Distance Check Approximation (#302)

* Distance check approximation

* Adjust for 180 deg wraparound in equirectangular distance approximation

server/src/actions/calculateDistance.ts

@@ -1,18 +1,55 @@
-const degreesToRadians = (degrees: number) => {
-    return degrees * Math.PI / 180;
+import { Location } from "../types/Location";
+
+const degToRad = Math.PI / 180.0;
+const radians = (degrees: number) => degrees * degToRad;
+
+// Radius of Earth in meters
+const radiusOfEarth = 6371000;
+
+// Radius squared of Earth in square meters
+const radiusOfEarthSqr = radiusOfEarth * radiusOfEarth;
+
+export const isWithinRadiusMeters = (p1: Location, p2: Location, r: number): boolean => {
+    // The equirectangular approximation becomes significantly inaccurate at distances about about 1.5 km 
+    if (r > 1500.0) {
+        return haversineDistanceCheck(p1, p2, r);
+    } else {
+        return equirectangularDistanceCheck(p1, p2, r);
+    }
+}
+
+const getEquirectangularDistanceSqr = (p1: Location, p2: Location) => {
+    // Calculate the difference in longitude, adjusting for the 180 deg wraparound
+    var dLon = p2.lon - p1.lon;
+    if (dLon > 180.0) dLon -= 360.0;
+    if (dLon < -180.0) dLon += 360.0;
+
+    const dx = radians(dLon) * Math.cos(radians(p2.lat + p1.lat) / 2.0);
+    const dy = radians(p2.lat - p1.lat);
+
+    return radiusOfEarthSqr * (dx * dx + dy * dy);
+}
+
+// An approximate distance check which maps spherical points onto a flat surface to quickly estimate distance
+const equirectangularDistanceCheck = (p1: Location, p2: Location, r: number): boolean => {
+    const rSqr = r * r;
+    const distSqr = getEquirectangularDistanceSqr(p1, p2);
+
+    return distSqr <= rSqr;
 }
 
-export const calculateDistanceInMeters = (lat1: number, lon1: number, lat2: number, lon2: number) => {
-    const earthRadiusKm = 6371;
+// A more accurate distance check for points on the surface of a sphere
+const haversineDistanceCheck = (p1: Location, p2: Location, r: number): boolean => {
+    const lat1 = radians(p1.lat);
+    const lon1 = radians(p1.lon);
+    const lat2 = radians(p2.lat);
+    const lon2 = radians(p2.lon);
 
-    const dLat = degreesToRadians(lat2-lat1);
-    const dLon = degreesToRadians(lon2-lon1);
+    const dLat = lat2 - lat1;
+    const dLon = lon2 - lon1;
 
-    lat1 = degreesToRadians(lat1);
-    lat2 = degreesToRadians(lat2);
+    const a = Math.pow(Math.sin(dLat / 2.0), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dLon / 2.0), 2);
+    const c = 2.0 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
 
-    const a = Math.sin(dLat/2) * Math.sin(dLat/2) +
-            Math.sin(dLon/2) * Math.sin(dLon/2) * Math.cos(lat1) * Math.cos(lat2); 
-    const c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a)); 
-    return earthRadiusKm * c * 1000;
+    return c * radiusOfEarth <= r;
 }

server/src/index.ts

@@ -16,7 +16,7 @@ import { ConnectedUser } from "./types/User";
 import { getAuth } from "firebase-admin/auth";
 import Mailgun from "mailgun.js";
 import { messagesCollection } from "./utilities/firebaseInit";
-import { calculateDistanceInMeters } from "./actions/calculateDistance";
+import { isWithinRadiusMeters } from "./actions/calculateDistance";
 import { scheduleCron } from "./actions/deleter";
 import mainRouter from "./routes/mainRouteHandler";
 
@@ -80,20 +80,10 @@ io.on("connection", async (socket: any) => {
         if (change.type === "added") {
           console.log("New message: ", change.doc.data());
 
-          const messageLat = change.doc.data().location.lat;
-          const messageLon = change.doc.data().location.lon;
+          const messageLocation = change.doc.data().location;
+          const userLocation = defaultConnectedUser.location;
 
-          const userLat = defaultConnectedUser.location.lat;
-          const userLon = defaultConnectedUser.location.lon;
-
-          const distance = calculateDistanceInMeters(
-            messageLat,
-            messageLon,
-            userLat,
-            userLon
-          );
-
-          if (distance < message_outreach_radius) {
+          if (isWithinRadiusMeters(userLocation, messageLocation, message_outreach_radius)) {
             console.log(`Message is within ${message_outreach_radius} meters of the user ${socket.id}.`);
             socket.emit("message", change.doc.data());
           } else {

server/src/types/Location.ts

@@ -0,0 +1,5 @@
+export interface Location {
+    lat: number
+    lon: number
+    geohash: string
+}

server/src/types/User.ts

@@ -1,3 +1,5 @@
+import { Location } from "./Location"
+
 export interface UserConfig {
   uid: string
   isConnected: boolean
@@ -21,9 +23,5 @@ export interface UserConfig {
 export interface ConnectedUser {
     uid: string
     socketId: string
-    location: {
-        lat: number
-        lon: number
-        geohash: string
-    },
+    location: Location
 }