We solve the following problem: given a polynomial of order $n$ and
 the corresponding Bezier tensor product patches over an
unstructured regular quadrilateral mesh with nodes of any valence,
 find a solution to the  $G^{1}1$  or  $C^{1}1$ approximation (resp.
 interpolation ) problem !  Constraints defining regularity conditions
 across patches have to be satisfied. The resulting number of free
 degrees of freedom must be such that for instance  the interpolation
 problem has a solution! This is similar to studying the minimal
 determining set (MDS) for a $C^{1}1$ continuity construction.
 
 We consider a given arbitrary quadrilateral mesh,that can include a
 cubic boundary curve and the final surface approximation or PDE
 solution is obtained by energy methods. We completely solve the
 problem and show that there is always a solution for $n\ge 5$ and
 under some mesh restrictions for $n=4$.
 
 From a practical point of view, the present work provides a way to
 build first order smooth interpolation/approximation and solutions to
 partial differential equations for arbitrary structures of
 quadrilateral meshes .
 
 We will also discuss how this work can contribute to IGA, in the light
 of a recent result by J. Peters.  (Joint work with Tanya Matskewich)