# Smooth region boundary

I have a 2D region that is defined by the union of a number of polygons (the list of the polygons is available here). I can easily visualize the region using

Region[RegionUnion @@ data]


In the given example, the region looks something like this:

However, if you evaluate

InputForm@Show@Region[RegionUnion @@ data]


you can see that the Graphics object is still made up of the individual polygons. Because of this, exporting the graphic as a PDF (in the real case, I have a diagram with many regions) generates a relatively large file, which I want to avoid.

Also, if you zoom in on the right end of the region, you can see some artefacts in the region boundary, that could be smoothed out.

I tried

Region[DiscretizeRegion[RegionUnion @@ data, MeshQualityGoal -> "Minimal"]]


without much success. Is there an easy way to get a simple expression (for example, points defining a single polygon) for a smooth region boundary in such a case?

## 1 Answer

Some reduction can be achieved by using BoundaryDiscretizeRegion[] and careful extraction of the boundary points:

Import["http://pastebin.com/raw/azNJSbVg", "Package"];
bdr = BoundaryDiscretizeRegion[RegionUnion @@ data];

pts = MeshCoordinates[bdr];
polys = Polygon[pts[[#]]] & /@
Map[First, FindCycle[DirectedEdge @@@ (First /@ MeshCells[bdr, 1]), ∞, All], {2}];

{Length[data], Length[polys]}
{57, 10}

Graphics[{Red, EdgeForm[White], polys}]