A touch sensor is provided including a controller and a planar layout having an edge and an interior portion. Further including a connector coupling the touch controller to the layout; a substrate made of a first material; and sensing elements made of a second material formed on the substrate and covering the layout without overlapping. Sensing elements have non-monotonic widths from the center along two perpendicular directions, and a centroid. The touch sensor including pass-through traces to couple edge to interior portions to determine two-dimensional locations for touches using a weighting that is proportional to an overlap area of the sensor elements and their centroids. The substrate may be made of a dielectric and the sensing elements made of a conductor. A method for using a controller circuit having a memory to store centroid locations and determine a two-dimensional location on a touch screen as above is also provided.