"alphaQuad" <alp### [at] earthlinknet> wrote:

> Ideas well explained, should be enough. I think I need more (being slow) or need
> to read that 4 more times. Starting to find something to read now. I really
> think pov needs a gdm.inc include file. (and will once I understand this)

Here is an image showing, on the left, a line arrangment, on the right, its
generalized-dual zonogonal tiling. Here, n=9. Since there no more than two
lines ever intersect in one point, the only zonogons are rhombs.

Notice that in the line arrangement, there is a central hollow area bounded by
nine segments. In the tiling, there is a central vertex, where nine edges meet.

The right-most point of intersection in the line arrangement corresponds to the
right-most rhomb in the tiling.

There are thirty-six points of intersection in the arrangement, and thirty-six
rhombs in the tiling.

There are eighteen unbounded regions between lines around the arrangement; and
eighteen vertices are on the boundary of the tiling.

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