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Questions tagged [map-projections]

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Computing circle and line intersection given in terms of longitude and latitude

Suppose i have a circle whose mid point is given by $(X,Y)$ where $X$ and $Y$ represent longitude and latitude. The radius of the circle is 1 KM. Now If i have line given by $(X_1,Y_1)$ and $(X_2,...
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1answer
45 views

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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1answer
64 views

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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2answers
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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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1answer
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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 ...
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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 ....
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58 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) ...
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Am I doing Equirectangular Projection incorrectly?

Currently, I am making a 360 video app in Unity. I successfully make the video to render by using a shader that does equirectangular projection found on the Internet. Now I am trying to set some ...
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transformation function or projection to convert a 3d cartesian grid to spherical section grid

What is the transformation or projection to convert a 3D cartesian grid to spherical section grid with radii $(r_1, r_2)$, $\theta$ or latitude ($\theta_1$, $\theta_2$) and $\phi$ or longitude ($\...
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1answer
280 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 ...
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61 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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1answer
87 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 ...
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1answer
223 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 ...
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2answers
44 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 ...
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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 ...
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2answers
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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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356 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, ...
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Simple and fast presentation of theory about projections and universality

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 $Set$ ...
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About the inverse function

Hello. Does it always an inverse map don't exist? I know that a mapping is considered as a function . And I know that there are some functions as sine that has an inverse that is arcsin . So why might ...
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What is the name of this map projection?

Is there a name for the map projection that makes a circle out of a sphere, where, in polar coordinates, the angle is the bearing angle of the point and the radius is the distance (on the surface of ...
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1answer
174 views

Positive operator on a Hilbert Space

Let $H$ be a Hilbert space. Let $L: H \rightarrow H$ be a linear bounded positive operator (i.e. $\langle L(u), u \rangle \geq 0$ for all $u \in H$). A) Prove that $I+aL$ is bijective for ...
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1answer
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projection always yields to $0$? (what am I doing wrong)

Say we have vectors $x$ and $y$ in some inner product vectorspace. Then the projection of $x$ onto $y$ is given by: $\begin{aligned}P(x)=x-\frac{x\cdot y}{\Vert y\Vert ^2}y\end{aligned}$, but I would ...
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Points in Two surface Mapping Problem

First, this is 3d problem. I have two circle type line (closed), these line shape don't need to be Perfect Circle. They don't need to be in one plane. Based on the lines, we can get a surface and ...
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1answer
292 views

Projection in Banach Space

Let $X$ be a Banach Space and let $Y=\ker f \subset X$ be hyperplane in $X$. Prove that there exists a projection $P:X \to Y$ such that $||P||\leq 2$.
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1answer
734 views

Why restrict the domain of polar coordinates, cylindrical coordinates, spherical, etc?

For a change of variables one needs the mapping to be injective. In the book I'm reading, we restrict the mapping of polar coordinates $g(r,\theta)$ to the domain $r>0$ and $0<\theta<2\pi$. ...
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1answer
95 views

Distortions in a Subway Map

The NYC subway map - like most subway maps - isn't shown to scale. Is there a way to visually represent the distortion of the map in terms of area? More specifically, suppose you have the set of ...
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1answer
48 views

Approximation Theory, Projections and Hyperplanes [closed]

Let $X$ be a Banach space and let $Y = \ker f \subset X$ be a hyperplane in $X$ for some nonzero $f \in X'$ . Prove that if $P\colon X \longrightarrow Y$ is a continous projection, than there exists $...
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1answer
45 views

Working on a finite subspace

Let $X$ be a normed space and $L$ a finite dimensional linear subspace. I need to show that there exists finitely many $l_1,.....l_n \in L$ and $f_1,.....f_n \in X'$ such that $$ l = \sum_{i=1}^{n} ...
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I want to know the difference between metric projector and orthogonal projector?

Given a metric space $(X, \rho)$ and $A$ be its closed subset. Now for every $x \in X$ define $$P_A(x) = \{ y \in A : \rho(x, A) = \rho(y, x)\}$$ Now definition of metric projector is as follows: Let $...
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1answer
33 views

Surjectivity of a complex projection

Given is the projection $$u: \mathbb{C} \rightarrow \mathbb{R}: z \rightarrow Re(|iz|) - |iRe(z)|$$ which is $$u: \mathbb{C} \rightarrow \mathbb{R}: z \rightarrow |z| - |Re(z)|$$ when simplified....
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1answer
35 views

Help with surjectivity of a function

My function $f$ is as follows: $$f: \mathbb{R} \rightarrow \mathbb{R^2}: t \rightarrow (2cos(t), - sin(t))$$ Now, I'm fairly certain that the function isn't injective, as both sine and cosine are ...
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971 views

What is the difference between moment projection and information projection?

Moment projection is defined as $$\text{arg min}_{q\in Q} D(p||q)$$ while information projection is defined as $$\text{arg min}_{q\in Q} D(q||p)$$. Aside from the difference in the formula, how should ...
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515 views

Difference between orthogonal projection and oblique projection physically.

Let $A$ and $B$ be $n \times n$ matrices in $\mathbb{R}^n$, $N(B)$ denotes nullity of $B$. Let $C $ and $N(B)$ are complementary subspaces of $\mathbb{R}^n$. Let $P_c$ denotes the oblique projector ...
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Are projection and norm enough to define an inner product?

Given an inner product, one can define a projection and a norm. Can we do the opposite? That is, suppose we have: a complex vector space V a norm $|V|^2 : V \rightarrow \mathbb{R}$ such that: is ...
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646 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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3answers
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Projection onto a plane

I was looking at this post ($3D$ projection onto a plane) in which the answer describes how to project a given set of points onto any arbitrary plane. However, this transformation is still of the ...
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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, \...