The present invention embraces a system for measuring the 3D shape of an object using a structured light projector and an image sensor such as a scanner or camera. The structured light projector “projects” a pseudo random dot pattern onto the object that is positioned on a planar surface. The image sensor captures the 3D image of the object from the reflective surface and determines the dimensions or shape of the object. The surface displays the projected dot pattern and defines a grid based on the projected dot pattern. The dot pattern comprising a plurality of dots distributed on the grid such that neighboring dots within a certain sub-window size are unique sub-patterns. The neighboring dots are arranged in a staggered grid format relative to one axis of grid.