Ron,
I also agree, but 'truth in advertising' forces me to point out that
'spatio-temporal region' is not much of a restriction. Essentially, if you
extend ISO 19107 through subtyping GM_Object, you get viable domain spaces
for coverages.
For example, in ISO 19141: Moving Features, we've extended geometry to
involve a 3D object moving through 3D space during time. If you count
carefully, you can get 4, 7, or 10 dimensions. The 4 is geographic space x
time, the 7 is geographic space x object coordinates x time. For a moving
truck, you know the time, the spot on the highway your truck's 'reference
point' has reached, and the spot on the truck, which is a 3D offset from the
reference point. This collapses to 4D, but if you do it you lose the 'spot
on the truck' information, and fuzzy up the object trajectory. You can then
blissfully add 3 more D's for each set of motion derivative you want to
track. So, geo-space x time x truck-space x velocities-at-point-on-truck
gives you 10D If you express the motion derivatives as coverages, you get a
7D domain, and a 3D range.
BTW: Poincare's conjecture is trivial in 1, 2, 4, 5,... dimensions, but
unsolved in 3. Sometimes you just need to an extra dimension or two to move
around in.
Regards,
John
-----Original Message-----
On Behalf Of Ron Lake
Sent: Friday, May 13, 2005 12:20 PM
HI,
I agree with Simon's description - but it would not be difficult to
generalize the current coverage concept to allow the domain to be other than
a spatial-temporal region.
Ron
