Generating meshes from implicit surface models

An RBF surface model cannot readily be used in existing graphics and CAD software. Polygonal meshes or spline patches must be derived from the RBF representation. The traditional way of finding an explicit mesh representation is through an iso-surfacing algorithm such as Marching Cubes. Unfortunately, such algorithms can be inefficient. They often generate irregular and unnecessary facets and are usually restricted to sampling on a regular cubic lattice (a). Many common implementations also require evaluating and storing a complete 3D array of values and so they have large computational requirements.

What are the advantages of the FastRBF iso-surfacer?

The FastRBF^TM iso-surfacer improves on traditional methods in a number of ways. In particular, the functional nature of the RBF representation provides a critical advantage: we can evaluate the function and its gradient anywhere. This allows the iso-surfacer to produce meshes efficiently from RBFs. Spline patches are derived in a subsequent step. The principle innovations are:

• Surface following minimises computation of the RBF. Wavefronts emanate from seed points across the surface (see below). This allows us to avoid the computation and storage associated with a 3D voxel array.

• Low memory overheads result from storing only the advancing wavefronts. This enables reconstruction of large surfaces at high resolution.

• On-the-fly mesh optimisation reduces the number of facets and produces triangles with uniform aspect ratios. This avoids creating thin, elongated and small facets (b).

• Optimisation can be constrained to force facet vertices to lie on parallel plane (c).