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I have 2 of list data

CurveA = {{140.796, 31.3888}, {140.555, 31.5343}, {140.314, 31.6829}, {140.076, 31.8344}, {139.839, 31.9889}, {139.604, 32.1464}, {139.37, 32.3069}, {139.138, 32.4704}, {138.908, 32.6369}, {138.68, 32.8065}, {138.452, 32.9791}, {138.227, 33.1547}, {138.003, 33.3334}, {137.781, 33.5152}, {137.56, 33.7}, {137.341, 33.8879}, {137.123, 34.0789}, {136.907, 34.2729}, {136.692, 34.4701}, {136.479, 34.6704}, {136.267, 34.8738}, {136.057, 35.0804}}; CurveB = {{140.492, 31.5563}, {139.939, 31.8567}, {139.38, 32.1475}, {138.816, 32.4285}, {138.248, 32.6996}, {137.675, 32.9607}, {137.098, 33.2118}, {136.516, 33.4528}};

If I want to know the index or position of a pairs data (CurveA and CurveB) which have distance of 1 mm, how to do that? Here is the illustration:

enter image description here

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  • $\begingroup$ DistanceMatrix[]? $\endgroup$ Commented Jan 26, 2018 at 2:38

2 Answers 2

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One approach is to interpolate to find functions that represent the data and then find a root of that function. cA is the interpolation of CurveA, cB is the interpolation of CurveB, and you are looking for the value at which they are 1 apart:

cA = Interpolation[CurveA]; cB = Interpolation[CurveB]; FindRoot[cA[t] - cB[t] == 1, {t, 136}] {t -> 136.868}
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iFA = Interpolation[CurveA]; iFB = Interpolation[CurveB]; Quiet @ ListPlot[{CurveA, CurveB, CurveA, CurveB}, Joined -> {True, True, False, False}, PlotStyle -> {Blue, Green}, BaseStyle -> PointSize[.02], MeshStyle -> ({Red, Arrowheads[{-.05, .05}], Arrow@@#}&), MeshFunctions -> {iFA[#] - iFB[#] &}, Mesh -> {{1}}]

enter image description here

Update: The MeshStyle trick above does not work with ListLinePlot in version 11.2. It does work with Plot, so, in version 11.2, you can do 

Quiet@Plot[{iFA[t],iFB[t]}, {t, 156, 141}, MeshStyle -> ({Red, Arrowheads[{-.05, .05}], Arrow @@ #} &), MeshFunctions -> {iFA[#] - iFB[#] &}, Mesh -> {{1}}, Epilog-> {ListPlot[{CurveA, CurveB}, PlotTheme -> "OpenMarkers"][[1]]}]

enter image description here

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