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Preface to second edition

It is over 25 years since I first evolved OIL. At that time all diagrams had to be drawn by hand. OIL was designed to be written or typed (this was before the days of PC word processing). The situation now is very different, computers make it much easier to prepare complex diagrams than previously. However the extensive use of E- mail, in which only ASCI symbols can be sent suggests that there may still be a place for OIL. Certainly there has been much interest from those who are looking for new ways of providing folding instructions or analysing folding sequences .

I have, therefore, made a few amendments to the original OIL. The angle of a corner is now shown as <X if the angle is less than 90 degrees and >X if it is greater. I have adopted the double ended arrow to show a fold which is to made and then opened up again. A new instruction is included to show a 'tuck in' command. On occasions it is useful to locate a point or line terms of an existing crease line and the lower case letters have been used for this.

OIL is most suitable for relatively simple sequentially flat-folded models. It can handle complex folds since all origami is formed from connected or overlapped polygons. However the definition matrices become rather cumbersome to handle.

Preface to the first edition.

Our existing methods of writing down instructions for origami models have both advantages and disadvantages. Amongst the advantages is that one can quickly check one's progress against a picture of each stage and identify a surface fold easily. The disadvantages are that it requires considerable skill to prepare good drawings and they are expensive to reproduce. Further the present instructional system is not really precise enough about the layers to be manipulated in a fold or the exact location required for a fold. There is, therefore a case for considering whether a written language can be developed which does not depend upon the expertise of a draughtsman and which is precise. As a by-product such a language will of necessity enable us to study more closely the structure of folds and aid in classifying and identifying fold sequences and complexities.

I presented an origami draft of such a language in my paper "The Nature of Paper Folding" (Library reference J509,1971). Since then I have been developing the ideas and they are now at the point that I believe It useful to publish the present state of the language and to see how members feel about it I must thank Simon Williams for his most valuable proposal which enabled me to simplify some of the typical problems of representing reverse folds.

The language has two parts which occur in each step.

(I) Definition matrix - a formal statement in rows and columns uniquely identifying the points on the boundary or elsewhere of the model so far and defining any new locations needed for the next fold/s. To a certain extent the matrix can be used to check the accuracy of what has been folded so far.

(11) Fold Instructions - Usually these consist of identifying the two points which are to be brought into coincidence by a fold (or folds). On occasions two lines may be specified or a mixture of points and lines. It is always assumed that the smallest number of creases will be made to flatten the model with the coincidence as specified (e.g. one fold only if all layers are involved). If necessary the line along which a fold is to be made can be specified

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