input into a clustering algorithm for this application. Instead
the value of the surface normal direction needs to be exploited
on selected portions of the data set where there range of
directions is limited and can be used to resolve ambiguities
arising from planar regions in the data set.
4. REFINED COMPUTATIONAL APPROACH.
The minimum and maximum curvatures at a point have been
found to be the only uniformity measures that are suitable for
direct input into the selected clustering algorithm for this
application. These values do not introduce ambiguities or
uncertainties into the point grouping process, however
considering these two measures in isolation will group points
according to surface type alone, ie. planar, cylindrical,
spherical and conical. Further processing is required if points
on the same surface type but with different orientations are to
be split, along with points on the same surface type with
similar orientations but in different locations.
Thus, the following processing strategy will be adopted:
- Minimum and Maximum curvatures will be considered in
isolation: grouping points according to surface type alone.
A two dimensional version of Jolion’s algorithm will be
employed.
- Points on planes of different orientation will be split by
considering surface normal directions for planar portions of
the data set in isolation. This, limits the range of normals
to be considered, and reduces the complexity of the
ambiguities associated with this measure.
- The proximity of points will be evaluated to split points
lying on surfaces of the same type, but in distinctly
different locations.
- Edge points (ungrouped in a two dimensional clustering
algorithm) will be assigned to multiple point groups based
on the geometric fit of the point to the underlying surface
of each point group.
5. CONCLUSION.
The difficulties encountered in algorithm development detailed
in this paper are related to the application of the uniformity
and proximity measures to the generalisation of target fields.
The problems encountered do not indicate a failing of the
uniformity and proximity measures in concept, only in
application. The problems associated with the application of
these measures will be addressed with the development of the
refined computational approach, in which surface curvature
and surface normal data are not considered simultaneously.
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