The presently disclosed technology uses predefined handwriting characteristics to create and/or refine a stylus position interpolation function over time to provide more accurate and adaptive renderings of the user's handwriting on a touch screen. As the presently disclosed technology is performed on a specific device and uses data collected from one or more specific users, it adapts the stylus position interpolation function for any device-specific or user-specific variations. Further, as the stylus position interpolation function adapts iteratively over time, it may not converge and continues to adapt as the device ages, the user's habits change, or identify of the user changes, and environmental conditions of the device change.