We present a method for approximate 3D point sets alignment to register surfaces with varying degrees of overlap. The approach is based on a novel technique to extract dynamically the sets of coplanar 4-points from a 3D point set which are approximately congruent. The choice of bases from one 3D set to be matched to the others for possible registration is done automatically, and it is refined dynamically by controlling the width of the bases against the degree of overlap to be achieved at each iteration. Besides being an automatic way to perform the alignment, our method is a way to optimize the 4-points bases selection since it converges fast to appropriate bases as they are available. We show and compare reconstruction results using publicly available 3D scan data.