The gaussian centre and the projection centre of a set of points in r 3 .
Stéphane Durocher, David G. Kirkpatrick · Canadian Conference on Computational Geometry · 2004
Finding a centre point is a fundamental problem of geometry. The Euclidean centre, or centre of the smallest enclosing sphere, provides a natural definition for the centre of a set of points. As shown in [BBKS00] and [DK04], the Euclidean centre of a set of points * + -, is unstable; small perturbations at only a few points of can result in an arbitrarily large relative change in the position of the Euclidean centre. To define a centre . more stable than the Euclidean centre requires, at least for some sets of points, that . differ from the Euclidean centre. Presumably, remaining central to is desirable. These two factors are in opposition; high stability implies high eccentricty and vice-versa. In [DK04], the Gaussian centre of a set of points in the plane is introduced toward the objective of identifying a good centre that balances high stability with low eccentricty. The projection centre of a set of points in the plane is also defined and shown to be equivalent to the Gaussian centre.