In order to represent an arbitrary surface, the surface must be modeled implicitly as the level set of some function in 3-space.
In our RBF representation, a signed-distance distribution is formed from the raw surface data and a Radial Basis Function (RBF) is then fitted to this distribution. Though the RBF representation can be utilised directly as a solid model, in a Constructive Solid Geometry (CSG) framework,
current Computer Graphics and CAD software usually require explicit surface representations such as polygonal meshes.
A polygonal mesh is derived by the process of iso-surfacing the RBF.
Smooth interpolation between surface data is an inherent property of the mathematical description. RBFs are optimal interpolators in the sense that they minimise certain energy functionals (such as the second derivative).
They are well suited to modelling scattered data not lying on a regular grid and cope with sparse and densely sampled regions.
In the case of laser scan data, the RBF is often a more compact representation than the raw data. A further advantage of the functional representation is that it can be evaluated at the resolution required by the end application.
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