`pgr_withPointsVia`¶

pgr_withPointsVia - Route that goes through a list of vertices and/or points.

Availability

Version 4.0.0
- Function promoted to official.
Version 3.4.0
- New proposed function.

Description¶

Given a graph, a set of points on the graphs edges and a list of vertices, this function is equivalent to finding the shortest path between \(vertex_i\) and \(vertex_{i+1}\) (where \(vertex\) can be a vertex or a point on the graph) for all \(i < size\_of(via\;vertices)\).

Route:: is a sequence of paths.
Path:: is a section of the route.

The general algorithm is as follows:

Build the Graph with the new points.
- The points identifiers will be converted to negative values.
- The vertices identifiers will remain positive.
Execute a pgr_dijkstraVia - Proposed.

Boost Graph Inside

Signatures¶

One Via¶

pgr_withPointsVia(Edges SQL, Points SQL, via vertices, [options])

options: [directed, strict, U_turn_on_edge]

Returns set of (seq, path_id, path_seq, start_vid, end_vid, node, edge, cost, agg_cost, route_agg_cost)

OR EMPTY SET

Example:: Find the route that visits the vertices \(\{ -6, 15, -1\}\) in that order on a directed graph.

SELECT * FROM pgr_withPointsVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[-6, 15, -1]);
 seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------+----------------
   1 |       1 |        1 |        -6 |      15 |   -6 |    4 |  0.3 |        0 |              0
   2 |       1 |        2 |        -6 |      15 |    7 |    8 |    1 |      0.3 |            0.3
   3 |       1 |        3 |        -6 |      15 |   11 |    9 |    1 |      1.3 |            1.3
   4 |       1 |        4 |        -6 |      15 |   16 |   16 |    1 |      2.3 |            2.3
   5 |       1 |        5 |        -6 |      15 |   15 |   -1 |    0 |      3.3 |            3.3
   6 |       2 |        1 |        15 |      -1 |   15 |    3 |    1 |        0 |            3.3
   7 |       2 |        2 |        15 |      -1 |   10 |    2 |    1 |        1 |            4.3
   8 |       2 |        3 |        15 |      -1 |    6 |    1 |  0.6 |        2 |            5.3
   9 |       2 |        4 |        15 |      -1 |   -1 |   -2 |    0 |      2.6 |            5.9
(9 rows)

Parameters¶

Parameter	Type	Description
Edges SQL	`TEXT`	SQL query as described.
Points SQL	`TEXT`	SQL query as described.
via vertices	`ARRAY` [ ANY-INTEGER ]	Array of ordered vertices identifiers that are going to be visited. When positive it is considered a vertex identifier When negative it is considered a point identifier

Parameter

Type

Default

Description

Edges SQL

TEXT

SQL query as described.

Points SQL

TEXT

SQL query as described.

via vertices

ARRAY [ ANY-INTEGER ]

Array of ordered vertices identifiers that are going to be visited.

When positive it is considered a vertex identifier
When negative it is considered a point identifier

Where:

ANY-INTEGER:: SMALLINT, INTEGER, BIGINT
ANY-NUMERICAL:: SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Optional parameters¶

Column	Type	Default	Description
`directed`	`BOOLEAN`	`true`	When `true` the graph is considered Directed When `false` the graph is considered as Undirected.

Via optional parameters¶

Parameter	Type	Default	Description
`strict`	`BOOLEAN`	`false`	When `true` if a path is missing stops and returns EMPTY SET When `false` ignores missing paths returning all paths found
`U_turn_on_edge`	`BOOLEAN`	`true`	When `true` departing from a visited vertex will not try to avoid

With points optional parameters¶

Parameter	Type	Default	Description
`driving_side`	`CHAR`	`b`	Value in [`r`, `l`, `b`] indicating if the driving side is: `r` for right driving side. `l` for left driving side. `b` for both.
`details`	`BOOLEAN`	`false`	When `true` the results will include the points that are in the path. When `false` the results will not include the points that are in the path.

Parameter

Type

Default

Description

driving_side

CHAR

b

Value in [r, l, b] indicating if the driving side is:

r for right driving side.
l for left driving side.
b for both.

details

BOOLEAN

false

When true the results will include the points that are in the path.
When false the results will not include the points that are in the path.

Inner Queries¶

Edges SQL¶

Column	Type	Default	Description
`id`	ANY-INTEGER		Identifier of the edge.
`source`	ANY-INTEGER		Identifier of the first end point vertex of the edge.
`target`	ANY-INTEGER		Identifier of the second end point vertex of the edge.
`cost`	ANY-NUMERICAL		Weight of the edge (`source`, `target`)
`reverse_cost`	ANY-NUMERICAL	-1	Weight of the edge (`target`, `source`) When negative: edge (`target`, `source`) does not exist, therefore it’s not part of the graph.

Where:

ANY-INTEGER:: SMALLINT, INTEGER, BIGINT
ANY-NUMERICAL:: SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Points SQL¶

Parameter	Type	Default	Description
`pid`	ANY-INTEGER	value	Identifier of the point. Use with positive value, as internally will be converted to negative value If column is present, it can not be NULL. If column is not present, a sequential negative value will be given automatically.
`edge_id`	ANY-INTEGER		Identifier of the “closest” edge to the point.
`fraction`	ANY-NUMERICAL		Value in <0,1> that indicates the relative postition from the first end point of the edge.
`side`	`CHAR`	`b`	Value in [`b`, `r`, `l`, `NULL`] indicating if the point is: In the right `r`, In the left `l`, In both sides `b`, `NULL`

Where:

ANY-INTEGER:: SMALLINT, INTEGER, BIGINT
ANY-NUMERICAL:: SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Result columns¶

Column	Type	Description
`seq`	`INTEGER`	Sequential value starting from 1.
`path_id`	`INTEGER`	Identifier of a path. Has value 1 for the first path.
`path_seq`	`INTEGER`	Relative position in the path. Has value 1 for the beginning of a path.
`start_vid`	`BIGINT`	Identifier of the starting vertex of the path.
`end_vid`	`BIGINT`	Identifier of the ending vertex of the path.
`node`	`BIGINT`	Identifier of the node in the path from `start_vid` to `end_vid`.
`edge`	`BIGINT`	Identifier of the edge used to go from `node` to the next node in the path sequence. -1 for the last node of the path. -2 for the last node of the route.
`cost`	`FLOAT`	Cost to traverse from `node` using `edge` to the next node in the path sequence.
`agg_cost`	`FLOAT`	Aggregate cost from `start_vid` to `node`.
`route_agg_cost`	`FLOAT`	Total cost from `start_vid` of `seq = 1` to `end_vid` of the current `seq`.

Note

When start_vid, end_vid and node columns have negative values, the identifier is for a Point.

Additional Examples¶

Use pgr_findCloseEdges - Proposed in the Points SQL ¶

Visit from vertex \(1\) to the two locations on the graph of point (2.9, 1.8) in order of closeness to the graph.

SELECT * FROM pgr_withPointsVia(
  $e$ SELECT * FROM edges $e$,
  $p$ SELECT edge_id, round(fraction::numeric, 2) AS fraction, side
      FROM pgr_findCloseEdges(
        $$SELECT id, geom FROM edges$$,
        (SELECT ST_POINT(2.9, 1.8)),
        0.5, cap => 2)
  $p$,
  ARRAY[1, -1, -2], details => true);
 seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------+----------------
   1 |       1 |        1 |         1 |      -1 |    1 |    6 |    1 |        0 |              0
   2 |       1 |        2 |         1 |      -1 |    3 |    7 |    1 |        1 |              1
   3 |       1 |        3 |         1 |      -1 |    7 |    8 |  0.9 |        2 |              2
   4 |       1 |        4 |         1 |      -1 |   -2 |    8 |  0.1 |      2.9 |            2.9
   5 |       1 |        5 |         1 |      -1 |   11 |    9 |    1 |        3 |              3
   6 |       1 |        6 |         1 |      -1 |   16 |   16 |    1 |        4 |              4
   7 |       1 |        7 |         1 |      -1 |   15 |    3 |    1 |        5 |              5
   8 |       1 |        8 |         1 |      -1 |   10 |    5 |  0.8 |        6 |              6
   9 |       1 |        9 |         1 |      -1 |   -1 |   -1 |    0 |      6.8 |            6.8
  10 |       2 |        1 |        -1 |      -2 |   -1 |    5 |  0.2 |        0 |            6.8
  11 |       2 |        2 |        -1 |      -2 |   11 |    8 |  0.1 |      0.2 |              7
  12 |       2 |        3 |        -1 |      -2 |   -2 |   -2 |    0 |      0.3 |            7.1
(12 rows)

Point \(-1\) corresponds to the closest edge from point (2.9, 1.8).
Point \(-2\) corresponds to the next close edge from point (2.9, 1.8).
Point \(-2\) is visited on the route to from vertex \(1\) to Point \(-1\) (See row where \(seq = 4\)).

Usage variations ¶

All this examples are about the route that visits the vertices \(\{-1, 7, -3, 16, 15\}\) in that order on a directed graph.

SELECT * FROM pgr_withPointsVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[-1, 7, -3, 16, 15]);
 seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------+----------------
   1 |       1 |        1 |        -1 |       7 |   -1 |    1 |  0.6 |        0 |              0
   2 |       1 |        2 |        -1 |       7 |    6 |    4 |    1 |      0.6 |            0.6
   3 |       1 |        3 |        -1 |       7 |    7 |   -1 |    0 |      1.6 |            1.6
   4 |       2 |        1 |         7 |      -3 |    7 |   10 |    1 |        0 |            1.6
   5 |       2 |        2 |         7 |      -3 |    8 |   12 |  0.6 |        1 |            2.6
   6 |       2 |        3 |         7 |      -3 |   -3 |   -1 |    0 |      1.6 |            3.2
   7 |       3 |        1 |        -3 |      16 |   -3 |   12 |  0.4 |        0 |            3.2
   8 |       3 |        2 |        -3 |      16 |   12 |   13 |    1 |      0.4 |            3.6
   9 |       3 |        3 |        -3 |      16 |   17 |   15 |    1 |      1.4 |            4.6
  10 |       3 |        4 |        -3 |      16 |   16 |   -1 |    0 |      2.4 |            5.6
  11 |       4 |        1 |        16 |      15 |   16 |   16 |    1 |        0 |            5.6
  12 |       4 |        2 |        16 |      15 |   15 |   -2 |    0 |        1 |            6.6
(12 rows)

Aggregate cost of the third path.¶

SELECT agg_cost FROM  pgr_withPointsVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[-1, 7, -3, 16, 15])
WHERE path_id = 3 AND edge < 0;
 agg_cost
----------
      2.4
(1 row)

Route’s aggregate cost of the route at the end of the third path.¶

SELECT route_agg_cost FROM  pgr_withPointsVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[-1, 7, -3, 16, 15])
WHERE path_id = 3 AND edge < 0;
 route_agg_cost
----------------
            5.6
(1 row)

Nodes visited in the route.¶

SELECT row_number() over () as node_seq, node
FROM  pgr_withPointsVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[-1, 7, -3, 16, 15])
WHERE edge <> -1 ORDER BY seq;
 node_seq | node
----------+------
        1 |   -1
        2 |    6
        3 |    7
        4 |    8
        5 |   -3
        6 |   12
        7 |   17
        8 |   16
        9 |   15
(9 rows)

The aggregate costs of the route when the visited vertices are reached.¶

SELECT path_id, route_agg_cost FROM  pgr_withPointsVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[-1, 7, -3, 16, 15])
WHERE edge < 0;
 path_id | route_agg_cost
---------+----------------
       1 |            1.6
       2 |            3.2
       3 |            5.6
       4 |            6.6
(4 rows)

Status of “passes in front” or “visits” of the nodes and points.¶

SELECT seq, node,
CASE WHEN edge = -1 THEN 'visits'
ELSE 'passes in front'
END as status
FROM  pgr_withPointsVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[-1, 7, -3, 16, 15], details => true)
WHERE agg_cost <> 0 or seq = 1;
 seq | node |     status
-----+------+-----------------
   1 |   -1 | passes in front
   2 |    6 | passes in front
   3 |   -6 | passes in front
   4 |    7 | visits
   6 |    8 | passes in front
   7 |   -3 | visits
   9 |   12 | passes in front
  10 |   17 | passes in front
  11 |   -2 | passes in front
  12 |   16 | visits
  14 |   15 | passes in front
(11 rows)

pgr_withPointsVia¶

Description¶

Signatures¶

One Via¶

Parameters¶

Optional parameters¶

Via optional parameters¶

With points optional parameters¶

Inner Queries¶

Edges SQL¶

Points SQL¶

Result columns¶

Additional Examples¶

Use pgr_findCloseEdges - Proposed in the Points SQL¶

Usage variations¶

Aggregate cost of the third path.¶

Route’s aggregate cost of the route at the end of the third path.¶

Nodes visited in the route.¶

The aggregate costs of the route when the visited vertices are reached.¶

Status of “passes in front” or “visits” of the nodes and points.¶

See Also¶

`pgr_withPointsVia`¶

Use pgr_findCloseEdges - Proposed in the Points SQL ¶

Usage variations ¶