For question about stereographic projection, a particular mapping that projects a sphere onto a plane.
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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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stereographic projection problem
27.Suppose that z is the stereographic projection of $(\xi, \eta, \zeta)$ and 1/z is the projection of $(\xi', \eta', \zeta')$.
a. Show that $(\xi', \eta', \zeta') = (\xi, -\eta, 1-\zeta)$
b. Show ...
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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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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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182 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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82 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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75 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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Relationship among the angles between two regular arcs and their preimages on Riemann sphere
Is the angle between any two regular arcs in $\mathbb{C}$ equal to the angle between their spherical images (i.e. the images on the Riemann sphere by the inverse of the Stereographic projection) ? If ...
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1answer
151 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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217 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 ...
