of integer coefficient polynomials.

Let $P$ be the set of all polynomials with integer coefficients, one variable, and deg $n \ge 1$. A number is said to be algebraic, $\mathbb{A}$, if it is real and the solution to an element of $P$. ...
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### Name of a map coupled with the identity

Given a map $\tau:\Omega\longrightarrow \mathbb{R}$, is there a standard name for the map $\tilde{\tau}:\Omega\longrightarrow\Omega\times\mathbb{R}$ that maps $\omega$ to $(\omega,\tau(\omega))$? It ...
1 vote
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### Mapping of a unit circle to a lune of a unit sphere quarter

Uniform $\lambda$ spaced circles of unit radius through origin are given by $$(x-\lambda)^2 +(y-\lambda)^2 =1$$ include a net of constant curved differential length rhombuses. What is the equal ...
212 views

### Is Mercator projection an affine trasformation?

A practical example lead me to believe that a geographical projection, such as the Mercator projection, is an affine transformation. However, when I checked on Wikipedia: More generally, an affine ...
1 vote
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### How can I extract the equations from this 3D projection graph?

I'm trying to transform these plots to functions, but I'm having a hard time figuring out a formulaic 2D->3D transformation on this type of mapping. They collapsed an axis flat on the abscissa, and ...
71 views

### Vector Projections

I am watching a youtube video on Principal Component Analysis. It is written that the projection of vector $x_i$ onto vector $u_1$ is $proj_{u_{1}}(x_i) = {u_1}^T x_i u$ where $u$ is the unit vector ...
1 vote
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### Derivation of General form of Map Projections

In this paper, the following formulae are derived for the cylindrical and conic projections: Cylindrical: $T(\phi, \lambda)= (\lambda, h(\phi))$ for some function $h$. Examples include: Equi-...
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### How will the unit spheres volume change after mapping

Let $R^3$ be a vector space. Linear map $F$ will map base of $R^3$: $u_1=(1,2,-1)^T$, $u_2=(1,-3,3)^T$, $u_3=(-1,-2,2)^T$ on vectors $v_1=(-1,-3,5)^T$, $v_2=(2,5,-4)^T$, $v_3=(-2,-6,7)^T$. How will ...
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### Prove that $\pi$ is a quotient map which is neither open nor closed

Exercise: Let $X:=\mathbb{R}^2\smallsetminus((-1,1)\times(-2,2)\cup[2,3]\times[-2,2])\subset\mathbb{R}^2$ be equipped with the subspace topology and consider the map $\pi:X\rightarrow\mathbb{R}$, ...
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### How does one calculate the projections onto sub-spaces of $C^3$?

Given the following two sub-spaces of $C^3$: $W = \operatorname{span}[(1,0,0)] \,, U = \operatorname{span}[(1,1,0),(0,1,1)].$ I want to find the linear operators $P_u , P_w$ which represent the ...
1 vote
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### Two-point equidistant projection of the sphere

According to this Wikipedia article, there is a projection from the $2$-sphere to a region in the plane that preserves distances to two given points. The article says that the projection was first ...
1 vote
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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: ...
138 views

### 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
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### Covering from Dense Projection

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
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### 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
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### 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 ...
142 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 ...
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### 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 ...
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### 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 ...
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 ...