# pgRouting Manual (3.6)

## 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.

- withPoints - Family of functions - Functions based on Dijkstra algorithm.

- From the TRSP - Family of functions:

  - pgr_trsp_withPoints - Proposed - Vertex/Point routing with restrictions.

  - pgr_trspVia_withPoints - Proposed - Via Vertex/point routing with restrictions.

## 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

    - Use pgr_findCloseEdges in the Points SQL.

- 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`

## Advanced documentation

### About points

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

- On the TRSP - Family of functions 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 |      0.4 | 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.

## See Also

- withPoints - Family of functions

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