# pgr_withPoints - Proposed¶

pgr_withPoints - Devuelve la ruta más corta de un grafo con vértices temporales adicionales.

Funciones propuestas para la próxima versión mayor.

• No están oficialmente en la versión actual.

• Es probable que oficialmente formen parte del próximo lanzamiento:

• Las funciones hacen uso de ENTEROS y FLOTANTES

• Es posible que el nombre no cambie. (Pero todavía puede)

• Es posible que la firma no cambie. (Pero todavía puede)

• Es posible que la funcionalidad no cambie. (Pero todavía puede)

• Se han hecho pruebas con pgTap. Pero tal vez se necesiten más.

• Es posible que la documentación necesite un refinamiento.

• Versión 3.2.0

• Nueva función propuesta:

• pgr_withPoints(Combinaciones)

• Version 2.2.0

• Nueva función propuesta

## Descripción¶

Modificar el grafo para incluir puntos definidos por points_sql. Usando el algoritmo Dijkstra, busar la o las rutas más cortas

Las características principales son:

• El proceso se realiza sólo en las aristas con costos positivos.

• Los vértices del grafo son:

• positivo cuando pertenece a edges_sql

• negativo cuando pertenece a points_sql

• Valores son regresados cuando hay una ruta.

• Cuando el vértice inicial y el vértice final son los mismos, no hay ninguna ruta. - El agg_cost los valores no incluidos (v, v) es 0

• Cuando el vértice inicial y el vértice final son diferentes y no hay ninguna ruta: - En ell agg_cost los valores no incluidos (u, v) es ∞

• Para fines de optimización, se omite cualquier valor duplicado en start_vids o end_vids.

• Los valores devueltos se ordenan: - start_vid ascendente - end_vid ascendente

• Tiempo de ejecución: $$O(|start\_vids|\times(V \log V + E))$$

## Firmas¶

Resumen

pgr_withPoints(Edges SQL, Points SQL, start vid, end vid
[, directed] [, driving_side] [, details])
pgr_withPoints(Edges SQL, Points SQL, start vid, end vids
[, directed] [, driving_side] [, details])
pgr_withPoints(Edges SQL, Points SQL, start vids, end vid
[, directed] [, driving_side] [, details])
pgr_withPoints(Edges SQL, Points SQL, start vids, end vids
[, directed] [, driving_side] [, details])
pgr_withPoints(Edges SQL, Points SQL, Combinations SQL
[, directed] [, driving_side] [, details])
RETURNS (seq, path_seq, [start_vid,] [end_vid,] node, edge, cost, agg_cost)

### Uno a Uno¶

pgr_withPoints(Edges SQL, Points SQL, start vid, end vid
[, directed] [, driving_side] [, details])
RETURNS (seq, path_seq, node, edge, cost, agg_cost)
Ejemplo:

From point $$1$$ to vertex $$10$$ with details

SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
-1, 10,
details => true);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |   -1 |    1 |  0.6 |        0
2 |        2 |    6 |    4 |  0.7 |      0.6
3 |        3 |   -6 |    4 |  0.3 |      1.3
4 |        4 |    7 |    8 |    1 |      1.6
5 |        5 |   11 |    9 |    1 |      2.6
6 |        6 |   16 |   16 |    1 |      3.6
7 |        7 |   15 |    3 |    1 |      4.6
8 |        8 |   10 |   -1 |    0 |      5.6
(8 rows)



### Uno a Muchos¶

pgr_withPoints(Edges SQL, Points SQL, start vid, end vids
[, directed] [, driving_side] [, details])
RETURNS (seq, path_seq, end_vid, node, edge, cost, agg_cost)
Ejemplo:

From point $$1$$ to point $$3$$ and vertex $$7$$ on an undirected graph

SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
-1, ARRAY[-3, 7],
directed => false);
seq | path_seq | end_pid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 |        1 |      -3 |   -1 |    1 |  0.6 |        0
2 |        2 |      -3 |    6 |    4 |    1 |      0.6
3 |        3 |      -3 |    7 |   10 |    1 |      1.6
4 |        4 |      -3 |    8 |   12 |  0.6 |      2.6
5 |        5 |      -3 |   -3 |   -1 |    0 |      3.2
6 |        1 |       7 |   -1 |    1 |  0.6 |        0
7 |        2 |       7 |    6 |    4 |    1 |      0.6
8 |        3 |       7 |    7 |   -1 |    0 |      1.6
(8 rows)



### Muchos a Uno¶

pgr_withPoints(Edges SQL, Points SQL, start vids, end vid
[, directed] [, driving_side] [, details])
RETURNS (seq, path_seq, start_vid, node, edge, cost, agg_cost)
Ejemplo:

From point $$1$$ and vertex $$6$$ to point $$3$$

SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[-1, 6], -3);
seq | path_seq | start_pid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
1 |        1 |        -1 |   -1 |    1 |  0.6 |        0
2 |        2 |        -1 |    6 |    4 |    1 |      0.6
3 |        3 |        -1 |    7 |   10 |    1 |      1.6
4 |        4 |        -1 |    8 |   12 |  0.6 |      2.6
5 |        5 |        -1 |   -3 |   -1 |    0 |      3.2
6 |        1 |         6 |    6 |    4 |    1 |        0
7 |        2 |         6 |    7 |   10 |    1 |        1
8 |        3 |         6 |    8 |   12 |  0.6 |        2
9 |        4 |         6 |   -3 |   -1 |    0 |      2.6
(9 rows)



### Muchos a Muchos¶

pgr_withPoints(Edges SQL, Points SQL, start vids, end vids
[, directed] [, driving_side] [, details])
RETURNS (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
Ejemplo:

From point $$1$$ and vertex $$6$$ to point $$3$$ and vertex $$1$$

SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[-1, 6], ARRAY[-3, 1]);
seq | path_seq | start_pid | end_pid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 |        1 |        -1 |      -3 |   -1 |    1 |  0.6 |        0
2 |        2 |        -1 |      -3 |    6 |    4 |    1 |      0.6
3 |        3 |        -1 |      -3 |    7 |   10 |    1 |      1.6
4 |        4 |        -1 |      -3 |    8 |   12 |  0.6 |      2.6
5 |        5 |        -1 |      -3 |   -3 |   -1 |    0 |      3.2
6 |        1 |        -1 |       1 |   -1 |    1 |  0.6 |        0
7 |        2 |        -1 |       1 |    6 |    4 |    1 |      0.6
8 |        3 |        -1 |       1 |    7 |    7 |    1 |      1.6
9 |        4 |        -1 |       1 |    3 |    6 |    1 |      2.6
10 |        5 |        -1 |       1 |    1 |   -1 |    0 |      3.6
11 |        1 |         6 |      -3 |    6 |    4 |    1 |        0
12 |        2 |         6 |      -3 |    7 |   10 |    1 |        1
13 |        3 |         6 |      -3 |    8 |   12 |  0.6 |        2
14 |        4 |         6 |      -3 |   -3 |   -1 |    0 |      2.6
15 |        1 |         6 |       1 |    6 |    4 |    1 |        0
16 |        2 |         6 |       1 |    7 |    7 |    1 |        1
17 |        3 |         6 |       1 |    3 |    6 |    1 |        2
18 |        4 |         6 |       1 |    1 |   -1 |    0 |        3
(18 rows)



### Combinations¶

pgr_withPoints(Edges SQL, Points SQL, Combinations SQL,
[, directed] [, driving_side] [, details])
RETURNS (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
Ejemplo:

Two combinations

From point $$1$$ to vertex $$10$$, and from vertex $$6$$ to point $$3$$ with right side driving.

SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
'SELECT * FROM (VALUES (-1, 10), (6, -3)) AS combinations(source, target)',
driving_side => 'r', details => true);
seq | path_seq | start_pid | end_pid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 |        1 |        -1 |      10 |   -1 |    1 |  0.4 |        0
2 |        2 |        -1 |      10 |    5 |    1 |    1 |      0.4
3 |        3 |        -1 |      10 |    6 |    4 |  0.7 |      1.4
4 |        4 |        -1 |      10 |   -6 |    4 |  0.3 |      2.1
5 |        5 |        -1 |      10 |    7 |    8 |    1 |      2.4
6 |        6 |        -1 |      10 |   11 |    9 |    1 |      3.4
7 |        7 |        -1 |      10 |   16 |   16 |    1 |      4.4
8 |        8 |        -1 |      10 |   15 |    3 |    1 |      5.4
9 |        9 |        -1 |      10 |   10 |   -1 |    0 |      6.4
10 |        1 |         6 |      -3 |    6 |    4 |  0.7 |        0
11 |        2 |         6 |      -3 |   -6 |    4 |  0.3 |      0.7
12 |        3 |         6 |      -3 |    7 |   10 |    1 |        1
13 |        4 |         6 |      -3 |    8 |   12 |  0.6 |        2
14 |        5 |         6 |      -3 |   -3 |   -1 |    0 |      2.6
(14 rows)



## Parámetros¶

Columna

Tipo

Descripción

Edges SQL

TEXT

Edges SQL as described below

Points SQL

TEXT

Points SQL as described below

Combinations SQL

TEXT

Combinations SQL as described below

start vid

BIGINT

Identifier of the starting vertex of the path. Negative value is for point’s identifier.

start vids

ARRAY[BIGINT]

Array of identifiers of starting vertices. Negative values are for point’s identifiers.

end vid

BIGINT

Identifier of the ending vertex of the path. Negative value is for point’s identifier.

end vids

ARRAY[BIGINT]

Array of identifiers of ending vertices. Negative values are for point’s identifiers.

### Optional parameters¶

Columna

Tipo

x Defecto

Descripción

directed

BOOLEAN

true

• When true the graph is considered Directed

• When false the graph is considered as Undirected.

### With points optional parameters¶

Parámetro

Tipo

x Defecto

Descripción

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¶

Columna

Tipo

x Defecto

Descripción

id

ANY-INTEGER

Identificador de la arista.

source

ANY-INTEGER

Identificador del primer vértice de la arista.

target

ANY-INTEGER

Identificador del segundo vértice de la arista.

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.

Donde:

ENTEROS:

SMALLINT, INTEGER, BIGINT

FLOTANTES:

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

### Points SQL¶

Parámetro

Tipo

x Defecto

Descripción

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

Identificador de la arista «más cercana» al punto.

fraction

ANY-NUMERICAL

El valor en <0,1> que indica la posición relativa desde el primer punto de la arista.

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

Donde:

ENTEROS:

SMALLINT, INTEGER, BIGINT

FLOTANTES:

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

### Combinaciones SQL¶

Parámetro

Tipo

Descripción

source

ANY-INTEGER

Identifier of the departure vertex.

target

ANY-INTEGER

Identifier of the arrival vertex.

Donde:

ENTEROS:

SMALLINT, INTEGER, BIGINT

## Columnas de Resultados¶

Returns set of (seq, path_seq [, start_pid] [, end_pid], node, edge, cost, agg_cost)

Columna

Tipo

Descripción

seq

INTEGER

Sequential value starting from 1.

path_seq

INTEGER

Relative position in the path.

• 1 For the first row of the path.

start_pid

BIGINT

Identifier of a starting vertex/point of the path.

• When positive is the identifier of the starting vertex.

• When negative is the identifier of the starting point.

• Returned on Many to One and Many to Many

end_pid

BIGINT

Identifier of an ending vertex/point of the path.

• When positive is the identifier of the ending vertex.

• When negative is the identifier of the ending point.

• Returned on One to Many and Many to Many

node

BIGINT

Identifier of the node in the path from start_pid to end_pid.

• When positive is the identifier of the a vertex.

• When negative is the identifier of the a point.

edge

BIGINT

Identificador del borde utilizado para ir del node al siguiente nodo de la secuencia de ruta.

• -1 for the last row of the path.

cost

FLOAT

Cost to traverse from node using edge to the next node in the path sequence.

• 0 For the first row of the path.

agg_cost

FLOAT

Aggregate cost from start_vid to node.

• 0 For the first row of the path.

### Use pgr_findCloseEdges in the Points SQL.¶

Find the routes from vertex $$1$$ to the two closest locations on the graph of point (2.9, 1.8).

SELECT * FROM pgr_withPoints(
$e$ 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)
$p$,
1, ARRAY[-1, -2]);
seq | path_seq | end_pid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 |        1 |      -2 |    1 |    6 |    1 |        0
2 |        2 |      -2 |    3 |    7 |    1 |        1
3 |        3 |      -2 |    7 |    8 |  0.9 |        2
4 |        4 |      -2 |   -2 |   -1 |    0 |      2.9
5 |        1 |      -1 |    1 |    6 |    1 |        0
6 |        2 |      -1 |    3 |    7 |    1 |        1
7 |        3 |      -1 |    7 |    8 |    1 |        2
8 |        4 |      -1 |   11 |    9 |    1 |        3
9 |        5 |      -1 |   16 |   16 |    1 |        4
10 |        6 |      -1 |   15 |    3 |    1 |        5
11 |        7 |      -1 |   10 |    5 |  0.8 |        6
12 |        8 |      -1 |   -1 |   -1 |    0 |      6.8
(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).

### Usage variations¶

All the examples are about traveling from point $$1$$ and vertex $$5$$ to points $$\{2, 3, 6\}$$ and vertices $$\{10, 11\}$$

SELECT *
FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[5, -1], ARRAY[-2, -3, -6, 10, 11],
driving_side => 'r', details => true);
seq | path_seq | start_pid | end_pid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 |        1 |        -1 |      -6 |   -1 |    1 |  0.4 |        0
2 |        2 |        -1 |      -6 |    5 |    1 |    1 |      0.4
3 |        3 |        -1 |      -6 |    6 |    4 |  0.7 |      1.4
4 |        4 |        -1 |      -6 |   -6 |   -1 |    0 |      2.1
5 |        1 |        -1 |      -3 |   -1 |    1 |  0.4 |        0
6 |        2 |        -1 |      -3 |    5 |    1 |    1 |      0.4
7 |        3 |        -1 |      -3 |    6 |    4 |  0.7 |      1.4
8 |        4 |        -1 |      -3 |   -6 |    4 |  0.3 |      2.1
9 |        5 |        -1 |      -3 |    7 |   10 |    1 |      2.4
10 |        6 |        -1 |      -3 |    8 |   12 |  0.6 |      3.4
11 |        7 |        -1 |      -3 |   -3 |   -1 |    0 |        4
12 |        1 |        -1 |      -2 |   -1 |    1 |  0.4 |        0
13 |        2 |        -1 |      -2 |    5 |    1 |    1 |      0.4
14 |        3 |        -1 |      -2 |    6 |    4 |  0.7 |      1.4
15 |        4 |        -1 |      -2 |   -6 |    4 |  0.3 |      2.1
16 |        5 |        -1 |      -2 |    7 |    8 |    1 |      2.4
17 |        6 |        -1 |      -2 |   11 |    9 |    1 |      3.4
18 |        7 |        -1 |      -2 |   16 |   15 |  0.4 |      4.4
19 |        8 |        -1 |      -2 |   -2 |   -1 |    0 |      4.8
20 |        1 |        -1 |      10 |   -1 |    1 |  0.4 |        0
21 |        2 |        -1 |      10 |    5 |    1 |    1 |      0.4
22 |        3 |        -1 |      10 |    6 |    4 |  0.7 |      1.4
23 |        4 |        -1 |      10 |   -6 |    4 |  0.3 |      2.1
24 |        5 |        -1 |      10 |    7 |    8 |    1 |      2.4
25 |        6 |        -1 |      10 |   11 |    9 |    1 |      3.4
26 |        7 |        -1 |      10 |   16 |   16 |    1 |      4.4
27 |        8 |        -1 |      10 |   15 |    3 |    1 |      5.4
28 |        9 |        -1 |      10 |   10 |   -1 |    0 |      6.4
29 |        1 |        -1 |      11 |   -1 |    1 |  0.4 |        0
30 |        2 |        -1 |      11 |    5 |    1 |    1 |      0.4
31 |        3 |        -1 |      11 |    6 |    4 |  0.7 |      1.4
32 |        4 |        -1 |      11 |   -6 |    4 |  0.3 |      2.1
33 |        5 |        -1 |      11 |    7 |    8 |    1 |      2.4
34 |        6 |        -1 |      11 |   11 |   -1 |    0 |      3.4
35 |        1 |         5 |      -6 |    5 |    1 |    1 |        0
36 |        2 |         5 |      -6 |    6 |    4 |  0.7 |        1
37 |        3 |         5 |      -6 |   -6 |   -1 |    0 |      1.7
38 |        1 |         5 |      -3 |    5 |    1 |    1 |        0
39 |        2 |         5 |      -3 |    6 |    4 |  0.7 |        1
40 |        3 |         5 |      -3 |   -6 |    4 |  0.3 |      1.7
41 |        4 |         5 |      -3 |    7 |   10 |    1 |        2
42 |        5 |         5 |      -3 |    8 |   12 |  0.6 |        3
43 |        6 |         5 |      -3 |   -3 |   -1 |    0 |      3.6
44 |        1 |         5 |      -2 |    5 |    1 |    1 |        0
45 |        2 |         5 |      -2 |    6 |    4 |  0.7 |        1
46 |        3 |         5 |      -2 |   -6 |    4 |  0.3 |      1.7
47 |        4 |         5 |      -2 |    7 |    8 |    1 |        2
48 |        5 |         5 |      -2 |   11 |    9 |    1 |        3
49 |        6 |         5 |      -2 |   16 |   15 |  0.4 |        4
50 |        7 |         5 |      -2 |   -2 |   -1 |    0 |      4.4
51 |        1 |         5 |      10 |    5 |    1 |    1 |        0
52 |        2 |         5 |      10 |    6 |    4 |  0.7 |        1
53 |        3 |         5 |      10 |   -6 |    4 |  0.3 |      1.7
54 |        4 |         5 |      10 |    7 |    8 |    1 |        2
55 |        5 |         5 |      10 |   11 |    9 |    1 |        3
56 |        6 |         5 |      10 |   16 |   16 |    1 |        4
57 |        7 |         5 |      10 |   15 |    3 |    1 |        5
58 |        8 |         5 |      10 |   10 |   -1 |    0 |        6
59 |        1 |         5 |      11 |    5 |    1 |    1 |        0
60 |        2 |         5 |      11 |    6 |    4 |  0.7 |        1
61 |        3 |         5 |      11 |   -6 |    4 |  0.3 |      1.7
62 |        4 |         5 |      11 |    7 |    8 |    1 |        2
63 |        5 |         5 |      11 |   11 |   -1 |    0 |        3
(63 rows)



#### Passes in front or visits with right side driving.¶

For point $$6$$ and vertex $$11$$.

SELECT (start_pid || ' -> ' || end_pid ||' at ' || path_seq || 'th step')::TEXT AS path_at,
CASE WHEN edge = -1 THEN ' visits'
ELSE ' passes in front of'
END as status,
CASE WHEN node < 0 THEN 'Point'
ELSE 'Vertex'
END as is_a,
abs(node) as id
FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[5, -1], ARRAY[-2, -3, -6, 10, 11],
driving_side => 'r', details => true)
WHERE node IN (-6, 11);
path_at        |       status        |  is_a  | id
----------------------+---------------------+--------+----
-1 -> -6 at 4th step |  visits             | Point  |  6
-1 -> -3 at 4th step |  passes in front of | Point  |  6
-1 -> -2 at 4th step |  passes in front of | Point  |  6
-1 -> -2 at 6th step |  passes in front of | Vertex | 11
-1 -> 10 at 4th step |  passes in front of | Point  |  6
-1 -> 10 at 6th step |  passes in front of | Vertex | 11
-1 -> 11 at 4th step |  passes in front of | Point  |  6
-1 -> 11 at 6th step |  visits             | Vertex | 11
5 -> -6 at 3th step  |  visits             | Point  |  6
5 -> -3 at 3th step  |  passes in front of | Point  |  6
5 -> -2 at 3th step  |  passes in front of | Point  |  6
5 -> -2 at 5th step  |  passes in front of | Vertex | 11
5 -> 10 at 3th step  |  passes in front of | Point  |  6
5 -> 10 at 5th step  |  passes in front of | Vertex | 11
5 -> 11 at 3th step  |  passes in front of | Point  |  6
5 -> 11 at 5th step  |  visits             | Vertex | 11
(16 rows)



#### Passes in front or visits with left side driving.¶

For point $$6$$ and vertex $$11$$.

SELECT (start_pid || ' => ' || end_pid ||' at ' || path_seq || 'th step')::TEXT AS path_at,
CASE WHEN edge = -1 THEN ' visits'
ELSE ' passes in front of'
END as status,
CASE WHEN node < 0 THEN 'Point'
ELSE 'Vertex'
END as is_a,
abs(node) as id
FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[5, -1], ARRAY[-2, -3, -6, 10, 11],
driving_side => 'l', details => true)
WHERE node IN (-6, 11);
path_at        |       status        |  is_a  | id
----------------------+---------------------+--------+----
-1 => -6 at 3th step |  visits             | Point  |  6
-1 => -3 at 3th step |  passes in front of | Point  |  6
-1 => -2 at 3th step |  passes in front of | Point  |  6
-1 => -2 at 5th step |  passes in front of | Vertex | 11
-1 => 10 at 3th step |  passes in front of | Point  |  6
-1 => 10 at 5th step |  passes in front of | Vertex | 11
-1 => 11 at 3th step |  passes in front of | Point  |  6
-1 => 11 at 5th step |  visits             | Vertex | 11
5 => -6 at 4th step  |  visits             | Point  |  6
5 => -3 at 4th step  |  passes in front of | Point  |  6
5 => -2 at 4th step  |  passes in front of | Point  |  6
5 => -2 at 6th step  |  passes in front of | Vertex | 11
5 => 10 at 4th step  |  passes in front of | Point  |  6
5 => 10 at 6th step  |  passes in front of | Vertex | 11
5 => 11 at 4th step  |  passes in front of | Point  |  6
5 => 11 at 6th step  |  visits             | Vertex | 11
(16 rows)



Índices y tablas