Invalid scale when importing data using Mercator projection

[kolesar-andras]

I tried to import an .osm file into mapper version 0.6.1 using Mercator projection EPSG:3857. Measured lengths of roads are much larger than real length. This is because easting and norting units of Mercator projection are not meters (only at Equator). Ratio between real and displayed length equals to ratio of meters and easting/northing units and equals to cosine of average latitude.

I think users need to be warned when using a projection where projection units are not meters. Another solution could be using an average scale ratio between projection units and meters.

[dg0yt]

Why did you choose EPSG:3857?

It might make sense to warn users when the selected CRS is not suitable for local mapping as is the case with EPSG:3857 IMHO. (It is often tagged as "not a recognized geodetic system".) This would mean to create some kind of blacklist.

[dg0yt]

References:

Noel Zinn (2010): Web Mercator: Non-Conformal, Non-Mercator

[kolesar-andras]

I do not agree with author of this presentation. Names three projections:

• Ellipsoidal Mercator
• Spherical Mercator
• Web Mercator

Makes difference between Spherical Mercator and Web Mercator where these are the same. Declares Web Mercator as non-conformal and other two as conformal where all are conformal at small regions and all are non-conformal for larger areas.

I think EPSG:3857 is suitable for local mapping. OpenStreetMap uses this projection for editing by default.

Coordinates in database are stored as WGS-84 ellipsoidal latitude/longitude values and you can switch projection from Mercator to any EPSG code or projection descibed in PROJ WKT in JOSM editor. Contributors use different projections only when they use imagery that is not available in default EPSG:3857 projection.

Usual area of an orienteering is not noticeably affected by varying scale. On 5 kilometers from north to south edge of map cosine of latitude varies around the magnitude of 1/1000. It means that real scale of a 1:15000 scale map is 1:14992 on the north and 1:15008 on the south edge. It means a difference of 0.2 millimeters on the printed map.

[dg0yt]

Maybe both of us added some confusion to a valid point.

• We don't need to discuss the particularities of EPSG:3857. Any regular Mercator projection will do.
• We don't need to discuss OSM. It uses geographic coordinates.
• We need to be careful with terminology.

So you have chosen a Mercator projection for the spatial reference of your map. And you point out that the ratio of "grid units" and "meters on ground" is wrong. Correct?

Mapper effectively assumes that the "grid units" are more or less equal to meters on ground. This a sufficient assumption for some projections, within certain bounds of error. But the assumption does not hold in general. It does not take into account:

• distortion due to earth curvature between (flat) "grid units" and (curved) "meters on earth model" (significant e.g. for Mercator) : grid scale factor
• distortion due to ground height above earth model (significant for increased precision) : elevation factor
• grids that use a different unit of measurement (e.g. feet)

Reading Scale (Map) on Wikipedia, it seems to me that "point scale" and "particular scale" are synonyms for grid scale factor.

So the simplest thing we could do is to add a single, explicit "grid scale factor". It could be used as a combined grid-elevation factor for those that need it, or it could even convert units of measurement. The default value would be 1.0, any other value has to be provided by the user.

[kolesar-andras]

Simple and great solution!

[dg0yt]

With EPSG:3857, the problems are:

• The scale factor is different for E/W and N/S. This is the major shortcoming of that CRS. This will not be supported by Mapper. But I don't think there is a need to choose this CRS.
• The precise scale factors are more difficult to calculate than the standard 1 / cos phi.