*In the Air* uses an infinite set of formulas depending on a parameter w that can be specify by the (expert) user. The way the value of the parameter changes the behavior of the interpolation is directly related to how intense the influence of a value given by a data point at a specific moment on the approximation value on the whole plane. For low values of w (close to 0) the influence is lower and the approximation tends to be closer to the global average. For higher values of w (bigger than 1) approximative values are close to the value of the closest data point. (So, at the limit, it creates a Voronoy partition of the plane).

Which is the best value of w that determines the best approximation? It is complicated because this value might change in time and also among gases. It is the aim of this team to develop ways to calculate the best approximations comparing the real data with the values generated by the visualization.

The Interpolation Function

People are not interested in data that is tied to specific sites as they donĀ“t spend all their time at those places. *In the Air* uses an interpolation function to fill the information gaps of pollutant levels in the Madrid atmosphere. This yields an *approximate* value for points that are close or not so close to the 15 sensors informing this prototype

It is very important to understand that the data obtained by the interpolation is approximate, and its main purpose is to help users understand what happens throughout the city. There are several ways to obtain approximate values on points that are close to sensors. All "good" interpolations should derive a value of a point in proportion to the proximity to "known" data points.