How can I combine a list of Line[]'s into one continuous Line?
Here's a graph-based solution:
gr = Graph[linelist1 /. Line[List[v__]] :> UndirectedEdge[v]];
cycle = First@FindHamiltonianCycle[gr, 1];
Graphics[{Dashing[0.01], Line[Append[cycle[[All, 1]], cycle[[-1, 2]]]]}]
The goal here is to turn the collection of Line objects into a BoundaryMeshRegion, and then extract the boundary from that region. This is similar to user21's solution, but a bit more robust for this application.
mr = BoundaryDiscretizeGraphics[linelist2];
MeshPrimitives[mr, 2] /. Polygon[a__] :> Line[a] //
Graphics[{Dashing[0.01], #}] &
linelist1 = {Line[{{0.15042300130733277`,
0.09918669845167598`}, {0.15124668865085406`, 0.09522452324491057`}}],
Line[{{0.14961629841942972`, 0.10444571885174352`}, {0.15042300130733277`,
0.09918669845167598`}}],
Line[{{0.15124668865085406`, 0.09522452324491057`}, {0.15296330904994523`,
0.09071834061461313`}}],
Line[{{0.14933067532583966`, 0.10873463230613303`}, {0.14961629841942972`,
0.10444571885174352`}}],
Line[{{0.1492065391252379`, 0.11459136282769972`}, {0.14933067532583966`,
0.10873463230613303`}}],
Line[{{0.15296330904994523`, 0.09071834061461313`}, {0.15443233429278366`,
0.08720754178169458`}}],
Line[{{0.15443233429278366`, 0.08720754178169458`}, {0.15738657618834503`,
0.0837116800119704`}}],
Line[{{0.15738657618834503`, 0.0837116800119704`}, {0.1596507357294199`,
0.08081800622081214`}}],
Line[{{0.14938185651096897`, 0.11910808435898695`}, {0.1492065391252379`,
0.11459136282769972`}}],
Line[{{0.14978835086914977`, 0.1254736636010152`}, {0.14938185651096897`,
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Line[{{0.15077460730814868`, 0.1327981842766949`}, {0.15036790182308324`,
0.13013455437855134`}}],
Line[{{0.15036790182308324`, 0.13013455437855134`}, {0.14978835086914977`,
0.1254736636010152`}}],
Line[{{0.15120855329817068`, 0.13696037633048153`}, {0.15077460730814868`,
0.1327981842766949`}}],
Line[{{0.16277911871721887`, 0.07929367135576196`}, {0.16756504304577993`,
0.07669208018087739`}}],
Line[{{0.1596507357294199`, 0.08081800622081214`}, {0.16277911871721887`,
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Line[{{0.16756504304577993`, 0.07669208018087739`}, {0.17179084853507678`,
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Line[{{0.17179084853507678`, 0.07624695124973005`}, {0.17906280098426666`,
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Line[{{0.15257273308627697`, 0.14470958676131765`}, {0.15214869088284963`,
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Line[{{0.15214869088284963`, 0.14169046682959874`}, {0.15120855329817068`,
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Line[{{0.154380363176796`, 0.15329508718925586`}, {0.15336715187177208`,
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Line[{{0.15336715187177208`, 0.14894978414339125`}, {0.15257273308627697`,
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Line[{{0.15408201484170664`, 0.17090212421388687`}, {0.154380363176796`,
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Line[{{0.1846655098267246`, 0.07675733142107073`}, {0.19526513101961043`,
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0.4514099006447918`}}],
Line[{{0.5029083407423581`, 0.44889688974935993`}, {0.49919310111973014`,
0.45113398227358853`}}],
Line[{{0.4890646389147416`, 0.45348782067176335`}, {0.4838758910848437`,
0.45289412540402957`}}],
Line[{{0.49919310111973014`, 0.45113398227358853`}, {0.49332267538788155`,
0.45296691617990653`}}],
Line[{{0.49332267538788155`, 0.45296691617990653`}, {0.4890646389147416`,
0.45348782067176335`}}]};
Convert lines to points
pts = Flatten[linelist1 /. Line -> Identity, {2}][[1]];
Using ListCurvePathPlot
ListCurvePathPlot[pts,
Frame -> True,
Axes -> False,
PlotStyle -> Dashed]
Using FindCurvePath
curve = FindCurvePath[pts];
ListLinePlot[pts[[curve[[1]]]],
Frame -> True,
Axes -> False,
AspectRatio -> Automatic,
PlotStyle -> Dashed,
ImageSize -> 350]
