A functional representation of a surface, such as ARANZ's RBF, allows the error between a surface and a point on a mesh approximating the surface to be determined analytically. This facilitates the positioning of faces and vertices when simplfying a mesh.
The first example below demonstrates RBF-based mesh simplification of laser scan data. Initially an RBF was fitted to laser scans of a bust in order to automatically fill holes and generate a water-tight mesh. The RBF description was converted to the very fine mesh shown below left. Next the same RBF was used to simplify the mesh, while maintaining a high degree of accuracy.
In the second example surface colour and geometry are modelled by RBFs and jointly considered when simplifying the mesh to preserve both colour and geometry.
