"What is the best interpolation method for compute values inside circle?"
There are an infinite number of coordinates inside the circle. Are you trying to determine if a given coordinate (x,y) is inside the circle or are you trying to list a set of coordinates at a given interval (like a grid) that are inside the circle?
"Is there a function that sums the circumference to center of gravity and divides by two and places it at half the distance and repeat that?"
That's pretty specific, but it would be very easy to write such a function.
