A pointing detecting device is described. In an embodiment, a device comprises: a display; a processor; a storage containing instructions; wherein the instructions cause the processor to: select a set of points from a point cloud representing a pointing object in proximity or in contact of the display; determine the selected set of points as control points of a computational smooth surface representing the pointing object; determine a point nearest to the display on the computational smooth surface; based on the point nearest to the display, determine a point in a direction of a gradient of a curvature of the computational smooth surface; and report the point as a location of a desired pointing or touch action.