Custom Map Projections

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Read the documentation.

// This example defines an image map type using the Gall-Peters
// projection.
// https://en.wikipedia.org/wiki/Gall%E2%80%93Peters_projection

function initMap() {
  // Create a map. Use the Gall-Peters map type.
  var map = new google.maps.Map(document.getElementById('map'), {
    zoom: 0,
    center: {lat: 0, lng: 0},
    mapTypeControl: false
  });

  initGallPeters();
  map.mapTypes.set('gallPeters', gallPetersMapType);
  map.setMapTypeId('gallPeters');

  // Show the lat and lng under the mouse cursor.
  var coordsDiv = document.getElementById('coords');
  map.controls[google.maps.ControlPosition.TOP_CENTER].push(coordsDiv);
  map.addListener('mousemove', function(event) {
    coordsDiv.textContent =
        'lat: ' + Math.round(event.latLng.lat()) + ', ' +
        'lng: ' + Math.round(event.latLng.lng());
  });

  // Add some markers to the map.
  map.data.setStyle(function(feature) {
    return {
      title: feature.getProperty('name'),
      optimized: false
    };
  });
  map.data.addGeoJson(cities);
}

var gallPetersMapType;
function initGallPeters() {
  var GALL_PETERS_RANGE_X = 800;
  var GALL_PETERS_RANGE_Y = 512;

  // Fetch Gall-Peters tiles stored locally on our server.
  gallPetersMapType = new google.maps.ImageMapType({
    getTileUrl: function(coord, zoom) {
      var scale = 1 << zoom;

      // Wrap tiles horizontally.
      var x = ((coord.x % scale) + scale) % scale;

      // Don't wrap tiles vertically.
      var y = coord.y;
      if (y < 0 || y >= scale) return null;

      return 'https://developers.google.com/maps/documentation/' +
             'javascript/examples/full/images/gall-peters_' + zoom +
             '_' + x + '_' + y + '.png';
    },
    tileSize: new google.maps.Size(GALL_PETERS_RANGE_X, GALL_PETERS_RANGE_Y),
    minZoom: 0,
    maxZoom: 1,
    name: 'Gall-Peters'
  });

  // Describe the Gall-Peters projection used by these tiles.
  gallPetersMapType.projection = {
    fromLatLngToPoint: function(latLng) {
      var latRadians = latLng.lat() * Math.PI / 180;
      return new google.maps.Point(
          GALL_PETERS_RANGE_X * (0.5 + latLng.lng() / 360),
          GALL_PETERS_RANGE_Y * (0.5 - 0.5 * Math.sin(latRadians)));
    },
    fromPointToLatLng: function(point, noWrap) {
      var x = point.x / GALL_PETERS_RANGE_X;
      var y = Math.max(0, Math.min(1, point.y / GALL_PETERS_RANGE_Y));

      return new google.maps.LatLng(
          Math.asin(1 - 2 * y) * 180 / Math.PI,
          -180 + 360 * x,
          noWrap);
    }
  };
}

// GeoJSON, describing the locations and names of some cities.
var cities = {
  type: 'FeatureCollection',
  features: [{
    type: 'Feature',
    geometry: {type: 'Point', coordinates: [-87.650, 41.850]},
    properties: {name: 'Chicago'}
  }, {
    type: 'Feature',
    geometry: {type: 'Point', coordinates: [-149.900, 61.218]},
    properties: {name: 'Anchorage'}
  }, {
    type: 'Feature',
    geometry: {type: 'Point', coordinates: [-99.127, 19.427]},
    properties: {name: 'Mexico City'}
  }, {
    type: 'Feature',
    geometry: {type: 'Point', coordinates: [-0.126, 51.500]},
    properties: {name: 'London'}
  }, {
    type: 'Feature',
    geometry: {type: 'Point', coordinates: [28.045, -26.201]},
    properties: {name: 'Johannesburg'}
  }, {
    type: 'Feature',
    geometry: {type: 'Point', coordinates: [15.322, -4.325]},
    properties: {name: 'Kinshasa'}
  }, {
    type: 'Feature',
    geometry: {type: 'Point', coordinates: [151.207, -33.867]},
    properties: {name: 'Sydney'}
  }, {
    type: 'Feature',
    geometry: {type: 'Point', coordinates: [0, 0]},
    properties: {name: '0°N 0°E'}
  }]
};

<div id="map"></div>
<div id="coords"></div>

#coords {
  background-color: black;
  color: white;
  padding: 5px;
}

<!-- Replace the value of the key parameter with your own API key. -->
<script async defer src="https://maps.googleapis.com/maps/api/js?key=AIzaSyCkUOdZ5y7hMm0yrcCQoCvLwzdM6M8s5qk&callback=initMap"></script>

Try it yourself

You can experiment with this code in JSFiddle by clicking the <> icon in the top-right corner of the code window.

<!DOCTYPE html>
<html>
  <head>
    <meta charset="utf-8">
    <title>Custom Map Projections</title>
    <style>
      /* Always set the map height explicitly to define the size of the div
       * element that contains the map. */
      #map {
        height: 100%;
      }
      /* Optional: Makes the sample page fill the window. */
      html, body {
        height: 100%;
        margin: 0;
        padding: 0;
      }
      #coords {
        background-color: black;
        color: white;
        padding: 5px;
      }
    </style>
  </head>
  <body>
    <div id="map"></div>
    <div id="coords"></div>
    <script>
      // This example defines an image map type using the Gall-Peters
      // projection.
      // https://en.wikipedia.org/wiki/Gall%E2%80%93Peters_projection

      function initMap() {
        // Create a map. Use the Gall-Peters map type.
        var map = new google.maps.Map(document.getElementById('map'), {
          zoom: 0,
          center: {lat: 0, lng: 0},
          mapTypeControl: false
        });

        initGallPeters();
        map.mapTypes.set('gallPeters', gallPetersMapType);
        map.setMapTypeId('gallPeters');

        // Show the lat and lng under the mouse cursor.
        var coordsDiv = document.getElementById('coords');
        map.controls[google.maps.ControlPosition.TOP_CENTER].push(coordsDiv);
        map.addListener('mousemove', function(event) {
          coordsDiv.textContent =
              'lat: ' + Math.round(event.latLng.lat()) + ', ' +
              'lng: ' + Math.round(event.latLng.lng());
        });

        // Add some markers to the map.
        map.data.setStyle(function(feature) {
          return {
            title: feature.getProperty('name'),
            optimized: false
          };
        });
        map.data.addGeoJson(cities);
      }

      var gallPetersMapType;
      function initGallPeters() {
        var GALL_PETERS_RANGE_X = 800;
        var GALL_PETERS_RANGE_Y = 512;

        // Fetch Gall-Peters tiles stored locally on our server.
        gallPetersMapType = new google.maps.ImageMapType({
          getTileUrl: function(coord, zoom) {
            var scale = 1 << zoom;

            // Wrap tiles horizontally.
            var x = ((coord.x % scale) + scale) % scale;

            // Don't wrap tiles vertically.
            var y = coord.y;
            if (y < 0 || y >= scale) return null;

            return 'https://developers.google.com/maps/documentation/' +
                   'javascript/examples/full/images/gall-peters_' + zoom +
                   '_' + x + '_' + y + '.png';
          },
          tileSize: new google.maps.Size(GALL_PETERS_RANGE_X, GALL_PETERS_RANGE_Y),
          minZoom: 0,
          maxZoom: 1,
          name: 'Gall-Peters'
        });

        // Describe the Gall-Peters projection used by these tiles.
        gallPetersMapType.projection = {
          fromLatLngToPoint: function(latLng) {
            var latRadians = latLng.lat() * Math.PI / 180;
            return new google.maps.Point(
                GALL_PETERS_RANGE_X * (0.5 + latLng.lng() / 360),
                GALL_PETERS_RANGE_Y * (0.5 - 0.5 * Math.sin(latRadians)));
          },
          fromPointToLatLng: function(point, noWrap) {
            var x = point.x / GALL_PETERS_RANGE_X;
            var y = Math.max(0, Math.min(1, point.y / GALL_PETERS_RANGE_Y));

            return new google.maps.LatLng(
                Math.asin(1 - 2 * y) * 180 / Math.PI,
                -180 + 360 * x,
                noWrap);
          }
        };
      }

      // GeoJSON, describing the locations and names of some cities.
      var cities = {
        type: 'FeatureCollection',
        features: [{
          type: 'Feature',
          geometry: {type: 'Point', coordinates: [-87.650, 41.850]},
          properties: {name: 'Chicago'}
        }, {
          type: 'Feature',
          geometry: {type: 'Point', coordinates: [-149.900, 61.218]},
          properties: {name: 'Anchorage'}
        }, {
          type: 'Feature',
          geometry: {type: 'Point', coordinates: [-99.127, 19.427]},
          properties: {name: 'Mexico City'}
        }, {
          type: 'Feature',
          geometry: {type: 'Point', coordinates: [-0.126, 51.500]},
          properties: {name: 'London'}
        }, {
          type: 'Feature',
          geometry: {type: 'Point', coordinates: [28.045, -26.201]},
          properties: {name: 'Johannesburg'}
        }, {
          type: 'Feature',
          geometry: {type: 'Point', coordinates: [15.322, -4.325]},
          properties: {name: 'Kinshasa'}
        }, {
          type: 'Feature',
          geometry: {type: 'Point', coordinates: [151.207, -33.867]},
          properties: {name: 'Sydney'}
        }, {
          type: 'Feature',
          geometry: {type: 'Point', coordinates: [0, 0]},
          properties: {name: '0°N 0°E'}
        }]
      };
    </script>
    <script async defer src="https://maps.googleapis.com/maps/api/js?key=YOUR_API_KEY&callback=initMap"></script>
  </body>
</html>