# Random points on surfaces
**URL:** https://discourse.threejs.org/t/random-points-on-surfaces/34153
**Category:** Resources
**Tags:** points
**Created:** [January 26, 2022, 10:00pm UTC](https://discourse.threejs.org/t/random-points-on-surfaces/34153 "2022-01-26T22:00:39Z")
**Posts on this page:** 6
**Page:** 1
### Author:  [@prisoner849](https://discourse.threejs.org/u/prisoner849)
#### Post date: [January 26, 2022, 10:00pm UTC](https://discourse.threejs.org/t/random-points-on-surfaces/34153/1 "2022-01-26T22:00:39Z")
Hi community!
Maybe it will be useful for somebody.
Uniformly distributed points on surfaces (sphere, torus, ring).
Torus and ring are based on answers from here: [probability - uniform random points on a torus - Mathematics Stack Exchange](https://math.stackexchange.com/q/2017079/1018985)
Sphere is based on the `.randomDirection()` method of `THREE.Vector3()`.
Example: [JSFiddle](https://jsfiddle.net/prisoner849/yzx8fbqu/show)
Code:
```javascript
function getRandomPointsOnRing(R, r, count = 1000){
return new Array(count).fill(0).map(p => {
let rand = Math.random();
let radius = Math.sqrt(R * R * rand + (1 - rand) * r * r);
return new THREE.Vector3().setFromSphericalCoords(radius, Math.PI * 0.5, Math.random() * 2 * Math.PI);
});
}
function getRandomPointsOnTorus(R, r, count = 1000){
let pts = [];
let counter = 0;
let COUNT = count;
let U, V, W;
while(counter < COUNT){
U = Math.random();
V = Math.random();
W = Math.random();
let theta = 2 * Math.PI * U;
let phi = 2 * Math.PI * V;
if(W <= ((R + r * Math.cos(theta)) / (R + r))){
pts.push(new THREE.Vector3(
(R + r * Math.cos(theta)) * Math.cos(phi),
R + r * Math.cos(theta)) * Math.sin(phi),
r * Math.sin(theta)
))
counter++;
}
}
return pts;
}
```
---
### Author:  [@NHQue](https://discourse.threejs.org/u/NHQue)
#### Post date: [January 26, 2022, 10:03pm UTC](https://discourse.threejs.org/t/random-points-on-surfaces/34153/2 "2022-01-26T22:03:07Z")
Wow, this looks amazing!!
---
### Author:  [@amitlzkpa](https://discourse.threejs.org/u/amitlzkpa)
#### Post date: [February 2, 2022, 4:06pm UTC](https://discourse.threejs.org/t/random-points-on-surfaces/34153/3 "2022-02-02T16:06:41Z")
I have some samples of other (fractal) structures done similarly.
[Pyramid](https://jsfiddle.net/amitlzkpa/2rwsey9j/0)
[Cube](https://jsfiddle.net/amitlzkpa/aL5wmech/)
[Dodecahedron](https://jsfiddle.net/amitlzkpa/kaj1w5yr/)
[Octahedron](https://jsfiddle.net/amitlzkpa/y3fb9d1t/)
[Icosahedron](https://jsfiddle.net/amitlzkpa/qagL8d4z/)
---
### Author:  [@xyz\_Abc](https://discourse.threejs.org/u/xyz_Abc)
#### Post date: [November 17, 2022, 10:31am UTC](https://discourse.threejs.org/t/random-points-on-surfaces/34153/4 "2022-11-17T10:31:52Z")
can i ask how to convert the outer circle to a heart shape?
---
### Author:  [@hofk](https://discourse.threejs.org/u/hofk)
#### Post date: [November 17, 2022, 4:27pm UTC](https://discourse.threejs.org/t/random-points-on-surfaces/34153/5 "2022-11-17T16:27:14Z")
> [@xyz\_Abc](#):
>
> heart shape
From the [Collection of examples from discourse.threejs.org](https://discourse.threejs.org/t/collection-of-examples-from-discourse-threejs-org/4315)
[ProceduralHeart](https://hofk.de/main/discourse.threejs/2019/ProceduralHeart/ProceduralHeart.html)
From [Addon. Produces almost infinite many time-varying geometries with functions](https://discourse.threejs.org/t/addon-produces-almost-infinite-many-time-varying-geometries-with-functions/262)
see [examples THREEf](https://hofk.de/main/threejs/sandboxthreef/examplesTHREEf%20r136.html)
and
[form library THREEf.js](https://hofk.de/main/threejs/sandboxthreef/formLibrary136.html) :
```javascript
//0024 heart (pulsating by t) @author hofk
radiusSegments: 50,
height: 10,
withTop: true,
withBottom: true,
rCircHeight: function ( u, v, t ) { return 20 * ( u - 0.5 ) * ( u - 0.5 ) + 0.3 * Math.sin ( Math.PI * v ) + 0.3 * Math.sin( t ) },
moveX: function ( u, v, t ) { return -Math.cos( 2 * Math.PI * u ) },
topHeight: function ( u, t ) { return 0.6 * ( 1.4 + Math.cos ( Math.sin( t ) * Math.sin( t ) * u ) ) }
```
See also [Heart Curve -- from Wolfram MathWorld](https://mathworld.wolfram.com/HeartCurve.html)
---
### Author:  [@xyz\_Abc](https://discourse.threejs.org/u/xyz_Abc)
#### Post date: [November 20, 2022, 9:39am UTC](https://discourse.threejs.org/t/random-points-on-surfaces/34153/6 "2022-11-20T09:39:50Z")
Thankyou very much