3D Scattered Data
This area of ARANZ research is focused on modelling scalar distributions where a scalar attribute is described by a function of three variables (for example, position).
Common examples include measurements of temperature, density and electric potential.
Some vector fields can also be considered in this context, provided the components of the vector field are independent and
can therefore be modelled separately as scalar quantities.
We model 3D data with mathematical functions known as Radial Basis Functions (RBFs). RBFs minimise certain energy functionals (usually the second, third or higher derivatives).
In this sense RBFs are known as smoothest interpolatants.
The prime advantage of ARANZ's FastRBFTM software is
that you can easily model scattered data not acquired (or generated) on a regular grid. The
resulting functional model can be evaluated anywhere and is smooth and continuous. Gradients can be computed analytically. This facilitates the visualisation of scattered data since the function can be resampled on a plane for 2D reslicing or evaluated on a regular grid suitable for volume rendering or it can be evaluated on a surface.
The functional representation also results in new methods for approximatiing and smoothing noisy data.
FastRBFTM makes it possible to fit functional models to very large data sets consisting of millions of measurements on a PC, a task previously thought impossible.
Further information can be found on the following ARANZ web pages:
