Programmatically Break Down Complex Shapes into Simple Polygons

This should do about 75% of the job, I suppose.

divisions

Known issues …

  1. Doesn’t work if the slab has openings within
  2. Creates sub divisions as long as there are parallel edges.
  3. Sometimes creates boundaries beyond surface (adjust variable acc01 when this happens)

RectangularDivision.dyn (40.1 KB) (ver 2.8)

def Rect(srf:var[]..[])
{
	srf01 = List.Flatten(srf.Explode(),-1);
	srf02 = List.FilterByBoolMask(srf01,List.Count(srf01.Vertices.PointGeometry<1>)>3)["in"];
	crv00 = srf02.PerimeterCurves();
	pcv01 = PolyCurve.ByJoinedCurves(crv00);
	vtx01 = List.Flatten(srf02.Vertices.PointGeometry,-1);

	//Offset Perimter Curves Outwards
	seg01 = 100;
	off01 = List.Flatten(crv00,-1)[0].Length/seg01;
	pcv02 = pcv01<1>.Offset([off01,-off01]);
	pcv03 = List.FirstItem(pcv02<1>);
	pcv04 = List.LastItem(pcv02<1>);
	pcv05 = pcv03.Length > pcv04.Length ? pcv03 : pcv04;

	//Inward Vectors
	acc01 = 8;
	pnt01 = crv00<1><2>.PointAtParameter((0..1..#acc01));
	vct00 = crv00<1><2>.NormalAtParameter((0..1..#acc01));
	vct01 = List.GetItemAtIndex(vct00<1><2>,Math.Floor(acc01/2));
	pnt02 = List.Flatten(pnt01.Project(pcv05,vct01)<1><2>,-1);
	bln01 = List.AllTrue((pnt01.DistanceTo(pnt02)!=off01)<1><2>);
	vct02 = bln01 ? vct01 : vct01.Reverse();

	//Rectangle aligned to Surface Boundaries
	pnt03 = List.Flatten(pnt01.Project(pcv05,vct02)<1><2>,-1);
	dis01 = Math.Round(pnt01.DistanceTo(pnt03)-off01,6);
	bln02 = List.DropItems(dis01<1><2>,-1)==List.DropItems(dis01<1><2>,1);
	fil01 = List.IndexOf(bln02<1><2>,true);
	fil02 = fil01==-1 ? acc01 : fil01;
	fil03 = List.DropItems(bln02<1><2>,fil02<1><2>);
	fil04 = List.IndexOf(fil03<1><2>,false);
	fil05 = fil04 == -1 ? acc01-1 : fil04+1;
	fil06 = List.DropItems(pnt01<1><2>,fil02<1><2>);
	pnt04 = List.TakeItems(fil06<1><2>,fil05<1><2>);
	fil07 = List.DropItems(pnt03<1><2>,fil02<1><2>);
	pnt05 = List.TakeItems(fil07<1><2>,fil05<1><2>);
	lin01 = List.Clean(Line.ByStartPointEndPoint(pnt04,pnt05).ExtendEnd(-off01),false);
	bln03 = List.Count(List.RemoveIfNot(lin01.Intersect(pcv01)<1><2><3>,"Point")<1><2><3>)>2;
	lin02 = List.FilterByBoolMask(lin01,bln03)["out"];
	lin03 = List.FirstItem(lin02<1><2>);
	lin04 = List.LastItem(lin02<1><2>);
	vct03 = Vector.ByTwoPoints(lin03.PointAtParameter(0.5),lin04.PointAtParameter(0.5));
	vct04 = Vector.ByTwoPoints(lin04.PointAtParameter(0.5),lin03.PointAtParameter(0.5));

	//Shift edge towards Closest Vertex
	pnt06 = List.Transpose(vtx01<3>.Project(lin03<1><2>,vct03<1><2>)<1>);
	bln04 = DSCore.Object.IsNull(List.Count(pnt06<1><2><3>)>0)?true:List.Count(pnt06<1><2><3>)>0;
	dis02 = lin03.DistanceTo(List.FilterByBoolMask(vtx01,bln04<1><2>)["in"]);
	lin05 = lin03.Translate(vct04,List.MinimumItem(dis02));
	pnt07 = List.Transpose(vtx01<3>.Project(lin04<2><1>,vct04<2><1>)<1>);
	bln05 = DSCore.Object.IsNull(List.Count(pnt07<1><2><3>)>0)?true:List.Count(pnt07<1><2><3>)>0;
	dis03 = lin04.DistanceTo(List.FilterByBoolMask(vtx01,bln05<1><2>)["in"]);
	lin06 = lin04.Translate(vct03,List.MinimumItem(dis03));

	//Largest Rectangle
	lin07 = List.Transpose([lin05,lin06]);
	edg01 = List.FirstItem(lin07<1>);
	edg02 = List.LastItem(lin07<1>);
	pnt08 = List.Transpose(List.Transpose([edg01.StartPoint,edg01.EndPoint,edg02.EndPoint,edg02.StartPoint])<1>);
	rct01 = Rectangle.ByCornerPoints(pnt08);
	are01 = rct01.Patch().Area;
	rct02 = List.LastItem(List.SortByKey(rct01<1>,are01<1>)["sorted list"]<1>);
	return rct02;
};


def Divs(srf:var[]..[])
{
	divs = [Imperative]
	{
		c = 0;
		r = [];
		n = true;
		s = [];
		while (n)
		{
			r [c] = Rect(srf);
			sld01 = Surface.ByPatch(List.Flatten(r[c],-1));
			sld02 = Solid.ByUnion(Surface.Thicken(sld01,10));
			s [c] = Surface.SubtractFrom(srf,sld02);
			srf = List.Flatten(s[c],-1);
			n = List.Count(List.Flatten(r[c],-1))>0;
			c = c+1;

		}
		rct01 = List.DropItems(List.Flatten(r,-1),-1);
		prm01 = (List.LastItem(List.DropItems(List.Flatten(s,-1),-1)).Explode());
		return [rct01,prm01];
	}
	crv01 = PolyCurve.ByJoinedCurves(divs[1].PerimeterCurves());
	crv02 = List.Flatten([divs[0],crv01],1);


	return crv02;
};
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