In this work we analyze the space of geometrically smooth biquintic Bézier polynomials defined on a quadrilateral mesh M generated by the G1 Approximate Catmull-Clark scheme (G1 ACC) in [27]. With the use of quadratic gluing data functions, an explicit construction for an efficient set of basis functions generating the G1 ACC space is provided as well as a dimension formula. The global structure is therefore applied to solve point cloud data fitting problems defined over multipatch domains whose quality is demonstrated by numerical experiments presented in this paper performed over several data points possessing various features with interest for applied problems.