How do you make curved folds in origami?

Question

I was Googling about, and saw some images of Dr. David Huffman's models and the work of the Demaines, and was curious how one makes curved freehand folds with any precision.

So much of origami is taught as straight-line, corner-to-corner, or edge-to-edge straight folding. How do you make smooth, curved folds along predetermined lines?

Answer 1

Apart from just carefully folding along the curve with your fingers, following techniques get used:

• Embossing the line with a pointed object or (better) a used-up ballpoint pen. Folding along such an embossed line results in a relatively smooth fold even if the curve is complex.
• For some models (mostly the organic-looking ones), wet folding can allow very smooth lines to be folded. This is sometimes combined with scoring the paper using your fingernails. Daniel Chang uses such a technique for folding his realistic human faces.
• Robert J. Lang famously uses a laser tool to score the crease pattern into the paper. I was able to fold from such paper in one of his workshops and the scored line looks a row of tiny perforations which weaken the paper and guide your hand when you fold along the line.
• Some folders (e.g. Ekaterina Lukasheva) use digital plotter-like tools for embossing the paper.

Machine-embossed lines (the latter two examples) are of course much more precise than those made by hand, but even a line manually scored using a ball point pen can be surprisingly precise.

Answer 2

They're really creases, not true "folds" so the secret I've found is to not try and form them on a flat surface the way you would a straight fold but, instead, fold them in mid-air using your fingers (and nails if you have them) to support and shape the creases.

• start a crease in the direction you want (mountain or valley) by bending the paper in the desired direction but do not attempt to fold it flush.
• use your thumb and forefinger above the paper to create a crease with the middle finger in the crease below it to keep the paper from collapsing completely.
• shape the curve as you move along the paper.
• go slow and be patient

If you want to make really detailed shapes, consider etching the creases in first with a tool.

I found it was easier to start in the center of the curve and work outwards in both directions to achieve the curved shape.

Here's a video showing the process... note that, in this case, the creases are pre-etched in since this is a purpose-made piece of paper but you should be able to use the same method without the pre-etching.