Table of Contents
The temporal points that we have considered so far represent the movement of objects that can move freely on space since it is assumed that they can change their position from one location to the next one without any motion restriction. This is the case for animals and for flying objects such as planes or drones. However, in many cases, objects do not move freely in space but rather within spatially embedded networks such as routes or railways. In this case, it is necessary to take the embedded networks into account while describing the movements of these moving objects. Temporal network points account for these requirements.
Compared with the free-space temporal points, network-based points have the following advantages:
Network points provide road constraints that reflect the real movements of moving objects.
The geometric information is not stored with the moving point, but once and for all in the fixed networks. In this way, the location representations and interpolations are more precise.
Network points are more efficient in terms of data storage, location update, formulation of query, as well as indexing. These are discussed later in this document.
Temporal network points are based on pgRouting, a PostgreSQL extension for developing network routing applications and doing graph analysis. Therefore, temporal network points asume that the underlying network is defined in a table named ways, which has at least three columns: gid containing the unique route identifier, length containing the route length, and the_geom containing the route geometry.
There are two static network types, npoint (short for network point) and nsegment (short for network segment), which represent, respectively, a point and a segment of a route. An npoint value is composed of a route identifier and a float number in the range [0,1] determining a relative position of the route, where 0 corresponds to the begining of the route and 1 to the end of the route. An nsegment value is composed of a route identifier and two float numbers in the range [0,1] determining the start and end relative positions. A nsegment value whose start and end positions are equal corresponds to an npoint value.
The npoint type serves as base type for defining the temporal network point type tnpoint. The tnpoint type has similar functionality as the temporal point type tgeompoint with the exception that it only considers two dimensions. Thus, all functions and operators described before for the tgeompoint type are also applicable for the tnpoint type. In addition, there are specific functions defined for the tnpoint type.
An npoint value is a couple of the form (rid,position) where rid is a bigint value representing a route identifier and position is a float value in the range [0,1] indicating its relative position. The values 0 and 1 of position denote, respectively, the starting and the ending position of the route. The road distance between an npoint value and the starting position of route with identifier rid is computed by multiplying position by length, where length is the route length. Examples of input of network point values are as follows:
SELECT npoint 'Npoint(76, 0.3)'; SELECT npoint 'Npoint(64, 1.0)';
The constructor function for network points has one argument for the route identifier and one argument for the relative position. An example of a network point value defined with the constructor function is as follows:
SELECT npoint(76, 0.3);
An nsegment value is a triple of the form (rid,startPosition,endPosition) where rid is a bigint value representing a route identifier and startPosition and endPosition are float values in the range [0,1] such that startPosition ≤ endPosition. Semantically, a network segment represents a set of network points (rid,position) with startPosition ≤ position ≤ endPosition. If startPosition=0 and endPosition=1, the network segment is equivalent to the entire route. If startPosition=endPosition, the network segment represents into a single network point. Examples of input of network point values are as follows:
SELECT nsegment 'Nsegment(76, 0.3, 0.5)'; SELECT nsegment 'Nsegment(64, 0.5, 0.5)'; SELECT nsegment 'Nsegment(64, 0.0, 1.0)'; SELECT nsegment 'Nsegment(64, 1.0, 0.0)'; -- converted to nsegment 'Nsegment(64, 0.0, 1.0)';
As can be seen in the last example, the startPosition and endPosition values will be inverted to ensure that the condition startPosition ≤ endPosition is always satisfied. The constructor function for network segments has one argument for the route identifier and two optional arguments for the start and end positions. Examples of network segment values defined with the constructor function are as follows:
SELECT nsegment(76, 0.3, 0.3); SELECT nsegment(76); -- start and end position assumed to be 0 and 1 respectively SELECT nsegment(76, 0.5); -- end position assumed to be 1
Values of the npoint type can be converted to the nsegment type using an explicit CAST or using the :: notation as shown next.
SELECT npoint(76, 0.33)::nsegment;
Values of static network types must satisfy several constraints so that they are well defined. These constraints are given next.
The route identifier rid must be found in column gid of table ways.
The position, startPosition, and endPosition values must be in the range [0,1]. An error is raised whenever one of these constraints are not satisfied.
Examples of incorrect static network type values are as follows.
-- incorrect rid value SELECT npoint 'Npoint(87.5, 1.0)'; -- incorrect position value SELECT npoint 'Npoint(87, 2.0)'; -- rid value not found in the ways table SELECT npoint 'Npoint(99999999, 1.0)';
We give next the functions and operators for the static network types.
Set the precision of the position(s) of the network point or the network segment to the number of decimal places
setPrecision({npoint,nsegment},integer): {npoint,nsegment}
SELECT setPrecision(npoint(76, 0.123456789), 6); -- NPoint(76,0.123457) SELECT setPrecision(nsegment(76, 0.123456789, 0.223456789), 6); -- NSegment(76,0.123457,0.223457)
Get the route identifier
route({npoint,nsegment}): bigint
SELECT route(npoint 'Npoint(63, 0.3)'); -- 63 SELECT route(nsegment 'Nsegment(76, 0.3, 0.3)'); -- 76
Get the position
getPosition(npoint): float
SELECT getPosition(npoint 'Npoint(63, 0.3)'); -- 0.3
Get the start position
startPosition(npoint): float
SELECT startPosition(nsegment 'Nsegment(76, 0.3, 0.5)'); -- 0.3
Get the end position
endPosition(npoint): float
SELECT endPosition(nsegment 'Nsegment(76, 0.3, 0.5)'); -- 0.5
Values of the npoint and nsegment types can be converted to the geometry type using an explicit CAST or using the :: notation as shown next.
Cast a network point to a geometry
{npoint,nsegment}::geometry
SELECT ST_AsText(npoint(76, 0.33)::geometry); -- POINT(21.6338731332283 50.0545869554067) SELECT ST_AsText(nsegment(76, 0.33, 0.66)::geometry); -- LINESTRING(21.6338731332283 50.0545869554067,30.7475989651999 53.9185062927473) SELECT ST_AsText(nsegment(76, 0.33, 0.33)::geometry); -- POINT(21.6338731332283 50.0545869554067)
Similarly, geometry values of subtype point or linestring (restricted to two points) can be converted, respectively, to npoint and nsegment values using an explicit CAST or using the :: notation. For this, the route that intersects the given points must be found, where a tolerance of 0.00001 units (depending on the coordinate system) is assumed so a point and a route that are close are considered to intersect. If no such route is found, a null value is returned.
Cast a geometry to a network point
geometry::{npoint,nsegment}
SELECT geometry 'Point(279.269156511873 811.497076880187)'::npoint; -- NPoint(3,0.781413) SELECT geometry 'LINESTRING(406.729536784738 702.58583437902, 383.570801314823 845.137059419277)'::nsegment; -- NSegment(3,0.6,0.9) SELECT geometry 'Point(279.3 811.5)'::npoint; -- NULL SELECT geometry 'LINESTRING(406.7 702.6,383.6 845.1)'::nsegment; -- NULL
Two npoint values may be have different route identifiers but may represent the same spatial point at the intersection of the two routes. Function equals is used for testing spatial equality of network points.
Spatial equality for network points
equals(npoint, npoint)::Boolean
WITH inter(geom) AS ( SELECT st_intersection(t1.the_geom, t2.the_geom) FROM ways t1, ways t2 WHERE t1.gid = 1 AND t2.gid = 2), fractions(f1, f2) AS ( SELECT ST_LineLocatePoint(t1.the_geom, i.geom), ST_LineLocatePoint(t2.the_geom, i.geom) FROM ways t1, ways t2, inter i WHERE t1.gid = 1 AND t2.gid = 2) SELECT equals(npoint(1, f1), npoint(2, f2)) FROM fractions; -- true
The comparison operators (=, <, and so on) for static network types require that the left and right arguments be of the same type. Excepted the equality and inequality, the other comparison operators are not useful in the real world but allow B-tree indexes to be constructed on static network types.
Are the values equal?
{npoint,nsegment} = {npoint,nsegment}
SELECT npoint 'Npoint(3, 0.5)' = npoint 'Npoint(3, 0.5)'; -- true SELECT nsegment 'Nsegment(3, 0.5, 0.5)' = nsegment 'Nsegment(3, 0.5, 0.6)'; -- false
Are the values different?
{npoint,nsegment} <> {npoint,nsegment}
SELECT npoint 'Npoint(3, 0.5)' <> npoint 'Npoint(3, 0.6); -- true SELECT nsegment 'Nsegment(3, 0.5, 0.5)' <> nsegment 'Nsegment(3, 0.5, 0.5)'; -- false
Is the first value less than the second one?
{npoint,nsegment} < {npoint,nsegment}
SELECT nsegment 'Nsegment(3, 0.5, 0.5)' < nsegment 'Nsegment(3, 0.5, 0.6)'; -- true
Is the first value greater than the second one?
{npoint,nsegment} > {npoint,nsegment}
SELECT nsegment 'Nsegment(3, 0.5, 0.5)' > nsegment 'Nsegment(2, 0.5, 0.5)'; -- true
Is the first value less than or equal to the second one?
{npoint,nsegment} <= {npoint,nsegment}
SELECT npoint 'Npoint(1, 0.5)' <= npoint 'Npoint(2, 0.5)'; -- true
Is the first value greater than or equal to the second one?
{npoint,nsegment} >= {npoint,nsegment}
SELECT npoint 'Npoint(1, 0.6)' >= npoint 'Npoint(1, 0.5)'; -- true