Re: Bendy Light

From: Colin Watson (watson@csd.abdn.ac.uk)
Date: Mon 26 Feb 1996 - 12:53:51 EET


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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