Combining Rasterize with ParametricPlot

Question

The goal is to create an image like the one below

which was created using

ParametricPlot[{t, t^2}, {t, 0, 1}, Epilog -> Disk[{0.5, 0.5}, 0.09]]

but instead of using the Graphics primitive I want to use a Rasterized version of Disk.

Using the commands below, how can I duplicate the result?

bkgd = Rasterize[Disk[{0, 0}, 0.09]];
pplot = ParametricPlot[{t, t^2}, {t, 0, 1}];

It is important that ParametricPlot remain un-Rasterized.

Answer 1

First, you have to define bkgd differently because it's not a disk unless you make it a Graphics first:

bkgd = Rasterize[Graphics@Disk[{0, 0}, 0.09]];

Then use Inset:

ParametricPlot[{t, t^2}, {t, 0, 1}, 
Epilog -> {Inset[bkgd, {.5, .5}, Automatic, .2]}]

The position and size of the disk image are controlled by the last three arguments of Inset.

You will note that the last argument (the size scale) is a factor relative to the plot region (with 1 corresponding to the whole width).