Linked Questions

28 votes
12 answers
8k views

how to get $n$ equidistributed points on the unit sphere

We can get $n$ equidistributed points in the unit circle using CirclePoints. But how do you get $n$ equidistributed points on the unit sphere(surface of a ball)? ...
yode's user avatar
  • 26.8k
23 votes
5 answers
7k views

Spherical density plot of data set

I have a somewhat large number of 3-dimensional unit vectors ( ~ 100 000 unit vectors), and I am trying to visualize their distribution. First thing I tried was ...
a06e's user avatar
  • 11.4k
36 votes
3 answers
1k views

Implementing a planetary terrain generation algorithm

From this (now deleted) question I found this site where the author discusses a simple technique for random terrain generation on a sphere. The method discussed is as follows: start with a ...
b3m2a1's user avatar
  • 46.9k
27 votes
3 answers
3k views

Uniformly distributed n-dimensional probability vectors over a simplex

What's the right way to generate a random probability vector $p={p_1,\ldots,p_n} \in {(0,1)}^n$ where $\sum_i p_i=1$, uniformly distributed over the $(n-1)$-dimensional simplex? What I have is ...
Schiphol's user avatar
  • 375
13 votes
4 answers
3k views

Is there a way to randomly distribute points within a circle on the surface of a sphere?

I'm attempting to set up a situation where on a 3D sphere, I choose a random point and construct a circle around this point with some radius. I then want to randomly distribute points within this ...
UnBurleyvable's user avatar
29 votes
3 answers
2k views

Generating 250 random points crashes the kernel, but not 249

Fixed in 10.1.0. Consider the following function, which generates uniformly random points on the surface of the 2-sphere: ...
David Zhang's user avatar
  • 2,316
4 votes
3 answers
2k views

Generating a random walk with defined step size

By the following I'm trying to generate a list of random coordinates (ex. 4) each within unit distance from previous one, starting from origin. What am I doing wrong? ...
Sesna Secna's user avatar
2 votes
3 answers
499 views

Random reals according to conditions

I'd like to create a list of triplets $(x,y,z)$ which satisfy the following properties: $$0<x<1/2 \\ 0<y<1/2-x \\ -1<z<-2(x+y)$$ Basically I would like to uniformly generate random ...
Sheheryar Zaidi's user avatar
4 votes
5 answers
494 views

How to define a set of two random orthogonal unit vectors?

I need to define a random set of two orthogonal unit vectors. The code below doesn't give proper unit and orthogonal vectors : ...
Cham's user avatar
  • 4,093
2 votes
2 answers
2k views

Finding uniformly distributed random points on an ellipsoid

I am trying to generate a poincare map for a system whose reduced energy manifold looks like the following surface. (x/a)^2 +(y/b)^2 +(z/c)^2=1 I want to find a ...
Neo's user avatar
  • 53
4 votes
2 answers
743 views

How do you plot random points in three dimensions?

I've got a function that maps a 2D plane onto a sphere (I'm trying to learn about Geodesics). ...
Quark Soup's user avatar
  • 1,610
2 votes
1 answer
861 views

ListDensityPlot3D with opacity

Suppose I have a bunch of 3d data points, is there a way to plot a ListDensityPlot3D such that the opacity is determined by the number of nearest points to each ...
MKF's user avatar
  • 591
7 votes
1 answer
374 views

How to distribute points on a Sphere[] cap from a normal distribution?

I was wondering if one could distribute points on a "cap" of a sphere, following a normal distribution of the points instead of a uniform distribution. This normal could be centered at the ...
TumbiSapichu's user avatar
  • 1,603
1 vote
2 answers
275 views

Issue with casting a set of random points on a cylinder surface

Code: ...
e.doroskevic's user avatar
  • 5,969
1 vote
2 answers
146 views

Transfer distribution of points on a sphere to an Ellipsoid[]?

I've seen this cool function, which generates a given distribution of points on the unit sphere, known as Dimroth-Watson distribution: ...
TumbiSapichu's user avatar
  • 1,603

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