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Aksakal
Aksakal
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Is it possible to uniformly draw points over a $D-1$ dimensional2$ sphere, given that one has an algorithm to draw over the $D$ dimensional$D-1$ sphere in D-dimensional space?

in comments OP stated that a circle was meant not a disk as in original language
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Aksakal
Aksakal
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Is it possible to uniformly draw points over a $D-1$ dimensional disksphere, given that one has an algorithm to draw over the $D$ dimensional sphere?

Suppose I have the following scenario:

enter image description here

And I am aware of an algorithm to draw uniformly from (in this case) the 2-sphere. Does this same algorithm readily extend to the situation where I randomly take a "cut/slice" (shown in red above) and what points uniformly over this diskcircle?

Further, suppose now that I have a uniform random sampling algorithm over an arbitrary Riemannian manifold. Would the same principles necessarily apply?

Is it possible to uniformly draw points over a $D-1$ dimensional disk, given that one has an algorithm to draw over the $D$ dimensional sphere?

Suppose I have the following scenario:

enter image description here

And I am aware of an algorithm to draw uniformly from (in this case) the 2-sphere. Does this same algorithm readily extend to the situation where I randomly take a "cut/slice" (shown in red above) and what points uniformly over this disk?

Further, suppose now that I have a uniform random sampling algorithm over an arbitrary Riemannian manifold. Would the same principles necessarily apply?

Is it possible to uniformly draw points over a $D-1$ dimensional sphere, given that one has an algorithm to draw over the $D$ dimensional sphere?

Suppose I have the following scenario:

enter image description here

And I am aware of an algorithm to draw uniformly from (in this case) the 2-sphere. Does this same algorithm readily extend to the situation where I randomly take a "cut/slice" (shown in red above) and what points uniformly over this circle?

Further, suppose now that I have a uniform random sampling algorithm over an arbitrary Riemannian manifold. Would the same principles necessarily apply?

edited body
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kjetil b halvorsen ♦
kjetil b halvorsen ♦
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Suppose I have the following scenario:

enter image description here

And I am aware of an algorithm to draw uniformly from (in this case) the 2-sphere. Does this same algorithm readily extend to the situation where I randomly take a "cut/slice" (shown in red above) and what points uniformly over this disk?

Further, suppose now that I have a uniform random sampling algorithm over an arbitrary ReimannianRiemannian manifold. Would the same principles necessarily apply?

Suppose I have the following scenario:

enter image description here

And I am aware of an algorithm to draw uniformly from (in this case) the 2-sphere. Does this same algorithm readily extend to the situation where I randomly take a "cut/slice" (shown in red above) and what points uniformly over this disk?

Further, suppose now that I have a uniform random sampling algorithm over an arbitrary Reimannian manifold. Would the same principles necessarily apply?

Suppose I have the following scenario:

enter image description here

And I am aware of an algorithm to draw uniformly from (in this case) the 2-sphere. Does this same algorithm readily extend to the situation where I randomly take a "cut/slice" (shown in red above) and what points uniformly over this disk?

Further, suppose now that I have a uniform random sampling algorithm over an arbitrary Riemannian manifold. Would the same principles necessarily apply?

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tisPrimeTime
tisPrimeTime
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