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This map shows the antipode of each point on Earth's surface—the points where the blue and yellow overlap are land antipodes; most land has its antipodes in the ocean. This map uses the Lambert azimuthal equal-area projection. The yellow areas are the reflections through Earth's center of land masses of the opposite Western Hemisphere.
The two straight-line distances from any point on the map to the two control points are correct. 2021 Gott, Goldberg and Vanderbei’s Azimuthal Equidistant J. Richard Gott, Dave Goldberg and Robert J. Vanderbei: Gott, Goldberg and Vanderbei’s double-sided disk map was designed to minimize all six types of map distortions.
If the azimuthal equidistant projection map is centered about a point whose antipodal point lies on land and the map is extended to the maximum distance of 20,000 km (12,427 mi) the antipode point smears into a large circle. This is shown in the example of two maps centered about Los Angeles, and Taipei.
Lambert azimuthal equal-area projection of the world. The center is 0° N 0° E. The antipode is 0° N 180° E, near Kiribati in the Pacific Ocean.That point is represented by the entire circular boundary of the map, and the ocean around that point appears along the entire boundary.
The antipode of Point Nemo – the point on the surface of the Earth that is diametrically opposite of it – is located at roughly , in the Aktobe region of western Kazakhstan, roughly 50 km (30 miles) SSE of the town of Shubarkuduk
The centre of the water hemisphere is the antipode of the centre of the land hemisphere, and is therefore located at (near New Zealand's Bounty Islands in the Pacific Ocean An alternative assignment determines the centre of the land hemisphere to be at 47°24′42″N 2°37′15″W / 47.411667°N 2.620833°W / 47.411667; -2.620833 ...
If is the origin then the earth section is the great ellipse. (The origin would be co-linear with 2 antipodal points so a different point must be used in that case). Since there are infinitely many choices for , the above problem is really a class of problems (one for each plane).
The antipodal map preserves orientation (is homotopic to the identity map) [2] when is odd, and reverses it when is even. Its degree is ( − 1 ) n + 1 . {\displaystyle (-1)^{n+1}.} If antipodal points are identified (considered equivalent), the sphere becomes a model of real projective space .