Author: Laurence D. Finston
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Last updated: October 25, 2007
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| Cutting Out Figures |
Origami books generally provide instructions for cutting squares out of rectangles, equilateral triangles out of squares, strips of equilateral triangles out of rectangles, etc. The lines for cutting are found by folding. The figures are then cut out of the original sheet using scissors.
While the methods for finding the lines by folding are interesting in their own right, I recommend not using them, except where precision is not essential. In the case of polyhedron models built up of multiple origami figures, however, precision is essential if best results are to be achieved.
1. I recommend never using a scissors where a straight edge and a cutting knife can be used. Only sharp, pointed blades should be used. Paper and especially cardboard dulls blades quickly, so they should be sharpened (if possible) or replaced in time. Sharpening is preferable, but I'm not yet sure whether it's possible to sharpen disposable blades. Dull blades can be used for some other purpose where sharpness isn't essential, e.g., for sculpting in clay or wax or scraping. It seems a shame to just throw them out, which is why I have a jar full of them.
2. From the point of view of a draftsman (or a woodworker), it is unacceptable to divide two figures by cutting along a common edge. It is nearly impossible to draw or cut exactly down the center of a pre-drawn line, so that straight-edges are always laid either along the outside or the inside of the line. Even with a cutting knife with a razor-sharp blade, the cut has a noticeable width. In the unlikely event that one is able cut along the middle of a drawn line or a fold with reasonable accuracy, material will nevertheless be removed from each figure beside the edge. Even worse, any imprecision will result in more material being removed from one figure than the other. It is therefore far better to draw the lines for each figure in such a way that there is a sufficient gap between them. In this case, the figures should always be cut along the outside of the line.
3. I recommend drawing the lines rather than folding them for the sake of greater accuracy. Of course, they should be drawn using drafting tools: compasses, rulers, triangles, etc. The methods of folding lines depend on using previously folded lines and points found as intersections of folds as references for subsequently folded lines. In theory, this should work, but in practice, any errors (and they will occur) will propagate quickly, causing an unacceptable degree of inaccuracy. I tried using a folding sequence to create equilateral triangles from a large sheet of paper. The ones at the bottom were reasonably accurate, but the ones toward the top were unusable.
4. While one can learn to fold figures more accurately with practice, the method is unsuitable in principle and cannot be improved by any amount of skill or practice. On the other hand, laying out lines on paper using drafting tools is a great deal of work. Once one has done it once, it is usually possible to find an efficient way of laying out the same pattern repeatedly, e.g., by using several compasses set to the required lengths. However, the easiest way is probably to lay out the plans using a computer, print them out, fix them temporarily to the paper to be folded and cut the figures out by cutting through both layers. Internal lines can be scored, where appropriate, or transferred using graphite paper, transfer paper (for textiles — contains wax) or carbon paper (not recommended). In some cases, holes can be punched using a carbide scribe, or a needle may be run through both layers.
Of course, where two or more layers of paper are to be stitched together (a technique I find very useful), poking holes through the paper isn't a problem. However, once one overcomes the natural aversion to damaging the paper in this way, punching holes reveals itself as one of the best ways of marking paper. A hole can be punched with a scribe or a needle more accurately than a dot can be drawn with a pencil or even a technical pen. A compass whose foot lies in a hole won't slip. However, it's generally best to avoid punching holes in the vertices of the resulting polyhedron. Where holes are undesirable, other methods can be used, but these are generally less satisfactory from the point of view of accuracy and ease of use.