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Add Polygon centroid and center of mass #148

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Jul 27, 2021
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Add Polygon centroid and center of mass #148

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8add93c
Add Polygon.centroid() and Polygon.centerOfMass()
nighthawk Jul 19, 2021
d92435b
Update docs
nighthawk Jul 19, 2021
1b7c603
Linux compile fix
nighthawk Jul 19, 2021
b4345ef
Address code review
nighthawk Jul 20, 2021
b3f0f17
Add Polygon.center and normalize to [-180, 180] longitude
nighthawk Jul 22, 2021
0d6a864
Another Linux compile fix
nighthawk Jul 22, 2021
682201c
Update README.md
1ec5 Jul 27, 2021
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2 changes: 2 additions & 0 deletions README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -75,6 +75,8 @@ Turf.js | Turf-swift
[turf-bearing](https://turfjs.org/docs/#bearing) | `CLLocationCoordinate2D.direction(to:)`<br>`LocationCoordinate2D.direction(to:)` on Linux<br>`RadianCoordinate2D.direction(to:)`
[turf-bezier-spline](https://github.com/Turfjs/turf/tree/master/packages/turf-bezier-spline/) | `LineString.bezier(resolution:sharpness:)`
[turf-boolean-point-in-polygon](https://github.com/Turfjs/turf/tree/master/packages/turf-boolean-point-in-polygon) | `Polygon.contains(_:ignoreBoundary:)`
[turf-center-of-mass](http://turfjs.org/docs/#centerOfMass) | `Polygon.centerOfMass()` |
[turf-centroid](http://turfjs.org/docs/#centroid) | `Polygon.centroid()` |
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[turf-circle](https://turfjs.org/docs/#circle) | `Polygon(center:radius:vertices:)` |
[turf-destination](https://github.com/Turfjs/turf/tree/master/packages/turf-destination/) | `CLLocationCoordinate2D.coordinate(at:facing:)`<br>`LocationCoordinate2D.coordinate(at:facing:)` on Linux<br>`RadianCoordinate2D.coordinate(at:facing:)`
[turf-distance](https://github.com/Turfjs/turf/tree/master/packages/turf-distance/) | `CLLocationCoordinate2D.distance(to:)`<br>`LocationCoordinate2D.distance(to:)` on Linux<br>`RadianCoordinate2D.distance(to:)`
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4 changes: 2 additions & 2 deletions Sources/Turf/CoreLocation.swift
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Expand Up @@ -54,12 +54,12 @@ public struct LocationCoordinate2D {
/**
The latitude in degrees.
*/
public let latitude: LocationDegrees
public internal(set) var latitude: LocationDegrees
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/**
The longitude in degrees.
*/
public let longitude: LocationDegrees
public internal(set) var longitude: LocationDegrees

/**
Creates a degree-based geographic coordinate.
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53 changes: 52 additions & 1 deletion Sources/Turf/Geometries/Polygon.swift
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Expand Up @@ -297,4 +297,55 @@ extension Polygon {
ring[2].longitude == ring[0].longitude
)
}
}


/// Calculates the centroid using the mean of all vertices.
/// This lessens the effect of small islands and artifacts when calculating the centroid of a set of polygons.
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public func centroid() -> LocationCoordinate2D? {
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let coordinates = outerRing.coordinates.dropLast()
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In the future, once similar calculations are implemented for other geometry types, Geometry itself could have centroid and centerOfMass properties that pass through to type-specific implementations like this.

let summed = coordinates
.reduce(into: LocationCoordinate2D(latitude: 0, longitude: 0)) { acc, next in
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acc.latitude += next.latitude
acc.longitude += next.longitude
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}
return .init(
latitude: summed.latitude / Double(coordinates.count),
longitude: summed.longitude / Double(coordinates.count)
)
}

/// Calculates the [center of mass](https://en.wikipedia.org/wiki/Center_of_mass) using this formula: [Centroid of Polygon](https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon).
public func centerOfMass() -> LocationCoordinate2D? {
// First, we neutralize the feature (set it around coordinates [0,0]) to prevent rounding errors
// We take any point to translate all the points around 0
guard let center = centroid() else { return nil }
let coordinates = outerRing.coordinates
let neutralized = coordinates.map {
LocationCoordinate2D(latitude: $0.latitude - center.latitude, longitude: $0.longitude - center.longitude)
}

var signedArea: Double = 0
var sum = LocationCoordinate2D(latitude: 0, longitude: 0)
let zipped = zip(neutralized.prefix(upTo: neutralized.count - 1), neutralized.suffix(from: 1))
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Good use of zip(_:_:)!

for (pi, pj) in zipped {
let (xi, yi) = (pi.longitude, pi.latitude)
let (xj, yj) = (pj.longitude, pj.latitude)

// common factor to compute the signed area and the final coordinates
let a = xi * yj - xj * yi
signedArea += a
sum.longitude += (xi + xj) * a
sum.latitude += (yi + yj) * a
}
guard signedArea != 0 else { return center }

// compute signed area, and factorise 1/6A
let area = signedArea / 2
let areaFactor = 1 / (6 * area)

// final coordinates, adding back values that have been neutralized
return .init(
latitude: center.latitude + areaFactor * sum.latitude,
longitude: center.longitude + areaFactor * sum.longitude
)
}}
97 changes: 97 additions & 0 deletions Tests/TurfTests/PolygonTests.swift
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Expand Up @@ -142,6 +142,103 @@ class PolygonTests: XCTestCase {

XCTAssertEqual(expectedDiameter, diameter, accuracy: 0.25)
}

func testPolygonCentroid() {
// Adopted from https://github.com/Turfjs/turf/blob/3b20c568e5638f680cde39c26b56fbcf034133f2/packages/turf-centroid/test.js
let coordinate = LocationCoordinate2D(latitude: 45.75807143030368, longitude: 4.841194152832031)
let polygon = Polygon([
[
LocationCoordinate2D(latitude: 45.79398056386735, longitude: 4.8250579833984375),
LocationCoordinate2D(latitude: 45.79254427435898, longitude: 4.882392883300781),
LocationCoordinate2D(latitude: 45.76081677972451, longitude: 4.910373687744141),
LocationCoordinate2D(latitude: 45.7271539426975, longitude: 4.894924163818359),
LocationCoordinate2D(latitude: 45.71337148333104, longitude: 4.824199676513671),
LocationCoordinate2D(latitude: 45.74021417890731, longitude: 4.773387908935547),
LocationCoordinate2D(latitude: 45.778418789239055, longitude: 4.778022766113281),
LocationCoordinate2D(latitude: 45.79398056386735, longitude: 4.8250579833984375),
],
])
XCTAssertLessThan(polygon.centroid()!.distance(to: coordinate), 1)
}

func testPolygonImbalancedCentroid() {
// Adopted from https://github.com/Turfjs/turf/blob/3b20c568e5638f680cde39c26b56fbcf034133f2/packages/turf-centroid/test.js
let coordinate = LocationCoordinate2D(latitude: 45.78143055383553, longitude: 4.851791984156558)
let polygon = Polygon([
[
LocationCoordinate2D(latitude: 45.77258200374433, longitude: 4.854240417480469),
LocationCoordinate2D(latitude: 45.777431068484894, longitude: 4.8445844650268555),
LocationCoordinate2D(latitude: 45.778658234059755, longitude: 4.845442771911621),
LocationCoordinate2D(latitude: 45.779376562352425, longitude: 4.845914840698242),
LocationCoordinate2D(latitude: 45.78021460033108, longitude: 4.846644401550292),
LocationCoordinate2D(latitude: 45.78078326178593, longitude: 4.847245216369629),
LocationCoordinate2D(latitude: 45.78138184652523, longitude: 4.848060607910156),
LocationCoordinate2D(latitude: 45.78186070968964, longitude: 4.8487043380737305),
LocationCoordinate2D(latitude: 45.78248921135124, longitude: 4.849562644958495),
LocationCoordinate2D(latitude: 45.78302792142197, longitude: 4.850893020629883),
LocationCoordinate2D(latitude: 45.78374619341895, longitude: 4.852008819580077),
LocationCoordinate2D(latitude: 45.784075398324866, longitude: 4.852995872497559),
LocationCoordinate2D(latitude: 45.78443452873236, longitude: 4.853854179382324),
LocationCoordinate2D(latitude: 45.78470387501975, longitude: 4.8549699783325195),
LocationCoordinate2D(latitude: 45.784793656826345, longitude: 4.85569953918457),
LocationCoordinate2D(latitude: 45.784853511283764, longitude: 4.857330322265624),
LocationCoordinate2D(latitude: 45.78494329284938, longitude: 4.858231544494629),
LocationCoordinate2D(latitude: 45.784883438488365, longitude: 4.859304428100585),
LocationCoordinate2D(latitude: 45.77294120818474, longitude: 4.858360290527344),
LocationCoordinate2D(latitude: 45.77258200374433, longitude: 4.854240417480469)
],
])
XCTAssertLessThan(polygon.centroid()!.distance(to: coordinate), 1)
}

func testPolygonCentreOfMass() {
// Adopted from https://github.com/Turfjs/turf/blob/3b20c568e5638f680cde39c26b56fbcf034133f2/packages/turf-center-of-mass/test.js
let coordinate = LocationCoordinate2D(latitude: 45.75581209996416, longitude: 4.840728965137111)
let polygon = Polygon([
[
LocationCoordinate2D(latitude: 45.79398056386735, longitude: 4.8250579833984375),
LocationCoordinate2D(latitude: 45.79254427435898, longitude: 4.882392883300781),
LocationCoordinate2D(latitude: 45.76081677972451, longitude: 4.910373687744141),
LocationCoordinate2D(latitude: 45.7271539426975, longitude: 4.894924163818359),
LocationCoordinate2D(latitude: 45.71337148333104, longitude: 4.824199676513671),
LocationCoordinate2D(latitude: 45.74021417890731, longitude: 4.773387908935547),
LocationCoordinate2D(latitude: 45.778418789239055, longitude: 4.778022766113281),
LocationCoordinate2D(latitude: 45.79398056386735, longitude: 4.8250579833984375),
],
])
XCTAssertLessThan(polygon.centerOfMass()!.distance(to: coordinate), 1)
}

func testPolygonImbalancedCentreOfMass() {
// Adopted from https://github.com/Turfjs/turf/blob/3b20c568e5638f680cde39c26b56fbcf034133f2/packages/turf-center-of-mass/test.js
let coordinate = LocationCoordinate2D(latitude: 45.77877742486245, longitude: 4.853372894819807)
let polygon = Polygon([
[
LocationCoordinate2D(latitude: 45.77258200374433, longitude: 4.854240417480469),
LocationCoordinate2D(latitude: 45.777431068484894, longitude: 4.8445844650268555),
LocationCoordinate2D(latitude: 45.778658234059755, longitude: 4.845442771911621),
LocationCoordinate2D(latitude: 45.779376562352425, longitude: 4.845914840698242),
LocationCoordinate2D(latitude: 45.78021460033108, longitude: 4.846644401550292),
LocationCoordinate2D(latitude: 45.78078326178593, longitude: 4.847245216369629),
LocationCoordinate2D(latitude: 45.78138184652523, longitude: 4.848060607910156),
LocationCoordinate2D(latitude: 45.78186070968964, longitude: 4.8487043380737305),
LocationCoordinate2D(latitude: 45.78248921135124, longitude: 4.849562644958495),
LocationCoordinate2D(latitude: 45.78302792142197, longitude: 4.850893020629883),
LocationCoordinate2D(latitude: 45.78374619341895, longitude: 4.852008819580077),
LocationCoordinate2D(latitude: 45.784075398324866, longitude: 4.852995872497559),
LocationCoordinate2D(latitude: 45.78443452873236, longitude: 4.853854179382324),
LocationCoordinate2D(latitude: 45.78470387501975, longitude: 4.8549699783325195),
LocationCoordinate2D(latitude: 45.784793656826345, longitude: 4.85569953918457),
LocationCoordinate2D(latitude: 45.784853511283764, longitude: 4.857330322265624),
LocationCoordinate2D(latitude: 45.78494329284938, longitude: 4.858231544494629),
LocationCoordinate2D(latitude: 45.784883438488365, longitude: 4.859304428100585),
LocationCoordinate2D(latitude: 45.77294120818474, longitude: 4.858360290527344),
LocationCoordinate2D(latitude: 45.77258200374433, longitude: 4.854240417480469)
],
])
let center = polygon.centerOfMass()!
XCTAssertLessThan(center.distance(to: coordinate), 1)
}

func testSmoothClose() {
let original = [
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