An alternative technique [Šrá94a,ŠK98], which resides in registration of the distance to the object surface, eliminates the aforementioned problems. Of course, there are certain limits of its application to small objects and high curvature surfaces, as it is with all techniques working in the discrete space, but this new technique is still up to two orders of magnitude more precise than the filtering one.

The distance fields were later used for the object representation by several
authors.
Jones [Jon96] voxelized and subsequently rendered triangular meshes.
Gibson [Gib98] showed how the distance fields can be used to smooth out
surfaces in the segmented tomographic data by means of elastic surface nets.
Breen et al [BMW98,BM99] used the distance fields to construct offset
surfaces for superellipsoid models and to morph different geometric model
types (polygonal meshes, CSG models and tomographic scans)
in a single animation [DBM01].
A great potential of the distance field representation has been recently shown
in volume sculpting, where significant steps toward creation of the so-called
*digital clay* were performed. Traditional modeling and sculpting tools,
based on the surface representation (polygonal or parametric patches)
suffer from limitations
given by the representation, as, for example, insufficient versatility and
unintuitive user interface.
These drawbacks are eliminated if the object surfaces are represented by the
distance field isosurfaces (adaptive fields [Fri01], two level
hierarchies [Bær02]), due to their unconstrained deformation ability
and a possibility to implement intuitive sculpting operations (for example,
cutting, carving, sawing, spraying).

The problem of the discrete space representation of objects is that only
details with certain
minimal dimensions can be represented. One way how to decrease this minimal
dimension for the given volume resolution is to register a modified distance
profile instead of the plain distance itself. In [ŠK99]
*erfc* of the signed distance is used, which together with a suitable
reconstruction filter enables to decrease to about one half the volume
resolution while keeping the same quality of the details.
Another approach, issuing from the hierarchical representation of the distance
volume, was presented by Frisken et al [FPRJ00] and
Bærentzen [Bær02].
Here, the continuous distance field is hierarchically sampled, until a certain
homogeneity limit or maximal resolution is reached. This approach, although more
algorithmicaly and computationally complex than representation by regular
grids, this approach enables to represent simultaneously objects with
significantly different dimensions.