Is centre of minimum enclosing sphere the answer to this problem ??
If yes then considering x and y coordinates only, can't we find minimum enclosing circle's centre and then somehow search for required z coordinate because min_z <= z <= max_z .
min_z = min. z coordinate in given set of points
max_z = max. z_coordinate in given set of points
If yes then considering x and y coordinates only, can't we find minimum enclosing circle's centre and then somehow search for required z coordinate because min_z <= z <= max_z .
min_z = min. z coordinate in given set of points
max_z = max. z_coordinate in given set of points
Example: you have right triangle (1, 0, 0)-(0, 0, 1)-(0, 0, -1). And you are proecting it on OXY (throwing out third z-coordinate).
Minimal enclosing circle of (1, 0)-(0, 0)-(0, 0) has centre (0.5, 0).
But minimal enclosing sphere of third points in space has centre (0, 0, 0), because it's centre of the hypotenuse. 0.5 != 0 :-(
If it was true, you could project points on OXY and discover x,y coordinates of sphere, then project points on OYZ and discover y,z coordinates, so there wasn't any need to search z :-)