It is possible to generate a random Rectilinear Polygon (without holes) in WL? I found this option, but without any possibility to ask for a Rectilinear Polygon.
RandomPolygon["Convex", 2] $\begingroup$ $\endgroup$
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- 2$\begingroup$ Conjection: Each convex rectilinear polygon is an axis-aligned rectangle. Or maybe you have special notion of convexity for rectilinear polygons? If so, please make it precise. $\endgroup$Henrik Schumacher– Henrik Schumacher2020-01-12 12:40:33 +00:00Commented Jan 12, 2020 at 12:40
- $\begingroup$ yes, you are right. When I say convex, I mean without holes. $\endgroup$Kiril Danilchenko– Kiril Danilchenko2020-01-12 12:47:47 +00:00Commented Jan 12, 2020 at 12:47
- $\begingroup$ Ah, you mean connected and simply connected. $\endgroup$Henrik Schumacher– Henrik Schumacher2020-01-12 12:55:50 +00:00Commented Jan 12, 2020 at 12:55
- $\begingroup$ I'm not sure ... $\endgroup$Kiril Danilchenko– Kiril Danilchenko2020-01-12 13:04:43 +00:00Commented Jan 12, 2020 at 13:04
- $\begingroup$ In other words you ask for a set of numbers $x_i$ and $y_i$ such that $\sum_{i=1}^n x_i=0$ and $\sum_{i=1}^n y_i=0$, right? $\endgroup$yarchik– yarchik2020-01-12 13:59:07 +00:00Commented Jan 12, 2020 at 13:59
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2 Answers
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The number of vertices should be even and is given by 2 n below
RRPoly[n_] := Module[{x, y, indx, indy}, x = Accumulate[RandomReal[{-1, 1}, n]]; y = Accumulate[RandomReal[{-1, 1}, n]]; indx = Table[Quotient[i + 1, 2], {i, 2 n}]; indy = RotateLeft[indx]; Table[{x[[indx[[i]]]], y[[indy[[i]]]]}, {i, 2 n}] ] Generate 3 random polygons with random colors.
Graphics[{Opacity[0.9], Table[{RGBColor[RandomReal[{0, 1}, 3]], Polygon[RRPoly[5]]}, {k, 3}]}] 
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ClearAll[rectilinearPoly] rectilinearPoly = Polygon@(Join @@ (Partition[#, 2, 1, 1] /. {{a_Real, b_}, {c_, d_}} :> {{a, b}, {c, b}, {c, d}})) &; Examples:
SeedRandom[1] coords = RandomReal[{-1, 1}, {5, 6, 2}]; Row[Graphics[{EdgeForm[Gray], FaceForm[Opacity[.5, RandomColor[]]], rectilinearPoly@#, Red, PointSize[Medium], Point@#}, ImageSize -> 1 -> 100]& /@ (#[[FindShortestTour[#][[2]]]] & /@ coords), Spacer[5]] 
Row[Graphics[{EdgeForm[Gray], FaceForm[Opacity[.5, RandomColor[]]], rectilinearPoly@#, Red, PointSize[Medium], Point@#}, ImageSize -> 1 -> 100] & /@ coords, Spacer[5]] 
