Annex A: Terms and definitions ofthe ISO 19100 standards
243
geometrie aggregate
eolleetion of geometrie objeets that has no internal strueture (lS039 2003)
NOTE
No assumption about the spatial realtionship between the elements
ean be made.
geometrie boundary
boundary represented by a set of geometrie primitives of smaller geometrie dimension that limits the extent of a geometrie objeet (lS039 2003)
geometrie eomplex
set of disjoint geometrie primitives where the boundary of eaeh geometrie primitive
ean be represented as the union of other geometrie primitives of smaller dimension
within the same set (lS039 2003)
NOTE
The geometrie primitives in the set are disjoint in the sense that no
direet position is interior to more than one geometrie primitive. The set is closed under boundary operations, meaning that for eaeh element in the geometrie eomplex,
there is a eolleetion (also a geometrie eomplex) of geometrie primitives that represents the boundary of that element. Reeall that the boundary of a point (the only OD
primitive objeet type in geometry) is empty. Thus, ifthe largest dimension geometrie
primitive is a solid (3D), the eomposition of the boundary operator in this definition
terminates after at most 3 steps. It is also the ease that the boundary of any objeet is a
eycle.
geometrie dimension
largest number n sueh that eaeh direet position in a geometrie set ean be assoeiated
with a subset that has the direet position in its interior and is similar (isomorphie) to
Rn, Euclidean n-spaee (lS039 2003)
NOTE
Curves, beeause they are eontinuous images of a portion of the real
line, have geometrie dimension 1. Surfaees eannot be mapped to R 2 in their entirety,
but around eaeh point position, a small neighbourhood ean be found that resembles
(under eontinuous funetions) the interior ofthe unit eircle in R 2 , and are therefore 2dimensional. In this standard, most surfaee patehes (instanees of GM_SurfaeePateh)
are mapped to portions ofR 2 by their defining interpolation meehanisms.
geometrie objeet
spatial objeet representing a geometrie set (lS039 2003)
NOTE
A geometrie objeet eonsists of a geometrie primitive, a eolleetion
of geometrie primitives, or a geometrie eomplex treated as a single entity. A geometrie objeet may be the spatial representation of an objeet sueh as a feature or a signifieant part of a feature.
geometrie primitive
geometrie objeet representing a single, eonneeted, homogeneous element of spaee
(lS039 2003)
243
geometrie aggregate
eolleetion of geometrie objeets that has no internal strueture (lS039 2003)
NOTE
No assumption about the spatial realtionship between the elements
ean be made.
geometrie boundary
boundary represented by a set of geometrie primitives of smaller geometrie dimension that limits the extent of a geometrie objeet (lS039 2003)
geometrie eomplex
set of disjoint geometrie primitives where the boundary of eaeh geometrie primitive
ean be represented as the union of other geometrie primitives of smaller dimension
within the same set (lS039 2003)
NOTE
The geometrie primitives in the set are disjoint in the sense that no
direet position is interior to more than one geometrie primitive. The set is closed under boundary operations, meaning that for eaeh element in the geometrie eomplex,
there is a eolleetion (also a geometrie eomplex) of geometrie primitives that represents the boundary of that element. Reeall that the boundary of a point (the only OD
primitive objeet type in geometry) is empty. Thus, ifthe largest dimension geometrie
primitive is a solid (3D), the eomposition of the boundary operator in this definition
terminates after at most 3 steps. It is also the ease that the boundary of any objeet is a
eycle.
geometrie dimension
largest number n sueh that eaeh direet position in a geometrie set ean be assoeiated
with a subset that has the direet position in its interior and is similar (isomorphie) to
Rn, Euclidean n-spaee (lS039 2003)
NOTE
Curves, beeause they are eontinuous images of a portion of the real
line, have geometrie dimension 1. Surfaees eannot be mapped to R 2 in their entirety,
but around eaeh point position, a small neighbourhood ean be found that resembles
(under eontinuous funetions) the interior ofthe unit eircle in R 2 , and are therefore 2dimensional. In this standard, most surfaee patehes (instanees of GM_SurfaeePateh)
are mapped to portions ofR 2 by their defining interpolation meehanisms.
geometrie objeet
spatial objeet representing a geometrie set (lS039 2003)
NOTE
A geometrie objeet eonsists of a geometrie primitive, a eolleetion
of geometrie primitives, or a geometrie eomplex treated as a single entity. A geometrie objeet may be the spatial representation of an objeet sueh as a feature or a signifieant part of a feature.
geometrie primitive
geometrie objeet representing a single, eonneeted, homogeneous element of spaee
(lS039 2003)