Affine pseudo-distance

The number , equal to the modulus of the vector product of the vectors and , where is an arbitrary point in an equi-affine plane, is a point on a plane curve , is the affine parameter of the curve and is the tangent vector at the point . This number is called the affine pseudo-distance from to . If is held fixed, while is moved along the curve, the affine pseudo-distance from to will assume a stationary value if and only if lies on the affine normal of the curve at . An affine pseudo-distance in an equi-affine space can be defined in a similar manner for a given hypersurface.