Mfcttrf

Having some problems Generating random Polygons and then filtering by Area, specifically filter out degenerated polygons with undefined Area is crashing the kernel in 12.0.

randomThirdPoints[n_] := Table[1/3 RandomChoice[0,1,2,3],RandomChoice[0,1,2,3],n] 

Here are some random 4-gons in the unit square:

randomPolygons4 := Table[Polygon[randomThirdPoints[4]], 100]; 

This step is consistently crashing kernel:

randomPolygons4 // Map[Area]

similarly if using Select, AssociationMap and also using RegionQ instead of Area.

Are there some safer options? Ref Page doesn't seem to help.

One workaround for polygons with 4 different points:

Map[Area[DiscretizeGraphics[#]] &, randomPolygons4] 

The "possible issues" section of the documentation for Polygon says that

Degenerate polygons are not valid geometric regions

A degenerate polygon is a polygon that has two or more vertices which are the same.

The polygons that crash the kernel seem to be of this type. You can avoid the kernel crashes by not evaluating Area on such polygons, for example by using

If[DuplicatesFreeQ[vertices], Area[Polygon[vertices]], Undefined]

or you can modify your definition of randomThirdPoints so that it doesn't generate duplicate vertices:

randomThirdPoints[n_] := 1/3 RandomSample[Tuples[0, 1, 2, 3, 2], n]

Based on C.E.'s work, vertex deduplication must be done at the point of generation, eg:

randomThirdPoints[n_] := Module[pts,
 pts := Table[a RandomChoice[0,1,2,3],RandomChoice[0,1,2,3],n];
 p=pts;
 While[Not[DuplicateFreeQ[p]],p= pts]
 p
 ]

this generated safe Polygons:

Table[randomThirdPoints[4], 100] // Map[DuplicateFreeQ] // Apply[And]

True

Area works for all of these, though Undefined still need to be filtered:

Table[Polygon@randomThirdPoints[4], 20] // Map[Area]

4/27, 16/63, 1/6, 7/45, 1/3, 1/6, 1/2, Undefined, 1/9, 1/6, 2/5,
4/27, 1/9, 1/18, 11/54, 1/6, 1/9, 2/9, 1/2, 1/6

Is there a more compact syntax? I don't think I've used a While loop in 20 years.