Geodesy samples

Two small tables that every map developer ends up needing: how much ground a decimal place of a geographic coordinate covers, and how many metres a Web Mercator tile pixel covers at each zoom level.

Coordinate precision

geodesy/precision — CoordinatePrecision.cs

The number of decimal places you keep in a latitude/longitude decides storage size, display length and — most importantly — how precisely you can place something. The sample moves a point east by 1°, 0.1°, 0.01° … and measures the great-circle distance, at the equator, at 45° (mid-latitudes: Milan, Bordeaux, Minneapolis) and at 60°.

var basePoint = new Point(0, latitude);
var shifted = new Point(0.00001, latitude);            // 5 decimal places

var meters = SpatialUtility.GetSphericalLength(basePoint, shifted);

Output at latitude 45°:

decimal places	degrees	E/W distance
0	1	78.6 km
2	0.01	786 m
4	0.0001	7.86 m
5	0.00001	78.6 cm
6	0.000001	7.86 cm
8	0.00000001	0.8 mm

Rules of thumb: 4 decimals (~10 m) for general mapping, 5 (~1 m) for urban applications, 6 (~10 cm) for navigation, 7 or more for surveying. East–west distances shrink with the cosine of the latitude; north–south distances do not.

Further reading: How precise should lat/long storage be?

Web Mercator ground resolution and scale

geodesy/web-mercator-resolution — WebMercatorResolution.cs

Tile maps (Google, OSM, Bing, ...) use 256 px tiles in Web Mercator; at zoom level z the world is 2^z tiles wide. WebMercatorUtility gives the metres-per-pixel and the map scale for a zoom level and a latitude — the numbers behind Scalebar and the "nearest zoom level" shown in the WPF samples.

var metersPerPixel = WebMercatorUtility.CalculateGroundResolution(zoom, latitude);
var scale = WebMercatorUtility.CalculateMapScale(zoom, latitude);   // e.g. 1 / 36_978 at zoom 12, equator

A few rows of the output:

zoom	resolution @0°	resolution @45°	tiles
1	78.3 km	55.3 km	4
10	152.9 m	108.1 m	1,048,576
15	4.8 m	3.4 m	1,073,741,824
20	14.9 cm	10.6 cm	1,099,511,627,776

How to run

dotnet run --project samples/IRI.Maptor.Samples.Core -- geodesy/precision
dotnet run --project samples/IRI.Maptor.Samples.Core -- geodesy/web-mercator-resolution

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