What is negative squared euclidean distance?

Question

It is described as -||xi-xy||^2.

So for 2 two dimensional points do I code it like this?

- ((x1-x2) + (y1-y2))^2

or

-( (x1-x2)^2 + (y1-y2)^2 )

or

-(sqrt( (x1-x2)^2 + (y1-y2)^2 ))

or some other way?

Answer 1

The correct answer is

-( (x1-x2)^2 + (y1-y2)^2 )

The mathematical description is accurate, but not useful for implementation. It's stated as the square of the distance between the points, which if implemented directly would be something like:

len = sqrt( (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2) );
result = -( len*len );

which can simplified to

result = -( (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2) );

which is your #2.

Answer 2

The third is the negative of the distance. The second appears to be the negative of the square of the distance.