graphics - Discretize chart in a given interval

Using the following code:

plot = Plot[Sin[x], {x, -Pi, Pi}];
points = Cases[plot // Normal, Line[{x__}] -> x, Infinity];

ListPlot[points]

I get:

Question: Is it possible to thicken such discretization? Also, you can do so at any given internal interval to the graph?

Thank you for your invaluable help.

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EDIT:

To be honest I was wrong example, I try again.

plot = Show[Plot[Sin[x], {x, -Pi, Pi}]];

points = Cases[plot // Normal, Line[{x__}] -> x, Infinity];
ListPlot[points]

Here, in the latter case there is any hope to increase the points in a given interval, for example, in [-1,1]? Thanks again and sorry for my incompetence.