Web MercatorCaveat Utilitor

Phil Summerfield, PhDExxonMobil Technical Computing Companyphil.summerfield@exxonmobil.com

APSG 36November 18th, 2016

Agenda

Map Projections 101

IOGP Geodetic Parameter Dataset

Two Examples of Applications using Dataset

Web Mercator & Mercator Compared

IOGP Guidance Notes

Summary

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Whats involved in selecting aProjected Coordinate Reference System?

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Geoid (MSL)

SphereEllipsoid

WGS72/84

Datum & Ellipsoid Relationships(Ellipsoid + Datum Origin = Geodetic Datum)

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Datum (including ellipsoid)is the Foundation for

X,Y,Z Cartesian and/or Lat, Long, Ht

Projected

CRS

is derivative

of the Datum

(Geog CRS)

Stable Unstable w/o

Datum

Equator

Zp

XpYp

Php

Ellipsoid

Hierarchy of Mapping

Map ProjectionsDescribing a 3D ellipsoid with a flat piece of paper

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Map Projection = fn(3D Ellipsoid Flat Plane). It will introduce distortions!! Map Projections can preserve one or more from [Area, Shape, Direction,

Distance] but not all.

All Map Projections introduce distortion when converting a 3-dimensional ellipsoid to a flat representation:

Conformal preserve angles (and shapes) but not scale

Equal Area preserve relative scale but not shape

Distortions, Distortions, Distortions

7G

Common Map ProjectionsExamples

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Mercator (variant A)

Hotine Oblique Mercator (variant A)

American Polyconic

Hotine Oblique Mercator (variant B)

Cassini-Soldner

Lambert Azimuthal Equal Area

New Zealand Map Grid

Transverse Mercator

Polar Stereographic (variant A)

Lambert Conic Conformal (2SP)

Lambert Conic Conformal (2SP)

Oblique Stereographic

Krovak

Albers Equal Area

Lambert Conic Conformal (2SP)

CONUS (Lower 48 US States)Influence of Map Projection on Area Calculations

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Albers Equal Area Conic 8,072,019.56 km2 [+0.06%]Lambert Conformal Conic 7,193,234.60 km2 [-10.83%]Mercator Cylindrical 13,702,681.84 km2 [+69.86%]

Areas:Ellipsoidal 8,067,169.67 km2

Ignores the earth flattening at the poles to model a sphere

It is a valid map projection when used fit for purpose, e.g. popular web mapping services

Web Mercator coordinates should not be relied upon to derive metrics such as distances, areas, and directions from geographic features; gross errors will occur

EPSG Projected CRS 3857

WGS 84 / Pseudo-Mercator

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What is Web Mercator?

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Microsoft Bing Maps Tile System

Bing Maps provides a world map that users can directly manipulate to pan andzoom. To make this interaction as fast and responsive as possible, we chose to pre-render the map at many different levels of detail, and to cut each map into tiles forquick retrieval and display. This document describes the projection, coordinatesystems, and addressing scheme of the map tiles, which collectively are called theBing Maps Tile System.

To make the map seamless, and to ensure that aerial images from different sourcesline up properly, we have to use a single projection for the entire world. We chose touse the Mercator projection

Although the Mercator projection significantly distorts scale and area (particularlynear the poles), it has two important properties that outweigh the scale distortion:

SOURCE: https://msdn.microsoft.com/en-us/library/bb259689.aspx

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Microsoft Bing Maps Tile System

Its a conformal projection, which means that it preserves the shape of relativelysmall objects. This is especially important when showing aerial imagery, becausewe want to avoid distorting the shape of buildings. Square buildings should appearsquare, not rectangular.

Its a cylindrical projection, which means that north and south are always straightup and down, and west and east are always straight left and right.Since the Mercator projection goes to infinity at the poles, it doesnt actually showthe entire world. Using a square aspect ratio for the map, the maximum latitudeshown is approximately 85.05 degrees.

To simplify the calculations, we use the spherical form of this projection, not theellipsoidal form. Since the projection is used only for map display, and not fordisplaying numeric coordinates, we dont need the extra precision of an ellipsoidalprojection. The spherical projection causes approximately 0.33% scale distortion inthe Y direction, which is not visually noticeable.

SOURCE: https://msdn.microsoft.com/en-us/library/bb259689.aspx

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ESRI BlogWeb MercatorThe National Geospatial-Intelligence Agency (NGA) has released an advisory notice on theuse of the Web Mercator coordinate system in military and intelligence applications. In theadvisory, NGA warns about positional accuracy issues with Web Mercator, especially athigher latitudes, and reminds the community to use DoD approved World Geodetic System1984 (WGS 84) applications for all mission critical activities.

Web Mercator, called WGS 1984 Web Mercator (auxiliary sphere) in ArcGIS, and alsoknown as EPSG: 3857 (European Petroleum Survey Group) and WGS 84/PopularVisualisation Pseudo-Mercator, was popularized by Google and has become the mostcommonly-used coordinate system for web mapping applications. It is currently used byGoogle Maps, Bing Maps, and Esri ArcGIS Online basemaps, among others.

SOURCE: https://blogs.esri.com/esri/arcgis/2014/09/25/what-does-the-nga-web-mercator-advisory-mean-for-esri-defense-and-intelligence-users/

http://earth-info.nga.mil/GandG/wgs84/web_mercator/index.html

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ESRI BlogWeb MercatorThe accuracy issues that the NGA warns about are due to the Web Mercator coordinatesystems simplified representation of the Earth as a sphere. Because the Earth is actuallyflattened toward the poles (ellipsoidal), the positional accuracy of latitudes in Web Mercatordecline with distance away from the equator, relative to an ellipsoidal projection. In ArcGISthis is not likely to cause problems unless data in Web Mercator has its coordinate systeminadvertently described as being in an ellipsoidal Mercator version such as WorldMercator (EPSG: 3395), or vice versa. Another issue that is more likely to apply in ArcGIS isthat Web Mercator suffers from the drawback shared by other Mercator projections of scaledistortion near the poles.

Fortunately, ArcGIS supports and can project data between many different coordinatesystems, including Web Mercator and true WGS84 coordinate systems such as GeographicWGS84 and UTM WGS84. Applications built with ArcGIS that use the Web Mercatorcoordinate system can project feature geometries to a more appropriate coordinate systemfor measuring areas, distances, or coordinate locations.

SOURCE: https://blogs.esri.com/esri/arcgis/2014/09/25/what-does-the-nga-web-mercator-advisory-mean-for-esri-defense-and-intelligence-users/

http://earth-info.nga.mil/GandG/wgs84/web_mercator/(U) NGA WGS 84 and the Web Mercator Projection.pdf

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Google Maps APIWeb Maps JavaScript APIWhenever the Google Maps JavaScript API needs to translate a location in the world to alocation on a map (the screen), it needs to first translate latitude and longitude values into a"world" coordinate. This translation is accomplished using a map projection. Google Mapsuses the Mercator projection for this purpose.

The Earth is a three-dimensional sphere (approximately), while a map is a flat two-dimensional surface. The map that you see within the Google Maps JavaScript API, like anyflat map of the Earth, is a projection of that sphere onto a flat surface. In its simplest terms, aprojection can be defined as a mapping of latitude/longitude values into coordinates on theprojection's map.

SOURCE: https://developers.google.com/maps/documentation/javascript/maptypes?csw=1#MapCoordinates

https://en.wikipedia.org/wiki/Mercator_projection

IOGP Geodetic Parameter Dataset

de facto global standard for definitions

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EPSG Geodetic Parameter Registry

The EPSG Dataset is compliant with ISO 19111:2007 spatial referencing of coordinatesIn using the EPSG dataset users will find detailed information about the EPSG dataset and its contents, maintenance and terms of use.

The EPSG dataset is a repository of parameters required to:Define a coordinate reference system, which ensures that coordinates describe

positions unambiguouslyDefine datum transformations and co-ordinate conversions that allow

coordinates to be changed from one CRS to another. The transformations and conversions are collectively called coordinate operations

Online registry is available at www.epsg-registry.org Database is available in SQL and MS Access (snapshots)

(*European Petroleum Survey Group created the Parameter Dataset in 1994, now maintained by the IOGP as the Parameter Registry)

http://www.epsg-registry.org/

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EPSG Geodetic Parameter Registryv8.9.5 (as of November 5th, 2016)

Registry is a living document 473 geodetic datums

50% in the last 50 years91 new datums since 1984

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EPSG Geodetic Parameter RegistryInteractive View

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EPSG Geodetic Parameter RegistryReport View

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EPSG Geodetic Parameter RegistryMS Access Form View

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EPSG Geodetic Parameter RegistryMS Access Report View

EPSG Geodetic Parameter RegistryCRS definition includes Axes

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EPSG Geodetic Parameter RegistryCRS definition includes Axes and Order