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Add Polygon centroid and center of mass #148

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Jul 27, 2021
Merged

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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16 changes: 14 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 var latitude: LocationDegrees

/**
The longitude in degrees.
*/
public let longitude: LocationDegrees
public var longitude: LocationDegrees

/**
Creates a degree-based geographic coordinate.
Expand All @@ -71,6 +71,18 @@ public struct LocationCoordinate2D {
}
#endif

extension LocationCoordinate2D {
/**
Returns a normalized coordinate, wrapped to -180 and 180 degrees latitude
*/
var normalized: LocationCoordinate2D {
return .init(
latitude: latitude,
longitude: longitude.wrap(min: -180, max: 180)
)
}
}

extension LocationDirection {
/**
Returns a normalized number given min and max bounds.
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68 changes: 67 additions & 1 deletion Sources/Turf/Geometries/Polygon.swift
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Expand Up @@ -297,4 +297,70 @@ extension Polygon {
ring[2].longitude == ring[0].longitude
)
}
}

/// Calculates the absolute centre (of the bounding box).
public var center: LocationCoordinate2D? {
// This implementation is a port of: https://github.com/Turfjs/turf/blob/master/packages/turf-center/index.ts
return BoundingBox(from: outerRing.coordinates)
.map { .init(
latitude: ($0.southWest.latitude + $0.northEast.latitude) / 2,
longitude: ($0.southWest.longitude + $0.northEast.longitude) / 2
) }
}

/// 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 var centroid: LocationCoordinate2D? {
// This implementation is a port of: https://github.com/Turfjs/turf/blob/master/packages/turf-centroid/index.ts

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.

guard coordinates.count > 0 else { return nil }

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 LocationCoordinate2D(
latitude: summed.latitude / Double(coordinates.count),
longitude: summed.longitude / Double(coordinates.count)
).normalized
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}

/// 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 var centerOfMass: LocationCoordinate2D? {
// This implementation is a port of: https://github.com/Turfjs/turf/blob/master/packages/turf-center-of-mass/index.ts

// 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 LocationCoordinate2D(
latitude: center.latitude + areaFactor * sum.latitude,
longitude: center.longitude + areaFactor * sum.longitude
).normalized
}}
147 changes: 147 additions & 0 deletions Tests/TurfTests/PolygonTests.swift
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Expand Up @@ -142,6 +142,153 @@ class PolygonTests: XCTestCase {

XCTAssertEqual(expectedDiameter, diameter, accuracy: 0.25)
}

func testPolygonCentre() {
// Adopted from https://github.com/Turfjs/turf/blob/3b20c568e5638f680cde39c26b56fbcf034133f2/packages/turf-center/test.js
let coordinate = LocationCoordinate2D(latitude: 45.7536760235992, longitude: 4.841880798339844)
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I suppose the Lyon example would be more offset than expected when using mid(_:_:) because of a longstanding issue in which LocationCoordinate2D.distance(to:) uses a different approximation of the radius of the Earth than Turf.js does these days: #26.

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),
],
])
let center = polygon.center!
XCTAssertLessThan(center.distance(to: coordinate), 1)
}

func testPolygonImbalancedCentre() {
// Adopted from https://github.com/Turfjs/turf/blob/3b20c568e5638f680cde39c26b56fbcf034133f2/packages/turf-center/test.js
let coordinate = LocationCoordinate2D(latitude: 45.778762648296855, longitude: 4.851944446563721)
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.center!
XCTAssertLessThan(center.distance(to: coordinate), 1)
}

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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