Invariant-geometry conditions for the rational bi-quadratic Bézier surfaces

A generalisation of Patterson's work, on the invariants of the rational Bézier paths, to the case of surface patches is presented. An equation for the determination of the invariants for patches of degree (n,n) is derived and solved for the bi-quadratics – for which it is shown that seven independent, invariant functions exist. Explicit forms of the invariants are derived and a number of applications are presented.