Questions tagged [stereographic-projections]

For question about stereographic projection, a particular mapping that projects a sphere onto a plane.

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How to actually draw an epipolar line on a $2D$ image without OpenCV

Suppose I have the Fundamental Matrix $F$, a point correspondence $x$ $(1,2)$ and an image $(\text{height},\text{weight},3)$. The epipolar line is now given by $l'= Fx$ (with $x$ being converted to ...
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Show that any mapping from the extended complex plane to the Riemann Sphere back to the extended complex plane is a Möbius Transformation

Definitions: Extended Complex Plane $\mathbb{C}^\infty = \mathbb{C} \cup \{\infty\}$. Stereographic projection: A mapping from a sphere in $\mathbb{R}^3$ to the extended complex plane. Möbius ...
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Where do the circles go when you stereographically project the dodecahedron?

I'm going to ask what I think is surely a silly and simple question but I can't for the life of me work this out. I am interested in stereographically projecting a dodecahedron to the plane (in an ...
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How to project a portion of a sphere to a plane preserving distance?

Stereographic projection preserves angles but not distances. I've been lead to believe that it isn't possible to go from a sphere to a plane preserving distances between points, but is it possible to ...
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Stereographic Projection and Diffeomorphism

I am recently studying about stereographic projection and it is stated that the punctured 2-sphere $S^2\backslash \left\{0,0,1\right\}$ is diffeomorphic to $\mathbb{R}^2$. I want to prove this ...
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Bijective projection from a unit disk to a unit sphere

Is there any proper method that makes conformal one-to-one mapping (preserving the angles) from a unit disk to a unit sphere? I know with simple stereographic projection you can project a unit disk to ...
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What maps to a plane in a stereographic projection of a 3-sphere to $\mathbb{R}^3$?

Any straight line in a stereographic projecton from a 2-sphere to $\mathbb{R}^2$ maps back to a circle passing through the projection point. That I can see why: the rays between the projection point ...
Assuming I have a point $P=(a_0,...,a_{n})\in\mathbb{R}^n$, and a vector $\vec{v}=(v_0,...,v_{n+1})\in\vec{\mathbb{R}}^{n+1}$. I would like to project the point $P$ onto $S^n$ by doing an inverse ...
I would like to prove the existence and uniqueness of such a plane $P$, the truth is I can't think of a relatively simple way to prove it. Let $\Lambda$ be a circle lying in $S$. Then there is a ...