Fractal square-square subdivision

Fractal square-square subdivision

Post by Daniel Galat » Tue, 05 May 1992 05:42:25



This is a specific question about a specific technique used to generate fractal
terrains.  Square-square subdivision was introduced by Gavin Miller in
"The Definition and Rendering of Terrain Maps" (ACM SIGGRAPH, 20:4, 1986, pp.
39-48).

In this method, the plane is divided into 4 squares (p. 40 in Miller):

. ___ . ___ .
|     |     |
|     |     |
. ___ . ___ .
|     |     |
|     |     |
. ___ . ___ .

Then the heights of four points in each of these squares are set by weighted
averaging and random displacement:

. ___ . ___ .
| . . | . . |
| . . | . . |
. ___ . ___ .
| . . | . . |
| . . | . . |
. ___ . ___ .

This forms an inner lattice of 9 squares.  Again, four points are displaced in
each of these squares, and so on.

My question is, how are the heights determined for the vast majority of points
in the plane that aren't affected by the above scheme, that lie between the
lattice points in each iteration?  It is somewhat unclear in Miller's paper.

If anyone is familiar with this technique, please reply by e-mail, since I
don't normally read these groups.

Thanks in advance!!

-- Dan
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Dan Galatin        | "If all the girls attending [the Yale prom] were laid end

     _______       |     - Dorothy Parker