Antipodal Coordinates

Two points are called antipodal if they are at two opposite points on a circle or a sphere. They are also said to be diametrically opposed or that they are the most distant points of each other on a spheroid.

Example: On Earth, the north pole and the south pole are antipodes.

Here is an image presenting the earth globe with the continents presented once in yellow, and a second time in blue but with their antipodal coordinates (source wikipedia).

The portions where the yellow and blue continents overlap, are locations on Earth, where digging a rectilinear hole, perpendicular to the ground and passing through the center of the earth would land on another continent.

Example: The antipodes of France is near New-Zealand.

From the coordinates on a sphere, take the opposite value of the latitude (which is to put or remove a minus sign -), and remove or add 180 to the longitude (to keep it in the interval [-180; +180]) for GPS coordinates.

Example: The $ -12.345, 67.890 $ coordinates have for antipode $ 12.345, -112.11 $

From 3D Cartesian coordinates, take the opposite of each component (x, y, z) ie (-x, -y, -z)

The Earth is assimilated to a sphere, but in practice a more accurate model would be a spheroid (normal ellipsoid) or a geoid.