RandomPolygon

RandomPolygon[n]

gives a pseudorandom simple polygon with n vertex points.

RandomPolygon[spec]

gives a pseudorandom polygon with the specified specification spec.

RandomPolygon[spec,k]

gives a list of k pseudorandom polygons.

RandomPolygon[dspec,…]

gives a pseudorandom polygon in dimension d.

Details and Options

RandomPolygon gives a Polygon drawn from a specific distribution.
RandomPolygon is typically used in testing and verification of time complexity for algorithms.
Possible specifications spec include:

		{"Convex",n}	convex polygons with n vertex points
		{"Simple",n}	simple polygons with n vertex points
		{"StarShaped",n}	star‐shaped polygons with n vertex points
		{"ConvexHull",dist,n}	convex hull of n random points from the distribution dist

RandomPolygon[] gives a pseudorandom simple polygon with the number of vertex points chosen in the range {3,15} with equal probability.
RandomPolygon[n] is equivalent to RandomPolygon[{"Simple",n}].
RandomPolygon[{"ConvexHull",n}] gives the convex hull of n random points from the uniform distribution UniformDistribution[2] over the unit square.
RandomPolygon[spec,{k₁,k₂,…}] gives a k₁×k₂×… array of pseudorandom polygons.
RandomPolygon gives a different sequence of pseudorandom polygons whenever you run the Wolfram Language. By using SeedRandom, you can get a repeatable sequence.
RandomPolygon has the same options as Polygon with the following additions: [List of all options]
DataRange Automatic the range of vertex points to generate

WorkingPrecision MachinePrecision precision of vertex points
With the default setting DataRangeAutomatic, coordinates are chosen in the range 0 to 1.

List of all options

DataRange	Automatic	the range of vertex points to generate
VertexColors	Automatic	vertex colors to be interpolated
VertexNormals	Automatic	effective vertex normals for shading
VertexTextureCoordinates	None	coordinates for textures
WorkingPrecision	MachinePrecision	precision of vertex points

Examples

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Basic Examples (3)

Generate a random polygon:

Generate a list of random convex polygons:

Compute the area:

Generate a list of polygons in dimension 3:

Scope (15)

Basic Uses (6)

Generate a random polygon with a random number of vertex points:

Generate a random polygon with a given number of vertex points:

Generate a random polygon with a given number of vertex points in :

In :

Generate a list of polygons:

Generate multiple lists of polygons:

Generate a random polygon with a specified property:

Convex Polygons (2)

Generate a random convex polygon:

Random convex polygon in :

In :

Convex Hull Polygons (3)

Generate a random convex hull polygon:

Random convex hull polygon in :

In :

Generate a random convex hull polygon from the Dirichlet distribution:

Uniform distribution:

Normal distribution:

Binormal distribution:

Simple Polygons (2)

Generate a random simple polygon:

Random simple polygon in :

In :

Star‐Shaped Polygons (2)

Generate a random star-shaped polygon:

Random star-shaped polygon in :

In :

Options (8)

DataRange (1)

DataRange allows you to specify the range of vertex points to generate:

Specify a different range:

WorkingPrecision (1)

Generate a random polygon using machine arithmetic:

Using 30 digits of precision:

VertexColors (2)

Generate a random polygon with vertex colors:

Specify vertex colors for 3D random polygons:

VertexNormals (1)

Generate a random polygon; compute normal vectors using the cross product of edge vectors:

A triangle with normals:

Using different normals will affect shading:

VertexTextureCoordinates (3)

Texture mapping with 2D random polygons:

Repeat a texture by using non-unified texture coordinate values:

Texture mapping is preceded by VertexColors:

Applications (5)

Basic Uses (2)

Random polygons with 10 vertex points:

Convex polygons:

Star‐shaped polygons:

Generate random polygons for testing algorithms and verification of time complexity:

Time complexity for algorithms for convex polygons:

Simple polygons:

Geometry Probability (2)

Simulate random convex polygons and compute areas:

Estimate distribution:

Compare its histogram to the PDF:

Average area of polygons with 10 vertices over a unit square:

As goes to , the limit shape for random convex polygons is :

Other Applications (1)

Polygon classification using machine learning. Train a classifier function on polygon examples:

Use the classifier function to classify new polygons:

A simple polygon:

A star‐shaped polygon:

Properties & Relations (5)

Use SeedRandom to get repeatable random polygons:

Use BlockRandom to block one use of RandomPolygon from affecting others:

Use ConvexPolygonQ to check the property of a random polygon:

SimplePolygonQ:

The OuterPolygon of a random polygon is simple:

Random polygons do not have holes:

Using PolygonDecomposition to decompose a polygon into convex polygons:

Neat Examples (1)

Random polygon collections:

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RandomPolygon

Details and Options

List of all options

Examples

Basic Examples (3)