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The interpolation overshoots the next point and reverses direction. ParametricPlot[{line[[1]][tt], line[[2]][tt]}, {tt, 0.2, 0.3}, Epilog -> {Point[points[[All, 1 ;; 2]]]}] You can reduce the interpolation order to 1 or use a centripetal parametrization parametrizeCurve from J.M.'s answer. parametrizeCurve[pts_List, a : (_?NumericQ) : 1/2] := ...



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