Origami is visual. This requires a visual system be used to represent the steps involved in forming a model. There is an international diagramming system, which was first put forward by a Japanese, Akira Yoshizawa. In the west the system was pioneered by Samuel Randlett (US) and Robert Harbin (UK). All good origami books use this system. This site is not intended to teach the system, please refer to one of the readily available books.
Origami diagramming is like computer programming. All the steps must be there and they must be followed in one particular order to achieve the final desired result. [Note that other sequences equally good or even superior may exist, but only one sequence at a time can in reality be diagrammed or programmed]. The steps can be concise and elegant or long-winded and clumsy. The opportunity for errors is legion. The user is free to produce good or bad output, following the instructions. The same effort is required independent of the quality of the model.
The single most compelling argument is this : In order to pass on a folding sequence you can fold along with the recipients. This method has several limitations. You've only got one busy lifetime, so only small numbers of geographically local recipients can be taught. Your friends are (presumably) human, so they suffer from human failings - bad memory, inability to reproduce the instructions, divergence from the original sequence, etc... The answer to all this is : draw diagrams and give copies to all and sundry. It's a much less personally time consuming method. The information is consistent. It does not rely on the human memory.
I started out with pens and paper. The paper was usually from an A4 pad of architect's paper which is semi-opaque. Flat (2D) models can be placed under the paper and traced over lightly using a pencil, then inked in later. The pens I use are 0.1 mm for crease lines, 0.3 mm for fold and outline lines and 0.5 mm for enlarged views. I use dot shading a lot. This gives the best depth illusions. I usually photocopy, physically separate each step and shuffle them around until the best layout is apparent. Individual step drawings can be scaled using a photocopier, but this can be time consuming. I then glue the steps into final position. I add text from computer generated printouts.
Drawing 3D work is difficult. I'm not a trained illustrator. I struggle. It gets easier with practise. My fall back is to photograph a model against a contrasting background and trace over. Expensive and time consuming, but it gets the job done.
Within the last few years I've crossed the line and now draw using a computer. I started with the drawing package that is part of Lotus AmiPro (yes, right - the word processor). This works fine. It's got most of the tools needed. The only disadvantages are : fold indication lines have to be built up (no sissy propriety dot-dot or dash-dot lines available). It takes a little longer, but you can get there. The output can only be in WMF or BMP format. The quality of the output files is poor. It will also export as Word files, which are reasonable quality but only one page at a time. The Lotus fills are tricky. Do a test piece using all the lines and fills available and print it on your destination printer. If you change printers then print it all again on the new machine. Versions 3.0, 3.1 for Win 3.11 and '96 for Win 95 are all pretty much the same. The dot fill spacing is limited.
The drawing package in Microsoft Word can be used, but the irregular shape tool is a huge disappointment that costs eons of time re-trying until results are right.
I tried CorelDraw! (we don't see eye to eye!!). Earlier versions 3 & 4 which I used take too much hard disk space and require too much brain patterning on my behalf to learn. It's also a bit like using a sledgehammer to crack a nut.
I have now discovered Macromedia [formerly Aldus] Freehand. This program has more than AmiPro and outputs in high quality TIF format. What is even better, it will import (only via the clipboard mind you) all my old AmiPro drawings. I'm using version 5, a cover disk freebie, which runs under both Win 3.11 & Win 95.
I've briefly tried Adobe Illustrator. It is excellent. It contains far more than required for black and white drawings. The controls are similar to those in Freehand.
For example of AmiPro see Double Crane Wreath in the models section
For example of Freehand see Pine cone in the models section
I find the computer does have a few advantages. Layouts can be tried out on screen until the best is found, though print outs are strongly advised when doing comparisons. Step drawings can be scaled up or down to fit more exactly. Drawing can be quicker, since most following steps can be founded on a pasted and subsequently amended copy of the previous step. Text can be added directly at time of drawing. A stock of commonly used starting points (bases etc..) can be kept to seed into a new drawing. Finished drawings are instantly (well, almost) available. Drawing files can be sent over the Internet. Fills and font can be amended to suit the recipient (hopefully a publisher!).
The only disadvantage with computer diagrams is that they can be too perfect. Absolutely straight lines can be tiring to look at and the overall result appear artificial. The style, more often than not, is the software programmer's rather than the diagrammer's. I now believe this argument is over-rated and can be overcome by more work in preparing the diagrams.
In common with those that first start to diagram, I made mistakes. Initial efforts usually conveyed little of the 3D appearance of steps. For instance; The preliminary base is more than a small square - it has layers, some of which have open (raw) edges and some have closed (folded) edges. It also has colour on one side of the paper and white on the other. All this information must come across in the drawing. When I look back at my early drawings I see lots of mistakes that I would never reproduce now.
It is now possible to use a digital camera to picture each step of a folding sequence. This can take out the bulk of the drawing content, but it can never completely replace it. The equivalent of X-ray drawings are impossible using a camera, for instance. There still remains the addition of fold lines, directional arrows and explanatory text. It is a tedious job putting in the final touches. Final drawings can, however, be replaced relatively easily.
If you want to learn how to diagram then look (I mean really LOOK) at existing diagrams. Crib the best styles, nobody will know except yourself. I recommend Vicente Palacios's drawings (hand-drawn) as a model of clarity with the maximum of information per step. Francis Ow's drawings (hand-drawn) are good too, particularly with respect to dot shading. I recommend Robert Lang's and John Montroll's drawings (computer-drawn) as good examples in this genre. There are other fine diagrams about, but don't confine yourself to one particular favourite.
Diagrams are controlled distortions of reality. Their purpose is to clearly explain. If they fail to explain, then they are bad, no matter how well drawn or by whichever method they were produced. The moral of this is that proof-reading is a must, preferably by at least two independent persons.