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3.0 Folding

We now need to consider further facilities in the fold operation to give us the full range of instructions needed by a written symbolic language.

3.1 Coincidence of lines

On rare occasions it may be necessary to Indicate a fold by the coincidence of lines rather than points - provided there is no lack of precision.

Thus we may represent a bookfold in half of a square as :


3.3. Fold Box

If we wish to describe folds separately for the sake of clarity, yet indicate they must all be made together to achieve the fold, the instructions are written in a box, thus: -

Suppose we have:-

an inside reverse fold is required. So in OIL , when all the folds are to be shown explicitly, we have:-

ThIs shows the three seperate folds required in the move.1 - L is a closed edge and must be reversed In the fold, see (2.3.). Notice that fold lines have been used here - on occasions this exposes the structure of the fold more clearly.

Compare this with:-

in the normal notation of O.I.L., but see 5.1. move 2 for an example where even in this notation a box is essential.

3.4 Rotation Fold

Occasionally we need to rotate one part of a model while the rest remains stationary and then flatten at the new position This Is indicated in O.I.L. as (for example):-

(S -- K)---> + 45deg. K

This means rotate radius S-- K on axis K through 45deg. clockwise and flatten. Compare this with 1.2. and you will see it's exactly the same idea If, however, we are to rotate to a predefined point, then the instruction will read: -

S---K, X

Rotate point S to point K on axis X and flatten.

In both cases the layers can be Indicated on the fold arrows, but usually this will not be needed.

3.5 Pre-folding

At certain times we may wish to pre-crease - that is fold and open up again. This can be simply shown as:-


where i and j are the two points to be brought into coincidence -paper layers are indicated on the fold arrow as usual.

Where we then wish to use the pre-creases as a guide to locating folds these are indicated on the definition

matrix by using lower case letters.

In this example the lines are pre-creases. Notice where possible we still prefer to use the perimeter numbers.

Thus K= (1--b) = ( 3--2)

3.6 Soft and Angled Folds

Normally A-->B indicates a sharp hard crease in which A coinciding with B means a paper angle change of 180deg.. We may require a soft fold and for an angle less than 180deg.

A---> B, 90deg.

A---> B, soft

3.7 Stretch Folds

These are shown as:-


and means stretch out (or pull out or open up) P to T & then flatten model

3.8 Tuck In

Some models require a point or edge to be tucked in or under layers. This is shown in OIL as:-


The tuck in command is shown by the same locator being used. The top layers are to be tucked under the bottom layers. All layers are counted from the top at the 'A' location.

Where A is an identified location achieved in the previous fold.

t = 1/2 (a---b)

K = 1/2 t---1)

The first two lines define location K. The point 3 is then folded to this point.

The last instruction requires the first two layers at K to be tucked under the third layer. This is a special meaning given when the same location point is shown at the start and finish of the arrow.

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