The invention determines the location of multiple, simultaneous contact areas on a touch sensing region using a light source and several light detectors. The invention is robust against occlusion and many of the ambiguities that can arise with multiple, simultaneous contact areas. Generally, the light source is positioned such that light emanating the light source passes across the touch sensing region, and the light detector are positioned such that at least a portion of the light source is within the field of view of each light detector. The contact areas are determined by identifying positive fans corresponding to an angular sector of the field of view of a light detector in which the view of the light source is occluded and negative fans corresponding to an angular sector of the field of view of a light detector in which the view of the light source is not occluded. The positive fans and negative fans are then additively and subtractively combined, respectively, to determine the contact areas.