add MercatorCoordinate meterInMercatorCoordinateUnits method

src/geo/mercator_coordinate.js

@@ -3,12 +3,16 @@
 import LngLat from '../geo/lng_lat';
 import type {LngLatLike} from '../geo/lng_lat';
 
+/*
+ * The circumference of the world in meters at the equator.
+ */
+const circumferenceAtEquator = 2 * Math.PI * 6378137;
+
 /*
  * The circumference of the world in meters at the given latitude.
  */
 function circumferenceAtLatitude(latitude: number) {
-    const circumference = 2 * Math.PI * 6378137;
-    return circumference * Math.cos(latitude * Math.PI / 180);
+    return circumferenceAtEquator * Math.cos(latitude * Math.PI / 180);
 }
 
 export function mercatorXfromLng(lng: number) {
@@ -36,6 +40,19 @@ export function altitudeFromMercatorZ(z: number, y: number) {
     return z * circumferenceAtLatitude(latFromMercatorY(y));
 }
 
+/**
+ * Determine the Mercator scale factor for a given latitude, see
+ * https://en.wikipedia.org/wiki/Mercator_projection#Scale_factor
+ *
+ * At the equator the scale factor will be 1, which increases at higher latitudes.
+ *
+ * @param {number} lat Latitude
+ * @returns {number} scale factor
+ */
+export function mercatorScale(lat: number) {
+    return 1 / Math.cos(lat * Math.PI / 180);
+}
+
 /**
  * A `MercatorCoordinate` object represents a projected three dimensional position.
  *
@@ -113,6 +130,20 @@ class MercatorCoordinate {
     toAltitude() {
         return altitudeFromMercatorZ(this.z, this.y);
     }
+
+    /**
+     * Returns the distance of 1 meter in `MercatorCoordinate` units at this latitude.
+     *
+     * For coordinates in real world units using meters, this naturally provides the scale
+     * to transform into `MercatorCoordinate`s.
+     *
+     * @returns {number} Distance of 1 meter in `MercatorCoordinate` units.
+     */
+    meterInMercatorCoordinateUnits() {
+        // 1 meter / circumference at equator in meters * Mercator projection scale factor at this latitude
+        return 1 / circumferenceAtEquator * mercatorScale(latFromMercatorY(this.y));
+    }
+
 }
 
 export default MercatorCoordinate;

test/unit/geo/mercator_coordinate.test.js

@@ -1,6 +1,6 @@
 import { test } from '../../util/test';
 import LngLat from '../../../src/geo/lng_lat';
-import MercatorCoordinate from '../../../src/geo/mercator_coordinate';
+import MercatorCoordinate, { mercatorScale } from '../../../src/geo/mercator_coordinate';
 
 test('LngLat', (t) => {
     t.test('#constructor', (t) => {
@@ -27,5 +27,17 @@ test('LngLat', (t) => {
         t.end();
     });
 
+    t.test('#mercatorScale', (t) => {
+        t.equal(mercatorScale(0), 1, 'mercator scale at the equator');
+        t.equal(mercatorScale(45), 1.414213562373095, 'mercator scale at 45 degrees latitude');
+        t.end();
+    });
+
+    t.test('#meterInMercatorCoordinateUnits', (t) => {
+        const nullIsland = new LngLat(0, 0);
+        t.equal(MercatorCoordinate.fromLngLat(nullIsland).meterInMercatorCoordinateUnits(), 2.495320233665337e-8, 'length of 1 meter in MercatorCoordinate units at the equator');
+        t.end();
+    });
+
     t.end();
 });