Oval - Wikipedia

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To the definition of an oval in a projective plane

To the definition of an ovoid

Any line l meets Ω in at most two points, and
For any point P ∈ Ω there exists exactly one tangent line t through P, i.e., t ∩ Ω = {P}.

For finite planes (i.e. the set of points is finite) there is a more convenient characterization:[2]

For a finite projective plane of order n (i.e. any line contains n + 1 points) a set Ω of points is an oval if and only if |Ω| = n + 1 and no three points are collinear (on a common line).

An ovoid in a projective space is a set Ω of points such that:

In the finite case only for dimension 3 there exist ovoids. A convenient characterization is:

In a 3-dim. finite projective space of order n > 2 any pointset Ω is an ovoid if and only if |Ω| and no three points are collinear.[3]