Implement rhumbBearing function and test (#109)

* initial commit, stolen from @armantorkzaban

* fix formatting

* cleanup comments

README.md

@@ -89,7 +89,7 @@ Any new benchmarks must be named `*_benchmark.dart` and reside in the
 - [ ] pointOnFeature
 - [ ] polygonTangents
 - [ ] pointToLineDistance
-- [ ] rhumbBearing
+- [x] [rhumbBearing](https://github.com/dartclub/turf_dart/blob/main/lib/src/rhumb_bearing.dart)
 - [ ] rhumbDestination
 - [ ] rhumbDistance
 - [ ] square

lib/bearing.dart

@@ -1,3 +1,4 @@
 library turf_bearing;
 
 export 'src/bearing.dart';
+export 'src/rhumb_bearing.dart';

lib/src/rhumb_bearing.dart

@@ -0,0 +1,64 @@
+// https://en.wikipedia.org/wiki/Rhumb_line
+import 'package:turf/src/invariant.dart';
+import 'dart:math' as math;
+import '../helpers.dart';
+
+/// Takes two [Point] and finds the bearing angle between them along a Rhumb line
+/// i.e. the angle measured in degrees start the north line (0 degrees)
+/// [kFinal] calculates the final bearing if true.
+/// Returns bearing from north in decimal degrees, between -180 and 180 degrees (positive clockwise)
+/// example:
+/// ```dart
+/// var point1 = Feature(geometry: Point(coordinates: Position.of([-75.343, 39.984])), properties: {"marker-color": "#F00"});
+/// var point2 = Feature(geometry: Point(coordinates: Position.of([-75.534, 39.123])), properties: {"marker-color": "#00F"});
+/// var bearing = rhumbBearing(point1.geometry, point2.geometry);
+/// //addToMap
+/// var addToMap = [point1, point2];
+/// point1.properties['bearing'] = bearing;
+/// point2.properties['bearing'] = bearing;
+/// ```
+num rhumbBearing(Point start, Point end, {bool kFinal = false}) {
+  num bear360;
+  if (kFinal) {
+    bear360 = calculateRhumbBearing(getCoord(end), getCoord(start));
+  } else {
+    bear360 = calculateRhumbBearing(getCoord(start), getCoord(end));
+  }
+
+  var bear180 = bear360 > 180 ? -(360 - bear360) : bear360;
+
+  return bear180;
+}
+
+/// Returns the bearing from ‘this’ [Point] to destination [Point] along a rhumb line.
+/// Adapted from Geodesy: https://github.com/chrisveness/geodesy/blob/master/latlon-spherical.js
+/// Returns Bearing in degrees from north.
+/// example
+/// ```dart
+/// var p1 = Position.named(lng: 51.127, lat: 1.338);
+/// var p2 = Position.named(lng: 50.964, lat: 1.853);
+/// var d = p1.rhumbBearingTo(p2); // 116.7 m
+/// ```
+num calculateRhumbBearing(Position from, Position to) {
+  // φ => phi
+  // Δλ => deltaLambda
+  // Δψ => deltaPsi
+  // θ => theta
+  num phi1 = degreesToRadians(from.lat);
+  num phi2 = degreesToRadians(to.lat);
+  num deltaLambda = degreesToRadians(to.lng - from.lng);
+  // if deltaLambda over 180° take shorter rhumb line across the anti-meridian:
+  if (deltaLambda > math.pi) {
+    deltaLambda -= 2 * math.pi;
+  }
+  if (deltaLambda < -math.pi) {
+    deltaLambda += 2 * math.pi;
+  }
+
+  double deltaPsi = math
+      .log(math.tan(phi2 / 2 + math.pi / 4) / math.tan(phi1 / 2 + math.pi / 4));
+
+  double theta = math.atan2(deltaLambda, deltaPsi);
+
+  return (radiansToDegrees(theta) + 360) % 360;
+}

test/components/rhumb_bearing_test.dart

@@ -0,0 +1,46 @@
+import 'dart:convert';
+import 'dart:io';
+
+import 'package:test/test.dart';
+import 'package:turf/helpers.dart';
+import 'package:turf/src/rhumb_bearing.dart';
+
+main() {
+  group(
+    '',
+    () {
+      Directory inDir = Directory('./test/examples/rhumb_bearing/in');
+      for (var file in inDir.listSync(recursive: true)) {
+        if (file is File && file.path.endsWith('.geojson')) {
+          test(
+            file.path,
+            () {
+              var inSource = file.readAsStringSync();
+              var inGeom = GeoJSONObject.fromJson(jsonDecode(inSource));
+
+              var start = (inGeom as FeatureCollection).features[0];
+              var end = inGeom.features[1];
+              var initialBearing =
+                  rhumbBearing(start.geometry as Point, end.geometry as Point);
+              var finalBearing = rhumbBearing(
+                  start.geometry as Point, end.geometry as Point,
+                  kFinal: true);
+              var result = {
+                'initialBearing': initialBearing,
+                'finalBearing': finalBearing,
+              };
+
+              Directory outDir = Directory('./test/examples/rhumb_bearing/out');
+              for (var file in outDir.listSync(recursive: true)) {
+                if (file is File && file.path.endsWith('.json')) {
+                  var outSource = jsonDecode(file.readAsStringSync());
+                  expect(result, outSource);
+                }
+              }
+            },
+          );
+        }
+      }
+    },
+  );
+}

test/examples/rhumb_bearing/in/pair1.geojson

@@ -0,0 +1,31 @@
+{
+    "type": "FeatureCollection",
+    "features": [
+        {
+            "type": "Feature",
+            "properties": {
+                "marker-color": "#F00"
+            },
+            "geometry": {
+                "type": "Point",
+                "coordinates": [
+                    -75,
+                    45
+                ]
+            }
+        },
+        {
+            "type": "Feature",
+            "properties": {
+                "marker-color": "#00F"
+            },
+            "geometry": {
+                "type": "Point",
+                "coordinates": [
+                    20,
+                    60
+                ]
+            }
+        }
+    ]
+}

test/examples/rhumb_bearing/out/pair1.geojson

@@ -0,0 +1,71 @@
+{
+    "type": "FeatureCollection",
+    "features": [
+        {
+            "type": "Feature",
+            "properties": {
+                "marker-color": "#F00"
+            },
+            "geometry": {
+                "type": "Point",
+                "coordinates": [
+                    -75,
+                    45
+                ]
+            }
+        },
+        {
+            "type": "Feature",
+            "properties": {
+                "marker-color": "#00F"
+            },
+            "geometry": {
+                "type": "Point",
+                "coordinates": [
+                    20,
+                    60
+                ]
+            }
+        },
+        {
+            "type": "Feature",
+            "properties": {
+                "stroke": "#F00",
+                "stroke-width": 6
+            },
+            "geometry": {
+                "type": "LineString",
+                "coordinates": [
+                    [
+                        -75,
+                        45
+                    ],
+                    [
+                        -66.10068737769872,
+                        51.79325008492101
+                    ]
+                ]
+            }
+        },
+        {
+            "type": "Feature",
+            "properties": {
+                "stroke": "#00F",
+                "stroke-width": 6
+            },
+            "geometry": {
+                "type": "LineString",
+                "coordinates": [
+                    [
+                        20,
+                        60
+                    ],
+                    [
+                        2.3844816279733956,
+                        63.440396381483744
+                    ]
+                ]
+            }
+        }
+    ]
+}

test/examples/rhumb_bearing/out/pair1.json

@@ -0,0 +1,4 @@
+{
+    "initialBearing": 75.28061364784332,
+    "finalBearing": -104.7193863521567
+}