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Perspective on a Globe

Saturday, December 30, 2017 - 20:47 | Author: wabis | Topics: FlatEarth, Knowlegde, Geometry, Interactive
To comprehend how curvature on a globe is expected to look like, we have to comprehend how perspective distortions look on a Globe. In this article you can play with an App showing a grid of a Globe Model to see how it is distorted by perspective especially when viewing from low altitudes.

 Globe Perspective App

Real Images of Curvature

The earth is huge. If you are standing on low altitudes and look out over water it looks flat. But if you know how perspective works you can see curvature with the help of a zoom camera or telescope. The trick is to look along a very long straight object like the Causeway bridge at Lake Pontchartrain and zoom all the way in on the horizon. The resulting image from a Globe Simulation App and from a picture taken by Soundly through a telescope are shown below.

Note that the bridge is everywhere the same elevation over water, except at the ship passages. So the bridge follows the curvature of the earth perfectly.

This curvature over the horizon may look fake to you, because you may not be familiar with this kind of perspevtive. The reason why we see such a curvature here is because zoom compresses distances along the viewing direction and streches distances along the horizon. The huts are about 1.13 miles apart, but seem to be only a few meters apart. On the other hand some people may expect to see a similar curved horizon from left to right. But because of the magnification by the zoom lense you can only see less than a mile of the horizon, so you must not expect to see curvature from side to side.

Note that the approximation of Drop = Distance2 × 8", where the Distance is measured in miles and the Drop in inches, is not violated. The huts are about 1.13 miles apart, so the drop from hut to hut is about 10" = 25 cm, which matches what we see on the images. Because of the increasing compression in viewing direction with increasing distance, the horizontal distance between the huts decreases, which makes the arc of the bridge more and more pronounced at the horizon. This is due to Perspective on a Globe.

We have to keep in mind that we only see a small part of the earth from low altitudes. At 10 m altitude the horizon is a circle with center at the observer and a radius of only 7 miles = 11.3 km. That is nothing compared with the radius of the earth. Even at 10 km altitude we can only see 357 km of the earth and the horizon looks almost perfectly flat, because the horizon line is a circle around us as seen from a vertical position above its center.

Globe Perspective App

The App shows 2 views of the Globe:

  • Overview: The small sphere on the top right displays the Globe from above the camera. The small square represents the camera, looking in the direction of the top of the page. The blue cicle shows the horizon line as seen from the camera at the choosen altitude. The green rectangle/line shows the range that is dispayed on the Perspective View.
  • Perspective View: The Perspective View below the small sphere shows the view as seen from the cameras perspective. The camera is always pointing at the horizon. Note: the thin grid lines lay always behind the horizon.

Observations

From high altitudes the globe grid lines are almost perfect ellipses as we expect from everyday experience. But as we get closer and closer to the surface of the Globe, this ellipses get distorted more and more by perspective. In the visible part inside the horizon, the grid circles in viewing direction look straighter and straighter while the curve over the horizon gets more and more pronounced (Figure 1). This matches exactly what we see on the images above.

(Click: Zoom)
ZoomFigure 1
(Click: Zoom)
ZoomFigure 2

The curvature of the horizon as displayed in images is subject to the perspective distortion and is not part of a circle or an ellipse but rather part of a distorted circle. The horizon line appears stronger curved than the curvature of the earth as traced by a great circle (red horizontal line in Figure 2).

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