Is the 180 west the same as 180 east?

Question

I had a discussion about this topic with a co-worker.

We are working implementing a GPS validation system, and I told him the longitude -180 (or 180W) is not a valid longitude because a valid longitude is the same value as one of the angular values of the spherical coordinates, and the latitude is the another one.

In spherical coordinates:

Theta must be (-180,180]. Theta does not contain the -180 as a valid value

Phi must be [-90,90]. Phi contain both values as valid ones

He said to me there must be 2 values of meridian 180 (positive and negative 180 degrees, +180 & -180, or 180E and 180W), and there is no document specifies this issue: [45,-180] is a valid location? Is not the exact position as [45,180] one?

Any online tool I found on the net or code available includes both meridians as different values, but in the real world, are the same!

My question is: Is there any document specifies the 180 meridian can be positive and negative or any document specifies the 180 meridian must be unique? This co-worker does not accept any math demonstrations, therefore any spherical coordinate to rectangular coordinate system will not be a valid reference for this person.

Answer 1

Perhaps the coordinates of the bounding box for WGS84 could serve as proof? Or you could search for scholarly articles surrounding the creation/generation/adoption of WGS84 as a standard.

Answer 2

Basically, 180 east and west are the same. In other words, [45,180] is the exact same location as [45,-180].

In a geographic database, this has some practical consequences that should guide your validation process.

If you consider points, supposingly adimensional, you would expect a bijection between any coordinate and a location on the Ellipsoid. Therefore, you need to avoid ambiguities if you are located on the antimeridian of your Prime meridian. In this case, using (-180,180] is thus the best practice.

If you consider other geometric features (e.g. lines or polygons), you are in trouble when you cross the dateline (like the Fiji inhabitants). The rule is then defined by the data format. For instance, GeoJSON specification strongly suggest that all geometric feature must be split. In this case, you need duplicate coordinates (-180 and 180) at the split for the continuity of your feature (think of the road topology in the Fiji).

For raster (image) storage, the coordinates of the pixels are either top-left or center, but pixels are no dimensionless like points. For a complete and non overlapping grid, you need the size of the pixels to be a integer fraction of 360°. With top left coordinates, your valid pixels coordinates should ideally be [-180,180) to avoid overlap. Indeed, if your top left pixel was at 180°, then your last pixel would on the other side of the 180th meridian. On the other hand, using [-180,180) for pixels coordinates and appropriate pixe size gives you an extent of [-180,180]. With central coordiantes, this is more tricky. If you set the condition (i.e. [-180,180)) on pixel coordinates, then your extent is out of bounds (i.e. [-180-pixel_size/2,180-pixel_size/2) ).Otherwise, you can fix [-180,180] for the extent, which mean that your coordinates should be in [-180+pixel_size/2,180-pixel_size/2].