4.3 Spatial schema (ISO 19107)
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thus the parcel boundary is composed of a number of single curves.
Aggregates (dass GM_Aggregate) allow the grouping of geometrie elements
without any constraints. A typical example is a set of elevation points. Without aggregates being available the points could only be described as a number of individual
points; the aggregate allows them to be addressed as a single dataset like a named list
of points. Aggregations are named "multi primitives" such as multi points, multi
curve, multi surface, and multi solid (dasses GM_MultiPoint, GM_MultiCurve,
GM _ MultiSurface, and GM _MultiSolid).
Curves and Surfaces are orientable primitives (dass GM _ OrientablePrimitive)
while points and so lids are not. A curve is an orientable primitive because it has a
defining point sequence that may have a forward or a backward order. This property
is important if two or more curves form a dosed polygon or a composite curve. A
consecutive order of the points is required to correctly define the area as well as to
draw a correct line pattern without interruptions along the curve where the individual
curves meet.
A surface is an orientable primitive because either side may be the upside or
downside (dass GM _ OrientableSurface).
A curve (dass GM_Curve) consists of one or more curve segments (dass
GM_CurveSegment). A curve segment may have one of the following geometries:
are string, are string by bulge, spline curve, dothoid, geode sie string, conic, and offset curve (see also figure 4.3 in chapter 4, section 3.1).
The surface (dass GM_Surface) is either defined by a mosaic of surface patches
with a great number of different shapes or by a simpler pattern of joint polygons.
Surface patches might be parcels, areas of homogeneous land use, or local functional
descriptions of the shape of a terrain. The perspective on surface patches focuses on
every individual patch of the surface while the perspective on the pattern of joint
polygons instead focuses on the surface as a whole. The most prominent example is
a TIN (Triangulated Irregular Network) which results after processing a given set of
elevation points. If one point of the dataset is changed then the whole TIN will
change according to modifications of the triangles associated to the changed point.
The description of a complete surface with only one function is a rare case in geographie applications.
Under the restrietion that every surface patch must be neatly linked to its
neighbours in order to form a continuous surface without gaps, each patch (dass
GM _ SurfacePatch) in a mosaic may have an individual functional description.
A simple case of a surface patch is a dosed planar polygon (dass GM_Polygon).
A typical example is a parcel or a 2-dimensional feature in aland use dataset.
In ISO 19107 polygons are always planar. That means that all curves belonging to
the polygon are part of the same plane. Geometrically this is always true for triangles
only. Quadrangles and other polygons of higher order may have a 3D-shape. Those
polygon are not valid polygons according to ISO 19107. If all surface patches are triangles being a special case of polygons, the result might be looking the same as a
TIN. However, a pattern of triangles is a TIN only if the Delaunay criterion is valid
as explained below (see GM_Tin in chapter 4, section 3.3.3).
The most sophisticated type of surface patch is a parametric curve surface (dass
GM_ParametricCurveSurface). A simple example is a semi-sphere. For practical rea-
131
thus the parcel boundary is composed of a number of single curves.
Aggregates (dass GM_Aggregate) allow the grouping of geometrie elements
without any constraints. A typical example is a set of elevation points. Without aggregates being available the points could only be described as a number of individual
points; the aggregate allows them to be addressed as a single dataset like a named list
of points. Aggregations are named "multi primitives" such as multi points, multi
curve, multi surface, and multi solid (dasses GM_MultiPoint, GM_MultiCurve,
GM _ MultiSurface, and GM _MultiSolid).
Curves and Surfaces are orientable primitives (dass GM _ OrientablePrimitive)
while points and so lids are not. A curve is an orientable primitive because it has a
defining point sequence that may have a forward or a backward order. This property
is important if two or more curves form a dosed polygon or a composite curve. A
consecutive order of the points is required to correctly define the area as well as to
draw a correct line pattern without interruptions along the curve where the individual
curves meet.
A surface is an orientable primitive because either side may be the upside or
downside (dass GM _ OrientableSurface).
A curve (dass GM_Curve) consists of one or more curve segments (dass
GM_CurveSegment). A curve segment may have one of the following geometries:
are string, are string by bulge, spline curve, dothoid, geode sie string, conic, and offset curve (see also figure 4.3 in chapter 4, section 3.1).
The surface (dass GM_Surface) is either defined by a mosaic of surface patches
with a great number of different shapes or by a simpler pattern of joint polygons.
Surface patches might be parcels, areas of homogeneous land use, or local functional
descriptions of the shape of a terrain. The perspective on surface patches focuses on
every individual patch of the surface while the perspective on the pattern of joint
polygons instead focuses on the surface as a whole. The most prominent example is
a TIN (Triangulated Irregular Network) which results after processing a given set of
elevation points. If one point of the dataset is changed then the whole TIN will
change according to modifications of the triangles associated to the changed point.
The description of a complete surface with only one function is a rare case in geographie applications.
Under the restrietion that every surface patch must be neatly linked to its
neighbours in order to form a continuous surface without gaps, each patch (dass
GM _ SurfacePatch) in a mosaic may have an individual functional description.
A simple case of a surface patch is a dosed planar polygon (dass GM_Polygon).
A typical example is a parcel or a 2-dimensional feature in aland use dataset.
In ISO 19107 polygons are always planar. That means that all curves belonging to
the polygon are part of the same plane. Geometrically this is always true for triangles
only. Quadrangles and other polygons of higher order may have a 3D-shape. Those
polygon are not valid polygons according to ISO 19107. If all surface patches are triangles being a special case of polygons, the result might be looking the same as a
TIN. However, a pattern of triangles is a TIN only if the Delaunay criterion is valid
as explained below (see GM_Tin in chapter 4, section 3.3.3).
The most sophisticated type of surface patch is a parametric curve surface (dass
GM_ParametricCurveSurface). A simple example is a semi-sphere. For practical rea-