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# Untitled

a guest Jun 16th, 2019 63 Never
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1. Table[Polygon@Map[{Cos[#], Sin[#]} &,
2.    {RandomReal[{0, 2 Pi/3}],
3.     RandomReal[{2 Pi/3, 4 Pi/3}],
4.     RandomReal[{4 Pi/3, 2 Pi}]}], 3]
5. Graphics[{EdgeForm[Black], White, %}]
6.
7. {Polygon[{{-0.334165, 0.942514}, {-0.67166, 0.740859}, {-0.455064, -0.890459}}],
8.  Polygon[{{0.274586, 0.961563}, {-0.99882, -0.0485668}, {-0.454045, -0.890979}}],
9.  Polygon[{{0.832368, 0.554224}, {-0.977216, -0.212246}, {0.451922, -0.892057}}]}
10.
11. Table[triregion[i] = BoundaryDiscretizeGraphics[Graphics[triangles[[i]]]],
12.   {i, 1, Length[triangles]}]
13.
14. layerorder = {3, 2, 1}
15.
16. intersections = Flatten[
17.   Table[If[Length[
18.     RegionIntersection[
19.       triregion[layerorder[[i]]],
20.       triregion[layerorder[[j]]]]
21.     ] == 0, {layerorder[[i]], layerorder[[j]]}, Nothing],
22. {i, 1, 3}, {j, i + 1, 3}], 1]
23.
24. Out: {{3, 2}, {3, 1}, {2, 1}}
25.
26. Table[newregion[i] = triregion[i], {i, 20}];
27. Map[(newregion[#[[2]]] = RegionDifference[newregion[#[[2]]], triregion[#[[1]]]]) &,
28.   intersections];
29.
30. boundaries = Map[MeshPrimitives[#, 1] &, {newregion[1], newregion[2], newregion[3]}];
31. Show[Graphics /@ boundaries]
32.
33. d1 = {{-0.334165,0.942514},{-0.67166,0.740859},{-0.455064,-0.890459}};
34. d2 = {{0.274586,0.961563},{-0.99882,-0.0485668},{-0.454045,-0.890979}};
35. d3 = {{0.832368,0.554224},{-0.977216,-0.212246},{0.451922,-0.892057}};
36.
37. t1 = Line[Append[d1, First@d1]];
38. t2 = Line[Append[d2, First@d2]];
39. t3 = Line[Append[d3, First@d3]];
40.
41. p1 = Polygon[d1];
42. p2 = Polygon[d2];
43. p3 = Polygon[d3];
44.
45. r1 = t3;
46.
47. r2 = RegionDifference[t2, p3];
48.
49. r3 = RegionDifference[t1, RegionUnion[p2, p3]];
50.
51. DiscretizeRegion @ RegionUnion[r1, r2, r3]
52.
53. RegionUnion[r1, r2, r3]
54.
55. Region@RegionUnion[
56. Polygon[{{-0.334165, 0.942514}, {-0.67166, 0.740859}, {-0.455064, -0.890459}}],
57. Polygon[{{0.274586, 0.961563}, {-0.99882, -0.0485668}, {-0.454045, 0.890979}}],
58. Polygon[{{0.832368, 0.554224}, {-0.977216, -0.212246}, {0.451922, -0.892057}}]
59. ]
60.
61. In[1]:= pols=Table[Polygon@Map[{Cos[#], Sin[#]} &, {RandomReal[{0, 2 Pi/3}],
62. RandomReal[{2 Pi/3, 4 Pi/3}], RandomReal[{4 Pi/3, 2 Pi}]}], 3];
63. In[2]:= Graphics[{EdgeForm[Black], White, pols}];
64. In[3]:= DiscretizeGraphics@%;
65. In[4]:= Graphics@MeshPrimitives[%, 1];
66. In[5]:= reg=DiscretizeGraphics@%
67.
68. In[6]:= RegionDimension@reg
69. Out[16]= 1
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