Random 3D Point Cloud Generator

Generate bounded three-dimensional points with Euclidean distances from the origin.

Description

Generate 3D points with independently sampled coordinates and distances from the origin.

A three-dimensional point has x, y, and z coordinates. Its Euclidean distance from the origin is the length of that coordinate vector. Sampling each coordinate in one interval fills a cube rather than a sphere.^[1]

The output points array contains [x, y, z] arrays. originDistances is a parallel array of Euclidean distances in the same coordinate unit. Each point is sampled independently; the points do not describe connected random-walk steps.

When to use Random 3D Point Cloud Generator

Use it for 3D coordinate fixtures or vector-distance exercises inside a common per-axis interval.

How to use Random 3D Point Cloud Generator and understand its results

Enter integer pointCount from 1 through 128 and finite minimumCoordinate and maximumCoordinate whose absolute values do not exceed 1e100, with minimum no greater than maximum.
Run and read points in their returned order. The same bounds apply to every 3D coordinate axis.
Match originDistances[i] to points[i]. Choose any visualization or distance comparison between points separately.

coordinate = minimumCoordinate + randomDraw × (maximumCoordinate − minimumCoordinate)

3 independent draws are consumed per point. Distinct bounds describe a lower-inclusive, upper-exclusive sampling formula, subject to floating-point rounding.

origin distance = sqrt(x² + y² + z²)

The vector-magnitude calculator produces one origin distance for each completed point.

json

{
  "input": {
    "pointCount": 3,
    "minimumCoordinate": -10,
    "maximumCoordinate": 10
  },
  "randomDraw": 0.25,
  "output": {
    "originDistances": [
      8.660254037844386,
      8.660254037844386,
      8.660254037844386
    ],
    "points": [
      [
        -5,
        -5,
        -5
      ],
      [
        -5,
        -5,
        -5
      ],
      [
        -5,
        -5,
        -5
      ]
    ]
  }
}

Equal bounds are permitted and fix every coordinate to that value, although draws are still consumed. Repeated points are allowed. Reversed bounds, point counts outside 1–128, and invalid consumed draws fail.

Origin distance does not measure distance to the previous point or to the cloud’s centroid.

Limitations and assumptions

The default source is Math.random; no seed input or cryptographic entropy guarantee is provided. Repeated runs may select the same result, and the distribution depends on the random source.

There is no uniqueness, minimum separation, integer rounding, fixed radius, sphere/disk sampling, clustering, or topology. No bounding box, interpoint distances, faces, or volume estimate is returned.

Alternative or Complementary methods

Use the other dimension generator for fixtures in a different coordinate space. A deterministic measurement tool can check explicit coordinates without resampling them.

References

NumPy Reference: numpy.linalg.norm — NumPy Developers

Similar or alternative tools

Random 2D Point Cloud Generator
Generate independent points in another dimension using a common coordinate interval.
Vector Magnitude
Calculate the origin distance of an explicit coordinate vector.