# withPoints - Category¶

When points are added to the graph.

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.

## Introduction¶

The with points category modifies the graph on the fly by adding points on edges as required by the Points SQL query.

The functions within this category give the ability to process between arbitrary points located outside the original graph.

This category of functions was thought for routing vehicles, but might as well work for some other application not involving vehicles.

When given a point identifier pid that its being mapped to an edge with an identifier edge_id, with a fraction from the source to the target along the edge fraction and some additional information about which side of the edge the point is on side, then processing from arbitrary points can be done on fixed networks.

All this functions consider as many traits from the “real world” as possible:

• Kind of graph:

• directed graph

• undirected graph

• Arriving at the point:

• Compulsory arrival on the side of the segment where the point is located.

• On either side of the segment.

• Countries with:

• Right side driving

• Left side driving

• Some points are:

• Permanent: for example the set of points of clients stored in a table in the data base.

• The graph has been modified to permanently have those points as vertices.

• There is a table on the database that describes the points

• Temporal: for example points given through a web application

• The numbering of the points are handled with negative sign.

• This sign change is to avoid confusion when there is a vertex with the same identifier as the point identifier.

• Original point identifiers are to be positive.

• Transformation to negative is done internally.

• Interpretation of the sign on the node information of the output

• positive sign is a vertex of the original graph

• negative sign is a point of the Points SQL

## Parameters¶

Column

Type

Description

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¶

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

### 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

### Combinations SQL¶

Parameter

Type

Description

source

ANY-INTEGER

Identifier of the departure vertex.

target

ANY-INTEGER

Identifier of the arrival vertex.

Where:

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

For this section the following city (see Sample Data) 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
2 |      15 |      0.4 | r
3 |      12 |      0.6 | l
4 |       6 |      0.3 | 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.

#### Right driving side¶

• 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)

#### Left driving side¶

• 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

• 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 |      0.4 | r
(1 row)

#### On a right hand side driving network¶

Right driving side

• 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.

#### On a left hand side driving network¶

Left driving side

• 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.

#### When driving side does not matter¶

• 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.