Re: Bendy Light

From: Colin Watson <watson_at_csd.abdn.ac.uk>
Date: Mon, 26 Feb 1996 10:53:51 GMT


Alex Ferguson asked, amongst other things:
> Does "curved" mean in a circular,
> elliptical, parabolic, hyperbolic, or some other sort of arc?

Well, if you want to simulate a horizon similar to earth's (ie. so that the curve of the flat ground appears spherical) then the curve of the light has to be like a Tan graph:

A ray which is horizontal at source on the ground curves upwards gradually at first, then rapidly until it reaches (near) vertical. By the time the ray has travelled a distance equal to the "simulated radius" of the world (ie. in the x direction on the tan graph) the ray will be travelling vertically (ie. it will reach infinity in the y direction on the tan graph).

This has an interesting effect at very long distances. Looking down on the world from an orbital altitude (whatever that means) the flat world would appear spherical! No matter how high you flew, you couldn't see beyond the spherical horizon. From "space" the world would appear to be a globe. That is assuming that the dimensions of the flat world are larger than the simulated diameter (which is probably not the case for Glorantha - it's horizon is IMO as distant as earth's, but it's surface area is smaller; so from high-up it would look like part of a spherical shell).

Even more interesting is the case of light coming down from above. If we assume it follows the same path back; a ray which comes straight down from a star would curve towards the horizontal. Stars directly above you would still appear above you, but stars above a position far from yours would appear to be lower on the horizon. In fact the dome of the sky would not have to be a dome at all - it would be a plane parallel to the ground which just appeared to be a dome because of the curvature of the light!

Is anyone following this?

___
CW.


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