Tuesday, August 28, 2018

[qxgtgvli] X-ray Earth

A typical signpost points toward a destination along the surface of the earth, typically along the great circle shortest surface path or along a surface road.  Consider tilting it downward, pointing along the straight line through the earth to the destination.  Practically, this is useless unless you are aiming neutrinos, so it is art.  Straight line to destination seems more real than a great circle route passing over the horizon.  It is more 3D, reminding you the earth is round.

The limit of an infinite number of signposts all originating from a single point could be modeled as bowl-shaped hemisphere.  Reflect the bowl through a horizontal plane and get a projection of the earth's surface onto dome-shaped hemisphere, perhaps a bit easier to physically interact with than a bowl.  One has to imagine that the destination is along the ray starting from its corresponding point on the dome through the center of the dome.  Instead of projecting onto a dome or bowl, one can project onto a horizontal plane, yielding a standard far-side perspective azimuthal map projection (but nearly a gnomonic projection).  However, unlike a paper map, this map is bolted to the ground and the center of projection below the map is marked as part of the sculpture.

We can also imagine a smartphone app that does this, utilizing its orientation sensors and displaying on screen a map of the far side of the earth in the direction the phone is pointing.  If the phone isn't pointing downward, maybe display a star map.

Beyond just pointing in the correct direction, one can also make the signpost sign's length proportional to the distance (still through the earth) to the destination.  Repeating for every point on earth yields (I think) a globe with your current physical location at the top and aligned with the north-south meridian.

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