# `MultiPolygon`

Areas, at least one: a GeoJSON `MultiPolygon`.

[Geospatial](types.md#geospatial); not ordered; since Jadpo 0.1.0.

## Make one

Build one from its fields, `MultiPolygon { polygons: ... }`.

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

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

## Fields

| Field | Type |
|---|---|
| `polygons` | `List<`[`Polygon`](type-polygon.md)`>` |

## Text, JSON and storage

It has no single text form, so `text.from` and `text.parse` don't take it. JSON sends a GeoJSON geometry, its positions longitude first.

| 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]]]]}` |

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`.

## 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.

Like every standard type, it also has the contract's own operations: `text.format`, `json.read`, `json.write` and `==`. It isn't ordered, so `<` and sorting don't take it. [Every standard type meets one contract](../topics/every-standard-type-meets-one-contract.md) says how they work.