Meshless Methods in Computer Graphics and Visualization

Vaclav Skala
University of West Bohemia in Pilsen, Plzen

Meshless Methods in Computer Graphics and Visualization
Vaclav Skala
www.VaclavSkala.eu
Faculty of Applied Sciences, University of West Bohemia, Pilsen

Radial Basis Function (RBF) is a powerful mesh-free technique used for interpolation or approximation of irregularly scattered multi-dimensional spatio-temporal data.
It is based on a solution of a system of linear equations $\mathbf{A}\mathbf{x}=\mathbf{b}$.

Unlike grid-based techniques (e.g., finite differences or splines), RBFs depend only on the Euclidean distances between data points, making them naturally suited to problems where the sampling domain is non-uniform and the data are irregularly scattered.

Computational complexity is independent of the data dimensionality; it depends only on the number of interpolated values, not on the dimensionality.

The final interpolated values are then given in the analytical form $h= f(\mathbf{x})$, i.e., $h=f(x_1,\ldots,x_d)$ and fits the sparse data (acquired, observed, etc.) smoothly.