mjhjmtu

Is it possible to add to the Mesh points in a ParametricPlot the x-values in sort of a Callout-style way? E.g. on the following simple function:

ParametricPlot[Sin@x, .3 Log@(x^2), x, 0, 10, Mesh -> 20]

The points are on the plot (a little small), now there should be the x values (0,0.5,1,1.5,...) indicated next to the points, as said in form of as it is produced with Callout.

pp = ParametricPlot[Sin@x, .3 Log@(x^2), x, 0, 10, 
 Mesh -> Subdivide[0, 10, 20], MeshStyle -> PointSize[Large]];
points = Cases[Normal[pp], Point[x_] :> x, ∞];
Show[pp, ListPlot[Callout[#, #2] & @@@ 
 Transpose[SortBy[points, Last], N @ Rest@Subdivide[0, 10, 20]]], ImageSize -> 400]

Also

ParametricPlot[Sin@x, .3 Log@(x^2), x, 0, 10, 
 Epilog -> ListPlot[Callout[##2, #] & @@@ 
 Table[N@x, Sin@x, .3 Log @ (x^2), x, Subdivide[0, 10, 20]], 
 PlotStyle -> PointSize[Large]][[1]]]

Using Epilog

ParametricPlot[Sin@x, .3 Log@(x^2), x, 0, 10, 
 Epilog -> AbsolutePointSize[4], 
 Text[N[#], pt = Sin@#, .3 Log@(#^2), 0, If[IntegerQ[#], -2, 2]], 
 Red, Point[pt] & /@ Range[1/2, 10, 1/2]]