# pgr_trspVia_withPoints - Proposed¶

pgr_trspVia_withPoints - Route that goes through a list of vertices and/or points with restrictions.

Warning

Proposed functions for next mayor release.

• They are not officially in the current release.

• They will likely officially be part of the next mayor release:

• The functions make use of ANY-INTEGER and ANY-NUMERICAL

• Name might not change. (But still can)

• Signature might not change. (But still can)

• Functionality might not change. (But still can)

• pgTap tests have being done. But might need more.

• Documentation might need refinement.

Availability

• Version 3.4.0

• New proposed function:

pgr_trspVia_withPoints (One Via)

## Description¶

Given a graph, a set of restriction on the graph edges, 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 $$i < size\_of(via\;vertices)$$ trying not to use restricted paths.

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_withPointsVia - Proposed.

• For the set of paths of the solution that pass through a restriction then

• Execute the TRSP algorithm with restrictions for the path.

• NOTE when this is done, U_turn_on_edge flag is ignored.

Note

Do not use negative values on identifiers of the inner queries.

## Signatures¶

### One Via¶

pgr_trspVia_withPoints(Edges SQL, Restrictions 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 $$\{-6, 15, -5\}$$ in that order on an directed graph.

SELECT * FROM pgr_trspVia_withPoints(
$$SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id$$,
$$SELECT path, cost FROM restrictions$$,
$$SELECT pid, edge_id, side, fraction FROM pointsOfInterest$$,
ARRAY[-6, 15, -5]);
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 |   10 |    1 |      0.3 |            0.3
3 |       1 |        3 |        -6 |      15 |    8 |   12 |    1 |      1.3 |            1.3
4 |       1 |        4 |        -6 |      15 |   12 |   13 |    1 |      2.3 |            2.3
5 |       1 |        5 |        -6 |      15 |   17 |   15 |    1 |      3.3 |            3.3
6 |       1 |        6 |        -6 |      15 |   16 |   16 |    1 |      4.3 |            4.3
7 |       1 |        7 |        -6 |      15 |   15 |   -1 |    0 |      5.3 |            5.3
8 |       2 |        1 |        15 |      -5 |   15 |    3 |    1 |        0 |            5.3
9 |       2 |        2 |        15 |      -5 |   10 |    5 |  0.8 |        1 |            6.3
10 |       2 |        3 |        15 |      -5 |   -5 |   -2 |    0 |      1.8 |            7.1
(10 rows)



## Parameters¶

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

r

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

• r for right driving side

• l for left driving side

• Any other value will be considered as r

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

### Restrictions SQL¶

Column

Type

Description

path

ARRAY [ANY-INTEGER]

Sequence of edge identifiers that form a path that is not allowed to be taken. - Empty arrays or NULL arrays are ignored. - Arrays that have a NULL element will raise an exception.

Cost

ANY-NUMERICAL

Cost of taking the forbidden path.

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.

### Use pgr_findCloseEdges for points on the fly¶

Using pgr_findCloseEdges:

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_trspVia_withPoints(
$e$ SELECT * FROM edges $e$,
$r$ SELECT path, cost FROM restrictions $r$,
$p$ 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 |    8 |    1 |        3 |              3
6 |       1 |        6 |         1 |      -1 |    7 |   10 |    1 |        4 |              4
7 |       1 |        7 |         1 |      -1 |    8 |   12 |    1 |        5 |              5
8 |       1 |        8 |         1 |      -1 |   12 |   13 |    1 |        6 |              6
9 |       1 |        9 |         1 |      -1 |   17 |   15 |    1 |        7 |              7
10 |       1 |       10 |         1 |      -1 |   16 |   16 |    1 |        8 |              8
11 |       1 |       11 |         1 |      -1 |   15 |    3 |    1 |        9 |              9
12 |       1 |       12 |         1 |      -1 |   10 |    5 |  0.8 |       10 |             10
13 |       1 |       13 |         1 |      -1 |   -1 |   -1 |    0 |     10.8 |           10.8
14 |       2 |        1 |        -1 |      -2 |   -1 |    5 |  0.2 |        0 |           10.8
15 |       2 |        2 |        -1 |      -2 |   11 |    8 |    1 |      0.2 |             11
16 |       2 |        3 |        -1 |      -2 |    7 |    8 |  0.9 |      1.2 |             12
17 |       2 |        4 |        -1 |      -2 |   -2 |   -2 |    0 |      2.1 |           12.9
(17 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 $$\{-6, 7, -4, 8, -2\}$$ in that order on a directed graph.

SELECT * FROM pgr_trspVia_withPoints(
$$SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id$$,
$$SELECT path, cost FROM restrictions$$,
$$SELECT pid, edge_id, side, fraction FROM pointsOfInterest$$,
ARRAY[-6, 7, -4, 8, -2]
);
seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------+----------------
1 |       1 |        1 |        -6 |       7 |   -6 |    4 |  0.3 |        0 |              0
2 |       1 |        2 |        -6 |       7 |    7 |   -1 |    0 |      0.3 |            0.3
3 |       2 |        1 |         7 |      -4 |    7 |    7 |    1 |        0 |            0.3
4 |       2 |        2 |         7 |      -4 |    3 |    6 |  1.3 |        1 |            1.3
5 |       2 |        3 |         7 |      -4 |   -4 |   -1 |    0 |      2.3 |            2.6
6 |       3 |        1 |        -4 |       8 |   -4 |    6 |  0.7 |        0 |            2.6
7 |       3 |        2 |        -4 |       8 |    3 |    7 |    1 |      0.7 |            3.3
8 |       3 |        3 |        -4 |       8 |    7 |    4 |  0.6 |      1.7 |            4.3
9 |       3 |        4 |        -4 |       8 |    7 |   10 |    1 |      2.3 |            4.9
10 |       3 |        5 |        -4 |       8 |    8 |   -1 |    0 |      3.3 |            5.9
11 |       4 |        1 |         8 |      -2 |    8 |   10 |    1 |        0 |            5.9
12 |       4 |        2 |         8 |      -2 |    7 |    8 |    1 |        1 |            6.9
13 |       4 |        3 |         8 |      -2 |   11 |    9 |    1 |        2 |            7.9
14 |       4 |        4 |         8 |      -2 |   16 |   15 |  0.4 |        3 |            8.9
15 |       4 |        5 |         8 |      -2 |   -2 |   -2 |    0 |      3.4 |            9.3
(15 rows)



#### Aggregate cost of the third path.¶

SELECT agg_cost FROM  pgr_trspVia_withPoints(
$$SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id$$,
$$SELECT path, cost FROM restrictions$$,
$$SELECT pid, edge_id, side, fraction FROM pointsOfInterest$$,
ARRAY[-6, 7, -4, 8, -2]
)
WHERE path_id = 3 AND edge <0;
agg_cost
----------
3.3
(1 row)



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

SELECT route_agg_cost FROM  pgr_trspVia_withPoints(
$$SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id$$,
$$SELECT path, cost FROM restrictions$$,
$$SELECT pid, edge_id, side, fraction FROM pointsOfInterest$$,
ARRAY[-6, 7, -4, 8, -2]
)
WHERE path_id = 3 AND edge < 0;
route_agg_cost
----------------
5.9
(1 row)



#### Nodes visited in the route.¶

SELECT row_number() over () as node_seq, node
FROM  pgr_trspVia_withPoints(
$$SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id$$,
$$SELECT path, cost FROM restrictions$$,
$$SELECT pid, edge_id, side, fraction FROM pointsOfInterest$$,
ARRAY[-6, 7, -4, 8, -2]
)
WHERE edge <> -1 ORDER BY seq;
node_seq | node
----------+------
1 |   -6
2 |    7
3 |    3
4 |   -4
5 |    3
6 |    7
7 |    7
8 |    8
9 |    7
10 |   11
11 |   16
12 |   -2
(12 rows)



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

SELECT path_id, route_agg_cost FROM  pgr_trspVia_withPoints(
$$SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id$$,
$$SELECT path, cost FROM restrictions$$,
$$SELECT pid, edge_id, side, fraction FROM pointsOfInterest$$,
ARRAY[-6, 7, -4, 8, -2]
)
WHERE edge < 0;
path_id | route_agg_cost
---------+----------------
1 |            0.3
2 |            2.6
3 |            5.9
4 |            9.3
(4 rows)



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

SELECT seq, route_agg_cost, node, agg_cost ,
CASE WHEN edge = -1 THEN $$visits$$
ELSE $$passes in front$$
END as status
FROM  pgr_trspVia_withPoints(
$$SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id$$,
$$SELECT path, cost FROM restrictions$$,
$$SELECT pid, edge_id, side, fraction FROM pointsOfInterest$$,
ARRAY[-6, 7, -4, 8, -2])
WHERE agg_cost  <> 0 or seq = 1;
seq | route_agg_cost | node | agg_cost |     status
-----+----------------+------+----------+-----------------
1 |              0 |   -6 |        0 | passes in front
2 |            0.3 |    7 |      0.3 | visits
4 |            1.3 |    3 |        1 | passes in front
5 |            2.6 |   -4 |      2.3 | visits
7 |            3.3 |    3 |      0.7 | passes in front
8 |            4.3 |    7 |      1.7 | passes in front
9 |            4.9 |    7 |      2.3 | passes in front
10 |            5.9 |    8 |      3.3 | visits
12 |            6.9 |    7 |        1 | passes in front
13 |            7.9 |   11 |        2 | passes in front
14 |            8.9 |   16 |        3 | passes in front
15 |            9.3 |   -2 |      3.4 | passes in front
(12 rows)



### Simulation of how algorithm works.¶

The algorithm performs a pgr_withPointsVia - Proposed

SELECT * FROM pgr_withPointsVia(
$$SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id$$,
$$SELECT pid, edge_id, side, fraction FROM pointsOfInterest$$,
ARRAY[-6, 15, -5]);
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 |      -5 |   15 |    3 |    1 |        0 |            3.3
7 |       2 |        2 |        15 |      -5 |   10 |    5 |  0.8 |        1 |            4.3
8 |       2 |        3 |        15 |      -5 |   -5 |   -2 |    0 |      1.8 |            5.1
(8 rows)



Detects which of the paths pass through a restriction in this case is for the path_id = 1 from -6 to 15 because the path $$9 \rightarrow 16$$ is restricted.

Executes the TRSP algorithm for the conflicting paths.

SELECT 1 AS path_id, path_seq, start_vid, end_vid, node, edge, cost, agg_cost
FROM  pgr_trsp_withPoints(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
$$SELECT path, cost FROM restrictions$$,
$$SELECT pid, edge_id, side, fraction FROM pointsOfInterest$$,
-6, 15);
path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
---------+----------+-----------+---------+------+------+------+----------
1 |        1 |        -6 |      15 |   -6 |    4 |  0.3 |        0
1 |        2 |        -6 |      15 |    7 |   10 |    1 |      0.3
1 |        3 |        -6 |      15 |    8 |   12 |    1 |      1.3
1 |        4 |        -6 |      15 |   12 |   13 |    1 |      2.3
1 |        5 |        -6 |      15 |   17 |   15 |    1 |      3.3
1 |        6 |        -6 |      15 |   16 |   16 |    1 |      4.3
1 |        7 |        -6 |      15 |   15 |   -1 |    0 |      5.3
(7 rows)



From the pgr_withPointsVia - Proposed result it removes the conflicting paths and builds the solution with the results of the pgr_trsp - Proposed algorithm:

WITH
solutions AS (
SELECT path_id, path_seq, start_vid, end_vid, node, edge, cost, agg_cost
FROM  pgr_withPointsVia(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
$$SELECT pid, edge_id, side, fraction FROM pointsOfInterest$$,
ARRAY[-6, 15, -5]) WHERE path_id != 1
UNION
SELECT 1 AS path_id, path_seq, start_vid, end_vid, node, edge, cost, agg_cost
FROM  pgr_trsp_withPoints(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
$$SELECT path, cost FROM restrictions$$,
$$SELECT pid, edge_id, side, fraction FROM pointsOfInterest$$,
-6, 15)),
with_seq AS (
SELECT row_number() over(ORDER BY path_id, path_seq) AS seq, *
FROM solutions),
aggregation AS (SELECT seq, SUM(cost) OVER(ORDER BY seq) AS route_agg_cost FROM with_seq)
SELECT with_seq.*, COALESCE(route_agg_cost, 0) AS route_agg_cost
FROM with_seq LEFT JOIN aggregation ON (with_seq.seq = aggregation.seq + 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 |   10 |    1 |      0.3 |            0.3
3 |       1 |        3 |        -6 |      15 |    8 |   12 |    1 |      1.3 |            1.3
4 |       1 |        4 |        -6 |      15 |   12 |   13 |    1 |      2.3 |            2.3
5 |       1 |        5 |        -6 |      15 |   17 |   15 |    1 |      3.3 |            3.3
6 |       1 |        6 |        -6 |      15 |   16 |   16 |    1 |      4.3 |            4.3
7 |       1 |        7 |        -6 |      15 |   15 |   -1 |    0 |      5.3 |            5.3
8 |       2 |        1 |        15 |      -5 |   15 |    3 |    1 |        0 |            5.3
9 |       2 |        2 |        15 |      -5 |   10 |    5 |  0.8 |        1 |            6.3
10 |       2 |        3 |        15 |      -5 |   -5 |   -2 |    0 |      1.8 |            7.1
(10 rows)



Getting the same result as pgr_trspVia_withPoints:

SELECT * FROM  pgr_trspVia_withPoints(
$$SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id$$,
$$SELECT path, cost FROM restrictions$$,
$$SELECT pid, edge_id, side, fraction FROM pointsOfInterest$$,
ARRAY[-6, 15, -5]);
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 |   10 |    1 |      0.3 |            0.3
3 |       1 |        3 |        -6 |      15 |    8 |   12 |    1 |      1.3 |            1.3
4 |       1 |        4 |        -6 |      15 |   12 |   13 |    1 |      2.3 |            2.3
5 |       1 |        5 |        -6 |      15 |   17 |   15 |    1 |      3.3 |            3.3
6 |       1 |        6 |        -6 |      15 |   16 |   16 |    1 |      4.3 |            4.3
7 |       1 |        7 |        -6 |      15 |   15 |   -1 |    0 |      5.3 |            5.3
8 |       2 |        1 |        15 |      -5 |   15 |    3 |    1 |        0 |            5.3
9 |       2 |        2 |        15 |      -5 |   10 |    5 |  0.8 |        1 |            6.3
10 |       2 |        3 |        15 |      -5 |   -5 |   -2 |    0 |      1.8 |            7.1
(10 rows)


Example 8:

Sometimes U_turn_on_edge flag is ignored when is set to false.

The first step, doing a pgr_withPointsVia - Proposed does consider not making a U turn on the same edge. But the path $$9 \rightarrow 16$$ (Rows 4 and 5) is restricted and the result is using it.

SELECT * FROM  pgr_withPointsVia(
$$SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id$$,
$$SELECT pid, edge_id, side, fraction FROM pointsOfInterest$$,
ARRAY[6, 7, 6], U_turn_on_edge => false);
seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------+----------------
1 |       1 |        1 |         6 |       7 |    6 |    4 |    1 |        0 |              0
2 |       1 |        2 |         6 |       7 |    7 |   -1 |    0 |        1 |              1
3 |       2 |        1 |         7 |       6 |    7 |    8 |    1 |        0 |              1
4 |       2 |        2 |         7 |       6 |   11 |    9 |    1 |        1 |              2
5 |       2 |        3 |         7 |       6 |   16 |   16 |    1 |        2 |              3
6 |       2 |        4 |         7 |       6 |   15 |    3 |    1 |        3 |              4
7 |       2 |        5 |         7 |       6 |   10 |    2 |    1 |        4 |              5
8 |       2 |        6 |         7 |       6 |    6 |   -2 |    0 |        5 |              6
(8 rows)



When executing the pgr_trsp_withPoints - Proposed algorithm for the conflicting path, there is no U_turn_on_edge flag.

SELECT 5 AS path_id, path_seq, start_vid, end_vid, node, edge, cost, agg_cost
FROM  pgr_trsp_withPoints(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$,
$$SELECT path, cost FROM restrictions$$,
$$SELECT pid, edge_id, side, fraction FROM pointsOfInterest$$,
7, 6);
path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
---------+----------+-----------+---------+------+------+------+----------
5 |        1 |         7 |       6 |    7 |    4 |    1 |        0
5 |        2 |         7 |       6 |    6 |   -1 |    0 |        1
(2 rows)



Therefore the result ignores the U_turn_on_edge flag when set to false. From the pgr_withPointsVia - Proposed result it removes the conflicting paths and builds the solution with the results of the pgr_trsp - Proposed algorithm. In this case a U turn is been done using the same edge.

SELECT * FROM  pgr_trspVia_withPoints(
$$SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id$$,
$$SELECT path, cost FROM restrictions$$,
$$SELECT pid, edge_id, side, fraction FROM pointsOfInterest$$,
ARRAY[6, 7, 6], U_turn_on_edge => false);
seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------+----------------
1 |       1 |        1 |         6 |       7 |    6 |    4 |    1 |        0 |              0
2 |       1 |        2 |         6 |       7 |    7 |   -1 |    0 |        1 |              1
3 |       2 |        1 |         7 |       6 |    7 |    4 |    1 |        0 |              1
4 |       2 |        2 |         7 |       6 |    6 |   -2 |    0 |        1 |              2
(4 rows)