An Image-projective Desktop Varnamala Trainer (IDVT) called SAKSHAR has been designed to improve the learning by children through an interactive audio visual feedback system. This device uses a projector to render a virtual display, which permits production of large interactive displays with minimal cost. The user's hand is recognized with the help of a Microsoft Kinect Version 2. The entire system is portable, i.e., it can be projected on any planar surface. Since the Kinect does not give precise 3D coordinates of points for detecting a touch, a model of recognition of a touch purely based on the contact of the user's hand with the surface would not yield accurate results. We have instead modeled the touch action by using multiple points along the trajectory of the tracked point of the user's hand while hand makes contact with the surface. Fitting a curve through these points and analyzing the errors is used to make the detection of touch accurate.