Software to Determine the Centroid of a Star in a CCD Frame

Question:
Hi, This is probably a rather unique question, but I have not been able to find the answer anywhere else.
Assume I have a .fit frame from my CCD camera and it shows a star somewhere in the frame. I want to:
1) Identify exactly where the centroid of that star is (not just close, but the exact mathematical centroid of that stellar image). We can assume that that none of the pixels are saturated.
2) I want to move the centroid of that star to the exact center of the .fit frame (not approximately centered, but the exact mathematical center down to the accuracy of a pixel). I do not care if some of the outer parts of the frame are deleted in this process.
There must be software that can do this but I cannot find it. Do you know of any software that can do this? Thank you.
Answer:
You might find some advice on publicly-available software that can calculate the centroid of a star in a CCD frame and recenter that position in the frame on the Cloudy Nights Forum. It looks like there are several different software packages that can do this task.