A time function to express hand-drawn letters

An efficient function to express curves of hand-drawn letters is derived from a simple model of hand-drawing. The pen-tip is modeled as a point mass which is moved by force as constant as possible on a plane and is navigated to go through some characteristic points to form the curve's peculiar shape. The characteristic points are assumed to be where the pen-tip has locally minimal velocity and where it touches the baseline. Among those points, a steeple like the left bottom of 'h' is prominent, which is modeled as a pausing point where the tip should pause at a moment to alter its moving direction. The derived solution is a mixture of a fifth order spline with its knots placed at the characteristic points and a fourth order spline with those at the pausing ones. This mixed function is proven by computer experiments employing real hand-drawn data to be efficient in expressing hand-drawn letters. This means that the proposed model imitates hand-drawing.