# `MultiPolygon`

Several areas, at least one, that belong together.

Use it for one region made of separate pieces, such as a country with islands. For one connected area, use [`Polygon`](/docs/types/type-polygon.md).

## Shape

| Field | Type | Required? |
|---|---|---|
| `polygons` | `List<`[`Polygon`](/docs/types/type-polygon.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
MultiPolygon {
    polygons: [
        Polygon {
            outer: [
                Point { latitude: 0.0 longitude: 0.0 altitude: none },
                Point { latitude: 0.0 longitude: 1.0 altitude: none },
                Point { latitude: 1.0 longitude: 1.0 altitude: none },
                Point { latitude: 0.0 longitude: 0.0 altitude: none }
            ]
            holes: []
        }
    ]
}
```

## Good to know

- `==` 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":"MultiPolygon","coordinates":[[[[0,0],[1,0],[1,1],[0,1],[0,0]]],[[[2,2],[3,2],[3,3],[2,3],[2,2]]]]}
{"type":"MultiPolygon","coordinates":[[[[0,0],[1,0],[1,1],[0,1],[0,0]]]]}
```

## Details

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

`MultiPolygon` 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":"MultiPolygon","coordinates":[[[[0,0],[1,0],[1,1],[0,1],[0,0]]]]}` is stored as `'SRID=4326;MULTIPOLYGON (((0 0, 1 0, 1 1, 0 1, 0 0)))'::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":"MultiPolygon","coordinates":[[[[0,0],[1,0],[1,1],[0,1],[0,0]]],[[[2,2],[3,2],[3,3],[2,3],[2,2]]]]}` | `(((0°, 0°; 0°, 1° E; 1° N, 1° E; 1° N, 0°; 0°, 0°)), ((2° N, 2° E; 2° N, 3° E; 3° N, 3° E; 3° N, 2° E; 2° N, 2° E)))` |
| `{"type":"MultiPolygon","coordinates":[[[[0,0],[1,0],[1,1],[0,1],[0,0]]]]}` | `(((0°, 0°; 0°, 1° E; 1° N, 1° E; 1° N, 0°; 0°, 0°)))` |

### Operations

- `geo.area(shape: T) -> Area`: A `Polygon`'s or `MultiPolygon`'s area on the ellipsoid, each edge a geodesic and each ring the smaller of the two sides it bounds, holes taken away, rounded half to even to the square millimetre.
- `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.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>