# `Polygon`

An area with any holes: a GeoJSON `Polygon`, each ring closed with four points or more, the outer counterclockwise and each hole clockwise when written.

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

## Make one

Build one from its fields, `Polygon { outer: ...  holes: ... }`.

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

- `rings_valid`: `each ring closed and simple, no rings touching, holes inside the outer ring, every edge under half the globe`
- `altitudes_agree`: `every position with an altitude, or none`

## Fields

| Field | Type |
|---|---|
| `outer` | `List<`[`Point`](type-point.md)`>` |
| `holes` | `List<List<`[`Point`](type-point.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":"Polygon","coordinates":[[[0,0],[1,0],[1,1],[0,1],[0,0]]]}` |
| `{"type":"Polygon","coordinates":[[[0,0],[1,0],[1,1],[0,1],[0,0]],[[0.25,0.25],[0.25,0.75],[0.75,0.75],[0.75,0.25],[0.25,0.25]]]}` |

It is stored in one column named for the field, of type `geography`. `{"type":"Polygon","coordinates":[[[0,0],[1,0],[1,1],[0,1],[0,0]],[[0.25,0.25],[0.25,0.75],[0.75,0.75],[0.75,0.25],[0.25,0.25]]]}` is stored as `'SRID=4326;POLYGON ((0 0, 1 0, 1 1, 0 1, 0 0), (0.25 0.25, 0.25 0.75, 0.75 0.75, 0.75 0.25, 0.25 0.25))'::geography`.

## Shown to people

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

With `locale: Locale.en_gb`:

| Value | Shown |
|---|---|
| `{"type":"Polygon","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°))` |
| `{"type":"Polygon","coordinates":[[[0,0],[1,0],[1,1],[0,1],[0,0]],[[0.25,0.25],[0.25,0.75],[0.75,0.75],[0.75,0.25],[0.25,0.25]]]}` | `((0°, 0°; 0°, 1° E; 1° N, 1° E; 1° N, 0°; 0°, 0°), (0.25° N, 0.25° E; 0.75° N, 0.25° E; 0.75° N, 0.75° E; 0.25° N, 0.75° E; 0.25° N, 0.25° E))` |

## 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.