RandomPoint [reg]
gives a pseudorandom point uniformly distributed in the region reg.
RandomPoint [reg,n]
gives a list of n pseudorandom points uniformly distributed in the region reg.
RandomPoint [reg,{n1,n2,…}]
gives an n1×n2×… array of pseudorandom points.
RandomPoint [reg,…,{{xmin,xmax},…}]
restricts to the bounds .
RandomPoint
RandomPoint [reg]
gives a pseudorandom point uniformly distributed in the region reg.
RandomPoint [reg,n]
gives a list of n pseudorandom points uniformly distributed in the region reg.
RandomPoint [reg,{n1,n2,…}]
gives an n1×n2×… array of pseudorandom points.
RandomPoint [reg,…,{{xmin,xmax},…}]
restricts to the bounds .
Details and Options
- RandomPoint can generate random points for any RegionQ region that is also ConstantRegionQ .
- RandomPoint will generate points uniformly in the region reg.
- RandomPoint gives a different sequence of pseudorandom numbers whenever you run the Wolfram Language. You can start with a particular seed using SeedRandom .
- With the setting WorkingPrecision->p, random numbers of precision p will be generated.
Examples
open all close allBasic Examples (3)
Generate a list of points in a unit disk:
Generate multiple lists of points on a unit circle:
Generate a list of points in a standard cylinder:
Scope (22)
Basic Uses (5)
Generate a point in a unit ball region:
Generate a list of points for a triangle region:
Generate multiple lists of points for a unit disk region:
Generate points on an unbounded region within given bounds:
The random points are restricted to :
Generate points on an unbounded region within given bounds in :
Special Regions (6)
Regions in :
Regions in :
Visualize region points in :
Regions in :
Visualize region points in :
Regions in :
Formula Regions (3)
Implicit regions:
Visualize region points in :
Parametric regions:
Mesh Regions (4)
Derived Regions (4)
RegionIntersection of two regions:
RegionUnion of mixed-dimensional regions:
Points are generated for the maximum dimensional component:
Applications (24)
2D Galleries (9)
3D Galleries (6)
Generate a list of uniform random unit vectors in :
Parametric helix curve:
Implicit Viviani's curve:
Parametric torus surface:
Implicit eight solid:
Graphics3D scene:
Monte Carlo Methods (2)
Perform Monte Carlo integration to estimate the area of a unit disk:
Get the region bounds:
Uniformly sample over the bounding box of the region:
Count the number of samples inside the region:
Get the ratio of samples inside the region to the total number of sample points:
Get the bounding area:
Get the approximate area of the region:
Visualize the Minkowski sum (orange) of two regions:
Sum of points from two regions gives points of the Minkowski sum region:
Region Relations (3)
Compute an approximate bounding box for a region from random samples. The resulting bounding will be a subset of the true bounding box:
Compare with its region bounds:
Show that a region is not a subset of another:
Check if any point from a set of random points in the disk are not in the square:
Visualize the random points in the disk that are not in the square:
Determine that two regions are not equal:
Check if any point from a set of random points in the disk is not in the square, or vice versa:
Approximate Convexity (2)
Determine that a region is not convex by sampling, and show that there is a convex combination of the samples that is not a member of the original region:
Generate pairwise convex combinations of random points within the region:
If a point on a pairwise convex combination is not in the region, then the region is not convex:
Alternatively generate and test points in a convex hull of points:
Compute the approximate convex hull of a region from random points within the region:
Nearest and Farthest Points (2)
Find an approximate nearest point in a region by sampling the region and computing the nearest point to the samples. This gives an upper bound for the distance to the region:
Find the nearest point from a set of random points in the region:
Compare the resulting distance to the true minimum distance to the region:
Define a function that finds an approximate farthest point in a region:
Find the farthest point on a region from a given point:
Properties & Relations (6)
RandomPoint will generate points with uniform density:
Choosing random coordinate points from a region of points:
Corresponds to RandomChoice of coordinate points:
Choosing random points from a Cuboid region:
Corresponds to RandomVariate of a UniformDistribution :
Choosing random points from a Disk region:
Corresponds to RandomVariate of a WignerSemicircleDistribution :
Choosing random coordinate points from a Triangle region:
Corresponds to RandomVariate of a TriangularDistribution :
FindInstance can generate exact instances for special and formula regions:
However, instances are not uniform:
Related Guides
History
Text
Wolfram Research (2015), RandomPoint, Wolfram Language function, https://reference.wolfram.com/language/ref/RandomPoint.html.
CMS
Wolfram Language. 2015. "RandomPoint." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RandomPoint.html.
APA
Wolfram Language. (2015). RandomPoint. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RandomPoint.html
BibTeX
@misc{reference.wolfram_2025_randompoint, author="Wolfram Research", title="{RandomPoint}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/RandomPoint.html}", note=[Accessed: 17-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_randompoint, organization={Wolfram Research}, title={RandomPoint}, year={2015}, url={https://reference.wolfram.com/language/ref/RandomPoint.html}, note=[Accessed: 17-November-2025]}