# withPoints - Familia de funciones¶

Cuando los puntos también se dan como entrada:

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.

## Introducción¶

This family of functions belongs to the withPoints- Categoría and the functions that compose them are based one way or another on dijkstra algorithm.

Depending on the name:

• pgr_withPoints is pgr_dijkstra with points

• pgr_withPointsCost is pgr_dijkstraCost with points

• pgr_withPointsCostMatrix is pgr_dijkstraCostMatrix with points

• pgr_withPointsKSP is pgr_ksp with points

• pgr_withPointsDD is pgr_drivingDistance with points

• pgr_withPointsvia is pgr_dijkstraVia with points

## Parameters¶

Column

Type

Description

SQL Aristas

TEXT

Consulta de aristas como se describe a continuación

Points SQL

TEXT

Points SQL as described below

SQL Combinaciones

TEXT

SQL Combinaciones como se describe a abajo

vid de salida

BIGINT

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

vid salidas

ARRAY[BIGINT]

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

vid destino

BIGINT

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

vids destinos

ARRAY[BIGINT]

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

### Parámetros opcionales¶

Column

Type

x Defecto

Description

directed

BOOLEAN

true

• Cuando true el gráfo se considera Dirigido

• Cuando false el gráfo se considera No Dirigido.

### With points optional parameters¶

Parameter

Type

x Defecto

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.

## Consultas internas¶

### SQL de aristas¶

Column

Type

x Defecto

Description

id

ENTEROS

source

ENTEROS

Identifier of the first end point vertex of the edge.

target

ENTEROS

Identifier of the second end point vertex of the edge.

cost

FLOTANTES

Peso de la arista (source, target)

reverse_cost

FLOTANTES

-1

Peso de la arista (target, source)

• Cuando negativo: la arista (target, source) no existe, por lo tanto no es parte del grafo.

Where:

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

ANY-NUMERICAL:

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

### Points SQL¶

Parameter

Type

x Defecto

Description

pid

ENTEROS

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

ENTEROS

Identifier of the «closest» edge to the point.

fraction

FLOTANTES

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

### SQL Combinaciones¶

Parameter

Type

Description

source

ENTEROS

target

ENTEROS

Where:

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

For this section the following city (see Datos Muestra) some interesing points such as restaurant, supermarket, post office, etc. will be used as example.

• The graph is directed

• Red arrows show the (source, target) of the edge on the edge table

• Blue arrows show the (target, source) of the edge on the edge table

• Each point location shows where it is located with relation of the edge (source, target)

• On the right for points 2 and 4.

• On the left for points 1, 3 and 5.

• On both sides for point 6.

The representation on the data base follows the Points SQL description, and for this example:

SELECT pid, edge_id, fraction, side FROM pointsOfInterest;
pid | edge_id |      fraction      | side
-----+---------+--------------------+------
1 |       1 |                0.4 | l
4 |       6 |                0.3 | r
3 |      12 | 0.6000000000000001 | l
2 |      15 | 0.3999999999999999 | r
5 |       5 |                0.8 | l
6 |       4 |                0.7 | b
(6 rows)



### Driving side¶

In the the folowwing images:

• The squared vertices are the temporary vertices,

• The temporary vertices are added according to the driving side,

• visually showing the differences on how depending on the driving side the data is interpreted.

• Point 1 located on edge (6, 5)

• Point 2 located on edge (16, 17)

• Point 3 located on edge (8, 12)

• Point 4 located on edge (1, 3)

• Point 5 located on edge (10, 11)

• Point 6 located on edges (6, 7) and (7, 6)

• Point 1 located on edge (5, 6)

• Point 2 located on edge (17, 16)

• Point 3 located on edge (8, 12)

• Point 4 located on edge (3, 1)

• Point 5 located on edge (10, 11)

• Point 6 located on edges (6, 7) and (7, 6)

#### Driving side does not matter¶

• Like having all points to be considered in both sides b

• Prefered usage on undirected graphs

• On the TRSP - Familia de funciones this option is not valid

• Point 1 located on edge (5, 6) and (6, 5)

• Point 2 located on edge (17, 16)and 16, 17

• Point 3 located on edge (8, 12)

• Point 4 located on edge (3, 1) and (1, 3)

• Point 5 located on edge (10, 11)

• Point 6 located on edges (6, 7) and (7, 6)

### Creating temporary vertices¶

This section will demonstrate how a temporary vertex is created internally on the graph.

Problem

For edge:

SELECT id, source, target, cost, reverse_cost
FROM edges WHERE id = 15;
id | source | target | cost | reverse_cost
----+--------+--------+------+--------------
15 |     16 |     17 |    1 |            1
(1 row)



insert point:

SELECT pid, edge_id, fraction, side
FROM pointsOfInterest WHERE pid = 2;
pid | edge_id |      fraction      | side
-----+---------+--------------------+------
2 |      15 | 0.3999999999999999 | r
(1 row)



#### En una red de conducción del lado derecho¶

• Arrival to point -2 can be achived only via vertex 16.

• Does not affects edge (17, 16), therefore the edge is kept.

• It only affects the edge (16, 17), therefore the edge is removed.

• Create two new edges:

• Edge (16, -2) with cost 0.4 (original cost * fraction == $$1 * 0.4$$)

• Edge (-2, 17) with cost 0.6 (the remaing cost)

• The total cost of the additional edges is equal to the original cost.

• If more points are on the same edge, the process is repeated recursevly.

#### En una red de conducción del lado izquierdo¶

• Arrival to point -2 can be achived only via vertex 17.

• Does not affects edge (16, 17), therefore the edge is kept.

• It only affects the edge (17, 16), therefore the edge is removed.

• Create two new edges:

• Work with the original edge (16, 17) as the fraction is a fraction of the original:

• Edge (16, -2) with cost 0.4 (original cost * fraction == $$1 * 0.4$$)

• Edge (-2, 17) with cost 0.6 (the remaing cost)

• If more points are on the same edge, the process is repeated recursevly.

• Flip the Edges and add them to the graph:

• Edge (17, -2) becomes (-2, 16) with cost 0.4 and is added to the graph.

• Edge (-2, 16) becomes (17, -2) with cost 0.6 and is added to the graph.

• The total cost of the additional edges is equal to the original cost.

#### Cuando el lado de conducción no importa¶

• Arrival to point -2 can be achived via vertices 16 or 17.

• Affects the edges (16, 17) and (17, 16), therefore the edges are removed.

• Create four new edges:

• Work with the original edge (16, 17) as the fraction is a fraction of the original:

• Edge (16, -2) with cost 0.4 (original cost * fraction == $$1 * 0.4$$)

• Edge (-2, 17) with cost 0.6 (the remaing cost)

• If more points are on the same edge, the process is repeated recursevly.

• Flip the Edges and add all the edges to the graph:

• Edge (16, -2) is added to the graph.

• Edge (-2, 17) is added to the graph.

• Edge (16, -2) becomes (-2, 16) with cost 0.4 and is added to the graph.

• Edge (-2, 17) becomes (17, -2) with cost 0.6 and is added to the graph.

Índices y tablas