To fold (0,101) onto (51,50), the / fold needs to pass through (0,50) rather than (51,0). If I understand this correctly, the sequence is: 1. Start: {(0,0)} 2. Unfold(-) through {(0,50.5)} to obtain: {(0,0), (0,101)} This is a bottom-to-top unfold. 3. Fold(/) through (0,50) to obtain: {(0,0), (51,50)} This is a nw-to-se fold, so (0,0) is unchanged. This is the first described fold. 4. Fold(\) through (51,1) to obtain: {(0,0), (2,1)} This is a ne-to-sw fold, so (0,0) is unchanged. This is the second described fold. This general approach seems to work well when it's possible to isolate a single point on one side of a fold, allowing that one point to be moved without changing any of the others. In general, if you have a cluster of points, you can replicate it at a great distance away by unfolding about a distant crease line. You then need to eliminate those replicated points by folding inward, until only one replicated point is left. I believe this is always possible (see below). Once you're down to a single replicated point, you position it at the desired position near the original cluster. The process can then be repeated until the desired set has been contructed. To reduce a distant replicated cluster of points to a single point, I believe the following will work. Create the replicated cluster vertically above the original by folding upward about a distant horizontal crease line. Then perform a series of \ folds, folding ne-to-sw, until all of the replicated points lie on a single nw-se line. Then perform a series of / folds, folding nw-to-se, until you're down to a single replicated point. Tom Tomas Rokicki writes:
Sure. Let's see, 2,1 is odd so set a point at (0,101). Flip that bad boy up to (51,50) with a / mirror at (51,0), and then flip it to (2,1) with a \ mirror at (51,1).
On Wed, Oct 21, 2020 at 9:08 PM Allan Wechsler <acwacw@gmail.com> wrote:
I'm afraid I'm not following the explanation. Can you illustrate by showing a construction for {(0,0), (2,1)} ?