4.3 Spatial schema (ISO 19107)
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troduced. The origin of t is at the beginning of the curve and the value of t is the
length of the curve from the beginning. Using t, splines and clothoids can be expressed on the three separate planes xt, yt, and zt (Foley et al. 1987).
An off set curve requires the additional information of which spatial direction the
offset should be counted towards. This information is beyond the ISO 19107.
There are only a few geometries (such as lines and geodesics) that can be applied
to an n-dimensional space without mathematics that are beyond the scope of ISO
19107.
Map projections
The geometries of ISO 19107 are built on the Euclidean space. The ISO 19111
standardises the coordinate transformations and conversions, including map projections. They usually change coordinates from the Euclidean space to some other
space, like a sphere. With the exception of points, the map projection changes the
shape of all geometries because the modified geometries do not have the characteristics of the original geometries. For example, a line becomes an arc after projection
from a plane to a sphere.
4.3.3.2 Curves
A line string (class GM _LineString) consists of a sequence of line segments.
startPoint GM_LineString
GM LineSegment
~endPoint GM_LineString
GM_LineSegment
Fig. 4.4. GM _LineString
GM_LineSegment
A line segment (class GM_LineSegment) is a line between two given positions.
This line will either be straight or some other shape depending on the map projection.
133
troduced. The origin of t is at the beginning of the curve and the value of t is the
length of the curve from the beginning. Using t, splines and clothoids can be expressed on the three separate planes xt, yt, and zt (Foley et al. 1987).
An off set curve requires the additional information of which spatial direction the
offset should be counted towards. This information is beyond the ISO 19107.
There are only a few geometries (such as lines and geodesics) that can be applied
to an n-dimensional space without mathematics that are beyond the scope of ISO
19107.
Map projections
The geometries of ISO 19107 are built on the Euclidean space. The ISO 19111
standardises the coordinate transformations and conversions, including map projections. They usually change coordinates from the Euclidean space to some other
space, like a sphere. With the exception of points, the map projection changes the
shape of all geometries because the modified geometries do not have the characteristics of the original geometries. For example, a line becomes an arc after projection
from a plane to a sphere.
4.3.3.2 Curves
A line string (class GM _LineString) consists of a sequence of line segments.
startPoint GM_LineString
GM LineSegment
~endPoint GM_LineString
GM_LineSegment
Fig. 4.4. GM _LineString
GM_LineSegment
A line segment (class GM_LineSegment) is a line between two given positions.
This line will either be straight or some other shape depending on the map projection.