Origami Circle Packing
We show that deciding whether a given set of circles can be packed into a rectangle an equilateral triangle or a unit square are np hard problems settling the complexity of these natural packing problems.
Origami circle packing. You can extend circle packing to using any shape hexagons 22 5 degree based structures etc. Lang s theories of circle packing and molecules in origami are what got me and many other complex folders started in designing what would become some of the most complex origami in the world of course the technical proficiency that goes into folding a piece does not in itself make it art. I hope that my explanations make sense it is hard to explain without pictures and lang does a much better job than me.
Several examples of such problems and. Circle packing for origami design is hard. On the positive side we show that any set of circles of total area 1 can be packed into a square of size 4 sqrt pi 2 2567.
Thus several problems in origami design can be reduced to finding an optimum packing of some number of circles of specified radii within a square or other convex polygon. Circle packing in a square. This video shows how to make origami using circle packing and box pleating concepts ex.
Lang has used the mathematics of circle packing to develop computer programs that aid in the design of complex origami figures. If you only use squares all of the creases can easily be filled in with 45 and 90 degree angle folds. Packing of circles one for each leaf node whose radius is given by the length of the edge incident to the corresponding node.
Circle packing has become an essential tool in origami design as each appendage on an origami figure requires a circle of paper. Box pleating allows you to do things easily that are very hard to do with straight circle packing.
