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I'm interested in the perspective of large objects, spanning enough distance that the spherical nature of the earth comes into play.

How would one do the proper constructions to accurately draw this curvature? See this curve for example. How would one actually accurately represent the red line in a composition? enter image description here

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  • Skyler, I think you may have positioned your horizon line in the wrong spot. Shouldn't the horizon line fall where the sky meets the water? Try following you perspectival lines back to the vanishing point with the horizon drawn where the sky meets the water. – John Vukelic Jul 16 '17 at 22:49
  • That's the question I had. That would certainly be the case if the earth were planar. – Skyler Jul 17 '17 at 0:47
  • Admittedly I think the vanishing point should be somewhat lower in this pic, but not exactly at the horizon – Skyler Jul 17 '17 at 0:49
  • The lines of perspective should all curve, using the same points for all the buildings, rather than merely the first two. Often the vanishing point will end up "out of sight" as a result of the curvature of the sphere in the image.Whenever the upper two curves becomes lower than the lower curve, that part of the image is blocked by the horizon, even though the vanishing point has not been reached. – user2268 Jul 17 '17 at 1:59
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    @GypsySpellweaver Can you expand that into a full answer? – Erica Jul 17 '17 at 11:49
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The vanishing point, provided the parallel lines are on the ground plane, is on the horizon and it will always be eye-level . The horizon can be looked at as the sum of all of the vanishing points. For someone standing at 5'7" the horizon is 2.9 miles away from the viewer.

I think it is possible the curve you see above is because the ground is not flat (relative to the curve of the earth,) ie. there is a slight hill there, or the line of the shore is not perfectly straight. The curve of the Earth is so gradual you will not see its effect from the ground. So unless those shacks are over 2000 feet apart the horizon is not 2.9 miles away in this image. Keep in mind the camera lens has a big part in how distorted the perspective becomes. Think of a picture from a fish-eye lens.

However, to get the kind of perspective effect you are talking about, where you are fitting an exaggerated perspective onto the drawing plane, you would use curved lines. This is called Spherical or Curvilinear Perspective. M.C. Escher is a great artist to study to see this technique in action. The fish-eye lens distortion previously mentioned is a perfect example of spherical perspective.

The wikipedia entry for Curvilinear Perspective is a bit dry. But here is a nice artistic perspective on it, pun intended.

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