Affine pseudo-distance

The number $ \rho = ( \overline{ {MM ^ {*} }}\; , \mathbf t ) $, equal to the modulus of the vector product of the vectors $ \overline{ {MM ^ {*} }}\; $ and $ \mathbf t $, where $ M ^ {*} $ is an arbitrary point in an equi-affine plane, $ M $ is a point on a plane curve $ \mathbf r = \mathbf r (s) $, $ s $ is the affine parameter of the curve and $ \mathbf t = d \mathbf r / ds $ is the tangent vector at the point $ M $. This number $ \rho $ is called the affine pseudo-distance from $ M ^ {*} $ to $ M $. If $ M ^ {*} $ is held fixed, while $ M $ is moved along the curve, the affine pseudo-distance from $ M ^ {*} $ to $ M $ will assume a stationary value if and only if $ M ^ {*} $ lies on the affine normal of the curve at $ M $. An affine pseudo-distance in an equi-affine space can be defined in a similar manner for a given hypersurface.