An optical touch screen that utilizes a planar transparent sheet and that is configured to determine the position of a touch event on the transparent sheet is disclosed. Light-source elements and light-sensing elements are operably disposed at the transparent sheet perimeter. Light is detected over lines-of-sight between the light-source elements and the light-sensing elements. Attenuated lines-of-sight due to a touch event are determined. Polygons are established by overlapping triangles defined by the limiting lines of sight for each light-sensing element. Polygons with attenuations below the attenuation threshold are eliminated. The centers of the remaining polygons are then determined to establish the locations of the touch events. The systems and methods provide robust detection of multiple touch events.