New oogl object classes

[rmorris <rmorris at uxb.liv.ac.uk>]

Hi,
	I've been thinking that it might be useful to have a couple
of new oogl object classes.

	The first of these is a class for vector fields. At present
you can either draw a vector field as a set of VECT's, but neither
end of the lines is distinguished as a base point, if I'm applying
a non-linear transformation to a vector, I want to transform the
base point, but use the derivatives of the transformation to find the
new direction, if the vector is just a line both points will be transformed,
not what is desired. The alternative is to pretend that the normals in
an OFF etc, are tangent vectors, again we have problems with transformations
as normals are actually bi-vectors, or the duals of vectors. The
standard rules for transforming normals do not apply to vectors, for
instance the mapping x -> 2x effects normal and tangent vectors to
the unit sphere differently. So what is required of a class for tangent
vectors, 1) Each vector has a base point and direction componant,
2) the vectors may or may not be oriented, they may or may not be of
unit length, they can be coloured; 3) some type of topological information
might be useful, eg for a curve, you could have a set of tangents to
the curve, including information about which order the vectors come in,
this information could be similar to that used in an OFF but we might
to use 3-cells (tetrahedra) for vector fields defined over a region of
space. The need for vector fields was first brought to my attention,
by the question "Can you draw the set principal directions along
a parabolic line on a surface?"
"yep easy, this is just a set of lines", "now can you find where each
of these lines insersect a plane, and draw the curve in the plane?",
"Ah, not without cheating and knowing that the oogl object is actually
suposed to be tangent vector along a curve."

So wouldn't a class for tanget vectors be nice. The other class is that
of n-dimensional manifolds in R^m, not directly visulisable by geomview, but
posibly useful for aplication programs, I just know there are pople in
our department, who thing anything less than 6 just isn't intresting.

A final comment on classes and objects, I'd realy like to include
coments in with my data, describing exactly what the file represented,
and still keep that information after the data has been read into geomview
and saved.

	Ho hum, let us know what you think of these ideas,

		bye for now
				Rich