An improved high resolution method and apparatus are described for sensing and determining the spatial coordinates of a movable object with respect to a energized conductive surface. The coordinates of the object are precisely measured with respect to a two-dimensional coordinate system independent of the third orthogonal dimension, thereby avoiding significant measurement errors due to variations of the object position in the third orthogonal dimension. The system also ascertains the coordinate position of the object in this third dimension, which can then be utilized as an independent control variable in the system. Further, the system can accommodate a number of energized conductive surfaces over which the object may be positioned and can determine the spatial coordinates of the object with respect to any such surface. In general, the system of the present invention can ascertain the generalized n-tuple position vector of the object with respect to each of a plurality of generalized, energized conductive surfaces. In any of the foregoing forms, the energized conductive surfaces can be transparent. The system described improves the precision and accuracy of the location of the selected point and hence the precision and accuracy of the spatial coordinates calculated by the system for display. The improvement in system performance is the result of innovations in fundamental design concepts utilized throughout the system.