Detecting and aligning structured signals such as point grids plays a fundamental role in many signal processing applications. Joint determination of non-grid points and estimation of non-linear spatial distortions applied to the grid is a key challenge for grid alignment. This paper proposes a candidate solution. The method described herein starts from a small nearly regular region found in the point set and then expands the list of candidate points included in the grid. The proposed method was tested on geometrically transformed point sets and sets of locations derived from imagery of 3D prints. It is shown that a low-complexity grid alignment method can nonetheless achieve high grid alignment accuracy.