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

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find the shortest distance between two lines [duplicate]

Let L1 be the line passing through the point P1=(−9, −7, 14) with direction vector →d1=[−2, −1, 3]T, and let L2 be the line passing through the point P2=(9, −8, 9) with direction vector →d2=[2, −3, ...
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shortest distance from point to line

Let $L_1$ be the line passing through the point $P_1=(−1, 5, −2)$ with direction vector $\vec{d}=[−3, 2, 3]T$, and let $L_2$ be the line passing through the point $P_2=(2, −5, 5)$ with the same ...
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22 views

Find the image of the following circles on the sphere under stereographic projection

Find the image of the following circles on the sphere under stereographic projection from the north pole onto the equatorial plane: $C = S^2 ∩ \{(x_1, x_2, x_3) \;|\; x_1 = x_2\}$ $C = S^2 ∩ \{(x_1, ...
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Stereographic Projection proofs(pathagorean triples)

So I recently stumbled upon a proof using stereographic projection to prove Euclid's formula for generating Pythagorean triples: for all $m,n\in \mathbb{N}$, ...
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Stereographic Projection

Could anyone find a stereographic projection of a $4$-dimensional object with $1$ zero-dimensional hole, $8$ one-dimensional holes, $6$ two-dimensional holes, $8$ three-dimensional holes, and lastly ...
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253 views

How to construct three mutually orthogonal circles in stereographic projection?

I'm new to spherical geometry and I enjoy doing ruler-and-compass constructions, so I'm trying to teach myself to do them in stereographic projection. I'm finding it challenging, to put it mildly. ...
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49 views

find f and $d_pf$

Let $$S_1=\{(x,y,z) | x^2+y^2+z^2=1\}-\{N\}$$ $$S_2= \{(x,y,z,0) | x,y\in \Bbb R\}$$ $f:S_1\to S_2$ $f$ is stereographic projection. ,where $\ell$ is a line passing through $N=(0,0,1)$ and $p$ ...
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Homogeneous matrix to represent rotation out of plane?

How to represent 2D homoheneous projection matrix $M=\left( \begin{array}{ccc} m_{00} & m_{01} & m_{02} \\ m_{10} & m_{11} & m_{12} \\ m_{20} & m_{21} & w \end{array} \right)$ ...
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53 views

Anamorphotic Projections onto Awkward Solid Surfaces

I have been experimenting with some 19th century picture development techniques that involve photochemical image projection: For flat pictures you first mix equal parts of chemicals like ferric ...
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349 views

How to calculate the angle between two vectors, defined by 3 points on the earth?

I want to develop a formula to calculate the angle between two vectors. The vectors will be OX and OY (from point O to X , and Y), where the points are defined by their latitude and longitude values. ...
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What is the proportion of table from this picture?

I have this picture and I know his height = 75cm Do you know how to find out its proportion like width and lenght using perspective projection?
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compute angle of rotation between two orthographic projections

I Have the orthographic projection of a unit cube with one of its vertex at origin as shown above. I have the x,y (no z) co ordinates of the projections. I would like to compute the angle of ...
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1answer
31 views

Looking for reference to a couple of proofs regarding the Stereographic Projection.

I'm looking for a reference to rigorous proofs of the following two claims (if someone is willing to write down a proof that would also be excellent): The Stereographic Projection is a Homeomorphism ...
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1answer
89 views

Ways to project arbitrary Fractals on 2D objects and 3D objects w different dimensions?

I am trying to create a house/texture in 3D and in 2D with fractals, perhaps related. My friend said that fractals can have different dimensions such as 1.74, 1, 4.71111... and pretty much anything. ...
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44 views

Show that T is the exterior of a circle centered at 0.

Let $ S = {(\xi, \eta, \zeta) \in \sum: \zeta \geq \zeta_0}$, where $ 0 < \zeta_0 < 1 $ and let T be the corresponding set in $ \mathbb{C} $. Show that T is the exterior of a circle centered at ...
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2answers
106 views

Prove that $|PF_{1}|+|PF_{2}|$ is Constant in an Elipse

Given an elipse with two focus $F_{1}$ an $F_{2}$, and $A$ is an arbitrary point at the elipse. Stright line $AF_{1}$ has another intersection point $B$ with the elipse, and $AF_{2}$ has another ...
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247 views

Equation of a line on a plane…

Hi this question belongs to camera projections but i cannot understand the mathematics... i am not getting how the cross product of two vectors (underlined in red) gives the equation of a ...
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116 views

Diametrically opposite points go to diametrically opposite points under stereographic projection

I asked this question before here but I didn’t get a proper answer. So here I am stating it more clearly : Suppose $P_1$ and $P_2$ are two diametrically opposite points of a circle $C$ in the ...
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115 views

Change in angle between curves due to stereographic projection

Suppose I have say two curves on the complex plane intersecting at a point $P$. Then is the angle between those curves at $P$ same as the angle between their spherical images on the Riemann Sphere (by ...
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232 views

Transformation under rotation of Riemann sphere

Suppose the Riemann sphere $S$ is rotated by the angle $\phi$ round the diameter whose end points have $a,-1/\bar{a} $ (which have antipodal preimages) as stereographic projections. Suppose moreover, ...
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456 views

Radius of the inverse image of a circle under stereographic projection

I need to find the radius of the circle on the Riemann sphere $S$ whose stereographic projection is $C(a;r)$, i.e. the circle with centre $a$ and radius $r$ in the complex plane. I have observed ...