When you say convert curves, what do you mean exactly? I am assuming that you are talking about vector objects somehow and not talking about the curves adjustment feature that adjusts color tones in the image.
Is it converting a vector object to a raster object, or, converting text or a raster object to a vector object?
Photoshop can convert any vector object into a raster object very easily. Photoshop can also take any font and make a vector object out of it with the Type Mask Tool and then converting the mask selection into a path. Paths in Photoshop are nothing but vector paths and very useful.
Photoshop can also work with any true vector object created in vector software by placing it in the Photoshop document as a Smart Object. You don't open or import the vector, you either use the Place feature, or copy and paste and then select Smart Object in the menu that appears when you paste the vector object. A Smart Object retains its full vector features until you rasterize the object.