How to create a list from a plot?

Question

This is motivated by this question.

Consider the list

list={0.2, 0.5, 0.7};

If I plot the data using ListLinePlot I get a curve like this

If I now apply interpolation using

ListLinePlot[{0., 0.2, 0., 0., 0.5, 0., 0., 0.7, 0.}, 
 InterpolationOrder -> 2]

I get

Now I wish to find the list which includes the interpolated values along with the zero values between 3 to 4 and 6 to 7 to generate Plot2.

How can I do this?

Answer 1

Update: A single list of points with negative y-values clipped to 0:

llp = ListLinePlot[{0., 0.2, 0., 0., 0.5, 0., 0., 0.7, 0.}, 
    InterpolationOrder -> 2,  PlotRange -> {-.2, 1}];
clippedpoints =  Cases[llp,  Line[x_] :> 
  Transpose[{#, Clip[#2, {0, Infinity}]} & @@ Transpose[x]], Infinity]

Show[llp, ListPlot[clippedpoints, PlotStyle -> Directive[Red, PointSize[.01]]], 
   PlotRange -> All]

True

---

Original answer:

llp = ListLinePlot[{0., 0.2, 0., 0., 0.5, 0., 0., 0.7, 0.}, 
  InterpolationOrder -> 2, PlotStyle -> Thick, PlotRange -> {0, All}]; 
points = Cases[llp, Line[x__] :> x, Infinity];

points // Short[#, 4] &

{{{1.,0.},{1.0234,0.00634228},{1.04853,0.0131544},{1.07539,0.0204362},{1.10399,0.0281879},<<45>>,{2.92412,0.0156563},{2.96203,0.00766473},{3.,3.46945*10^-18},{3.,0.}},{{<<18>>,0.},<<52>>},{<<1>>}}

Show[llp, ListPlot[points, PlotStyle -> Directive[Red, PointSize[.01]]], 
  PlotRange -> All]