Created by Mike Foster for Maptime Boston

I am a biker, sailor, and skier... and also

a geographer, planner, web guy, and educator.

MIT Department of Urban Studies and Planning

mjfoster@mit.edu | @mjfoster83

Don't they?

“Projections in web browsers are terrible and you should be ashamed of yourself”

- Calvin Metcalf

on web maps...

You can ignore about 90% of this, but please pay attention...

that last 10% matters!

To where were The Proclaimers walking?

*Hazel McKendrick*

Where The Proclaimers were *actually* walking.

*Kenneth Field*

Where is Boston?

North Korea's Missile Threat

I don't think this is right...

*The Economist*

North Korea's Missile Threat

There we go. Ahh!

*The Economist*

Let's talk map projections.

The science of accurately measuring and understanding the Earth's geometric shape, orientation in space, and gravitational field.

Geodesists define the Earth's surface as **a surface that closely approximates global mean sea level**, but across which gravity is everywhere equal. This is the geoid. **Geoids are lumpy because gravity varies from place to place** in response to local differences in topography and variations in the density of the materials in the Earth's interior.

Geoids are a little squat. Sea-level gravity is greater at the poles than the equator, a consequence of the Earth's oblate shape and centrifugal force.

Ellipsoids, or spheroids, are commonly used as surrogates for geoids so as to simplify the mathematics involved in relating a coordinate system grid with a model of the Earth's shape. Ellipsoids are good, but not perfect, approximations of geoids.

There are many ellipsoids. Local ellipsoids minimize differences between the geoid and ellipsoid on a local or regional scale.

Is the ellipsoid is optimized for North America.

Centered at Meade's Ranch, Kansas.

Where the geoidal height is considered to be zero.

Latitude and longitude of every other point in North America is based on distance and direction from Meade's Ranch.

**Clarke 1866** - North American Ellipsoid

**GRS 1980** - Geodetic Reference System of 1980 (Global)

**WGS 1984** - World Geodetic System of 1984 (Global)

Ellipsoid | Semi-major Axis (a) | Semi-minor Axis (b) |
---|---|---|

GRS 1980 | 6,378,137.0 m | 6,356,752.314140 m |

WGS 1984 | 6,378,137.0 m | 6,356,752.314245 m |

tl;dr

Very small differences in the semi-minor axis (north pole to south pole) result in minute difference in flattening.

Based off of ellipsoids, but allow for local variations in elevation.*Pssst... WGS 1984 is a 'global datum'...*

Regional Datum | Ellipsoid |
---|---|

1st NAD (1901) | Clarke 1866 |

NAD 1927 | Clarke 1866 |

NAD 1983 | GRS 1980 |

A point having a given latitude and longitude in NAD 1927 might be displaced on the order of tens of meters from another point having identical latitude and longitude in

NAD 1983. It is important to specify.

Datum | Longitude | Latitude |
---|---|---|

NAD 1927 | -122.466903686523 | 48.7440490722656 |

NAD 1983 | -122.46818353793 | 48.7438798543649 |

WGS 1984 | -122.46818353793 | 48.7438798534299 |

HARN stands for High Accuracy Reference Network. It is a statewide or regional upgrade in accuracy of NAD83.

GRS 1980 and WGS 1984 are not the best fit for any given region, but as benefits of a global system outweigh the greater accuracy, the global datums are becoming increasingly adopted.

The surface of the earth is curved, maps are flat.

A map projection is the mathematical transformation of the Earth to a flat surface.

- Conformality -
*distortion of shape* - Distance -
*distortion of distance* - Area -
*distortion of size* - Direction -
*distortion of direction*

**Conformal**-*local/small shapes are preserved***Equal Area**-*areas are preserved***Equidistant**-*distance from single location to other locations preserved***Azimuthal**-*direction from single location to other locations preserved*

- Earth intersects the plane on a small circle. All points on the circle have no distortion.
- The further away from the plane, the more error incurred.

- Conceptualized as the result of wrapping a cylinder of paper around the Earth.
- Mercator is best known.
- Conformal when scale is the same in both directions. Significant distortion away from meridian.

- Conceptualized as the result of wrapping a cone of paper around the Earth.
- Standard parallels where cone meets Earth. Map most accurate at these locations.
- Lambert Conformal Conic projection commonly used for North America.

Coordinate systems are used to accurately identify locations on the surface of the Earth.

- Geographic Coordinate System
- Projected Coordinate System

- Location measured from the curved surface of the earth.
- Units are latitude and longitude.
- "Unprojected" - in 3D
- i.e. WGS 1984, NAD 83
- CAN'T BE USED FOR CALCULATIONS

- Location measured from flattened surface.
- Units are meters, feet, and inches.
- "Projected" - in 2D
- i.e. UTM, State Plane
- USED FOR CALCULATIONS
*(with care)*

International Global Standard

- Cylindrical. Transverse. Cyclinder wrapped around the poles.
- 60 zones. 6 degrees each. Max Distortion: 0.04%

Boston is in Zone 19 North!

Northing and Easting. Measured in meters.

UTM Zone 19 North, **333,475.33**mE, **4,692,503.57**mN

Defined by each state. Can be more accurate than UTM.

Some states have several. Massachusetts has two.

Thank you, Doug Greenfield

The de facto standard for web mapping applications.

- Used by almost all major online map providers.
- Google, Bing, Mapquest, Mapbox, OpenStreetMap, etc.
- Slight, simplified variant of the Mercator.
- Simplified to save computing power.

“Projections in web browsers are terrible and you should be ashamed of yourself”

- Calvin Metcalf

- Based on WGS 1984 Spheroid.
- Huge distortion at poles. (Actually can't show poles!)
- Declared unacceptable for official use by US DOD and NGA. (What?!)

Get your data in the right projection using GIS software!

Common source of improper overlay. Standardize early.

Become friends with the reprojection tools.

- ArcMap
- QGIS

Leaflet does not (easily) use projections. D3 lets you!

- Name from the European Petroleum Survey Group (now defunct)
- Numeric system that specifies projection.
- Used in many online applications, QGIS, PostGIS, etc.

Spatial Reference | Code |
---|---|

WGS 1984 | EPSG:4326 |

NAD 1983 | EPSG:4269 |

WGS 84/UTM 19N | EPSG:32619 |

Maptime Boston's own Andy Woodruff

Bojan Savric - Oregon State University

Jason Davies

Tom Macwright

Click to visit

Enter the following to get a Mercator.

```
function project(x, y) {
return [x, ( 180/Math.PI) * ( 2 * Math.atan(Math.exp(y * Math.PI/180)) - Math.PI/2 )];
}
```

Gregor Aisch - Kartograph.js