  When considering regularity of surfaces, it is its geometry that is of
interest. Thus, the concept of geometric regularity or geometric continuity of
a specific order is a relevant concept. In this paper we discuss necessary and
sufficient conditions for a 4-patch surface to be geometrically continuous of
order one and two or, in other words, being tangent plane continuous and
curvature continuous respectively. The focus is on the regularity at the point
where the four patches meet and the compatibility conditions that must appear
in this case. In this article the compatibility conditions are proved to be
independent of the patch parametrization, i.e., the compatibility conditions
are universal. In the end of the paper these results are applied to a specific
parametrization such as Bezier representation in order to generalize a 4-patch
surface result by Sarraga.
