I have a set of 3D points. I can get the position of any 1 point, but there's too many for me to calculate the average by hand. I'm only able to get the average when the average coordinates are all a multiple of 500 (I'm using a visualizer program that only shows an indicator for the average position of the grouped points and not any coordinates for it, but will let me snap the average indicator to a grid. So I'm able to add an independent point on the same grid, visually line up the point with the average indicator, and get the average through the point's coordinates.). I can move the set of points to where the average of each coordinate is a multiple of 500 and get the average of the moved set. I can then check the position of any 1 point in the moved set.
For example, I have a set of 72 points. 1 point has the coordinates (-5165,1000,2200). When I shift the set, where its new average becomes a multiple of 500, the new average is (-1000,2000,2500). Looking at the same point after it's been shifted, its coordinates are now (-5331.65,1086.88,2368.48).
I'm wondering if it's possible to add a point to the set to where the new average will become a multiple of 500. So I'd like to add a point so that when I shift the set to the grid layout all the existing points will stay in place.
I know I can do this given the initial average by doing $$InitialAverage + ((InitialCoordinate - ShiftedCoordinate) * (CurrentPointCount + 1))$$ for each axis.
For example using the above values, the X coordinate would be: $$InitialAverage + ((-5165 - (-5331.65)) * (72 + 1)) = InitialAverage + (166.65 * 73) = InitialAverage + 12165.45$$
But I can't think of any way of achieving this without the initial average.