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Flat Earth Perspective

Flat Earth Perspective (Flerspective) is a special kind of mapping of the 3D world onto a 2D plane like the sensor of a camera or the retina of the eye. There are variations of this mapping. They all have in common, that they do not conform with the real law of Perspective and are proposed by Flat Earthers as an attempt to explain observations. The observations show the earth is a Globe if we assume the real law of Perspective.

For an implementation of Flerspective see:

If the Flat Earth model is selected you can choose 2 different "Perspective models" for the Flat Earth, although there exists only one single law of perspective in reality:

  • Normal applies the real law of Perspective on the Flat Earth model to map the 3D model onto the screen. This is the same law of perspective that is applied on the Globe model. You can't change the Perspective model on the Globe model.
  • Flerspective is a special transformation that is unique to this App. It applies a transformation T to the 3D model before the normal law of perspective is applied additionally to map the 3D model onto the screen. It is the perspective model that Flat Earthers proclaim.

The transformation T is such, that all Z-coordinates (vertical direction) of the 3D model are changed to linearly converge to eye level at the vanishing point (VP) distance in all directions. This corresponds to the side view Flat Earthers draw, where all objects and lines converge to a single VP. All lines that pass the vanishing distance are clipped. Objects behind the VP are not drawn.

Note: if the VP is placed infinitely far away, like it is in the real law of Perspective, then the Z-Coordinates would keep their values and the result is real Perspective.

The Flat Earth And The Law Of Perspective

The distance of the VP in the App is calculated such that it is the same as the Globe horizon distance, dependent on the observers altitude, plus the value of the VP Dist slider. This way the VP distance increases automatically with increasing altitude of the observer.

Note, that T only scales the vertical size of objects. The horizontal size remains fixed and only shrinks on the screen with increasing distance of an object due to the normal law of perspective. If the horizontal sizes were also scaled by T, then the gaps bewteen objects would get bigger when they move on parallel tracks into the distance, which can not be observed in reality. So T is not an affine transformation and has nothing to do with the law of perspective used in drawings and computer graphics. It is implemented for educational purposes only.

There are situations, like boats or bridges over water, where Flerspective seems to match observations: objects near eye level in the distance disappear, similar as on the Globe model, where they get hidden buttom first by the horizon. But zooming in on the horizon shows that Flerspective does not match observations. Most observations look very different than what Flerspective produces.

Flat Earthers may object that I did not implement the right kind of Perspective. But no Flat Earther is able to give me a precise mathematical description of Flerspective that could be implemented in code. Even in my version of Flerspective I had to fudge the numbers to match observations as good as possible. This is not necessary on the normal law of Perspective together with the Globe model.

More Informations about Flerspective

[1]
Law of Perspective Fallacies
https://www.theflatearthsociety.org/forum/index.php?topic=15589.0
[2]
The Flat Earth And The Law Of Perspective
http://coconutrevival.com/?p=1983
[3]
Everything is perspective on flat earth
https://www.thedailyplane.com/everything-is-perspective-on-flat-earth/
[4]
Sun setting illusion on the flat earth
https://flatgeocentricearth.wordpress.com/2015/12/02/sun-setting-illusion-on-the-flat-earth/
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