Multidimensional Scattered Time-varying Scattered Data Meshless Interpolation for Sensor Networks

Interpolation and approximation of scattered scalar and vector data is a part of a solution of many engineering problems. The methods are based mostly on some triangulation of the data domain, usually limited to 2D or 3D data, followed by an interpolation or an approximation to obtain a smooth result. This contribution presents a meshless approach based on the Radial Basis Functions (RBF). It is nearly dimensionless and it enables interpolation of time varying data, i.e. interpolation of scattered spatio-temporal varying data, i.e. interpolation in space-time domain without "time-frames". The meshless methods for scattered spatio-temporal data can be used for interpolation, approximation and evaluation of data acquired from buoys, sensor networks, sensors for tsunami, chemical and radiation detectors, ships and submarines detection, weather forecast, 3D vector fields compression and visualization, etc.