# `LineString`

A path of two points or more, in order.

Use it for a route, a road or a cable. For points in no order, use [`MultiPoint`](/docs/types/type-multi-point.md). For an enclosed area, use [`Polygon`](/docs/types/type-polygon.md).

## Shape

| Field | Type | Required? |
|---|---|---|
| `points` | `List<`[`Point`](/docs/types/type-point.md)`>` | Yes |

Its parts keep these rules, and a value that breaks one fails with the rule's name:

- `altitudes_agree`: every position with an altitude, or none

## Example

```jadpo
LineString {
    points: [
        Point { latitude: 51.5072 longitude: -0.1276 altitude: none },
        Point { latitude: 48.8566 longitude: 2.3522 altitude: none }
    ]
}
```

## Good to know

- Every point has an altitude, or none does.
- `geo.length` gives its length as a [`Length`](/docs/types/type-length.md).
- `==` tells you whether two are the same. `<` and `list.sort_by` don't take it, so sort by one of its parts instead.

## In JSON

A GeoJSON geometry, with each position's longitude first, in a request, a response or `json.write`:

```json
{"type":"LineString","coordinates":[[-0.1276,51.5072],[2.3522,48.8566]]}
{"type":"LineString","coordinates":[[0,0,10],[0.5,0.5,10],[1,0,12.5]]}
```

## Details

<details>
<summary>Text form, storage, how it is shown, and operations</summary>

`LineString` is in the group Geospatial, and has been in Jadpo since 0.1.0.

### Text form

It has no single text form, so `text.from` and `text.parse` don't take it.

### How it is stored

It is stored in one column named for the field, of type `geography`. `{"type":"LineString","coordinates":[[0,0,10],[0.5,0.5,10],[1,0,12.5]]}` is stored as `'SRID=4326;LINESTRING Z (0 0 10, 0.5 0.5 10, 1 0 12.5)'::geography`.

### How it is shown to people

`text.format(value, locale:)` shows it to people in their locale.

With `locale: Locale.en_gb`:

| Value | Shown |
|---|---|
| `{"type":"LineString","coordinates":[[-0.1276,51.5072],[2.3522,48.8566]]}` | `(51.5072° N, 0.1276° W; 48.8566° N, 2.3522° E)` |
| `{"type":"LineString","coordinates":[[0,0,10],[0.5,0.5,10],[1,0,12.5]]}` | `(0°, 0°, 10 m; 0.5° N, 0.5° E, 10 m; 0°, 1° E, 12.5 m)` |

### Operations

- `geo.bounding_box(shape: T) -> BoundingBox`: The smallest box of parallels and meridians holding the shape, an edge's highest or lowest point counted, across the antimeridian when that box is narrower; a shape holding a pole runs from -180 to 180.
- `geo.centroid(shape: T) -> Point`: The shape's centre on the sphere, as PostGIS's `ST_Centroid(x, false)` finds it: each point a unit vector, weighted by area, length or count by the shape's kind, summed, and back to latitude and longitude. It may lie outside a concave polygon.
- `geo.contains(a: T, b: U) -> Bool`: Whether no point of `b` lies outside `a`, edges included. `a` may be a `BoundingBox`, whose sides are compared directly, or a `Circle`, holding the points within its radius of its centre.
- `geo.intersects(a: T, b: U) -> Bool`: Whether the two share at least one point, edges included.
- `geo.length(line: T) -> Length`: A `LineString`'s or `MultiLineString`'s length: each edge measured as `distance` measures it, and summed.
- `geo.to_wkt(shape: T) -> Text`: The shape as WKT, longitude first, as PostGIS's `ST_AsText` writes it: `POINT(-0.1276 51.5072)`, `POINT Z (-0.1276 51.5072 35)` with an altitude, each ring in the order it holds its points.
- `geo.within(a: T, b: U, distance: Length?) -> Bool`: `geo.contains(b, a)`; or, with `distance:`, whether two points are at most that far apart, as `geo.distance` measures them.

It also takes `text.format`, `json.read`, `json.write` and `==`. [How every standard type behaves](/docs/every-standard-type-meets-one-contract.md) says how they work.

</details>