"The scheme smoothes the data by averaging a newly arrived data-point with the previously smoothed data-point, thus reducing the noise due to the discreteness of the pen location as measured by the tablet."

What Groner describes as noise due to discreteness, you would probably describe as pixelation. The figure below allows you to get a feel for the effects of pixelation or discretization on a smoothly drawn stroke. Press the Draw button to see the “real” path taken by the pen when drawing a smooth curve. Once the curve is drawn, press the Snap button to see the effect of forcing each point to lie on a discrete grid. Notice how the discretization introduces lots of little bumps, corners, and flat segments in what was previously a smooth curve.

Fortunately, we can smooth the tablet’s output to liberate these points from the impositions of a fixed grid. The smoothing operation is performed by averaging the position of each new quantized datapoint with the position of the last smoothed datapoint. We can geometrically perform this averaging by drawing a straight line between each quantized datapoint and the most recently smoothed datapoint. We then slide the quantized point along this line towards the previously smoothed point. The further we slide the point, the more we accentuate the effect of the smoothing. You can develop an intuition for this smoothing algorithm using the visualization below. The quantized datapoints are drawn in blue, and the smoothed points will be drawn in black. The three buttons allow you to specify how far each point should slide along the guideline. Higher percentages will lead to a smoother curve.
This simple smoothing scheme allows us to rid the data of unwanted bumps and jaggies while still maintaining the overall gesture of the stroke. Note however, that smoothing is a destructive process. Small flourishes of the pen will be obliterated by smoothing. For this reason, it’s crucially important to choose an appropriate smoothing factor.

Draw on the tablet below to see how this smoothing scheme will affect more interesting inputs. You can change the degree to which each stroke is smoothed by dragging the slider to the right of the visualization. Spend some time drawing letters, numbers, and simple shapes onto the tablet. I suggest that you begin by drawing a straight line from the bottom left to the top right of the tablet. Once this is done, slowly drag the slider to see how the stroke is transformed as the amount of smoothing is varied.

	Smoothing is based on the equations, XSi = XSi-1 + XRi YSi = YSi-1 + YRi XRi,YRi = coordinates of ith raw point XSi,YSi = coordinates of ith smoothed point Smoothing Factor: