In the field of timber construction, we work on surface design that is based on an iterative model called "IFS" (Iterated Function System). The modeled figures must meet certain properties in order to ensure their physical feasibility. For the construction of structures based on timber panels, we research in planarity constraints of quadrilateral meshes. First, we will introduce a particular model for a certain type of planar quadrilateral meshes. This surface model is defined as a certain combination of two polylines. Further, we present some basic properties of the iterative model employed, which is inspired by the IFS model. Finally, we define a surface model generated by an operator that combines two IFS, each describing a one curve.