22.5° Refs Engine

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The engine makes use of binary fractions to solve the crease pattern. This sets the maximum denominator of these fractions.

Since it is difficult in practice to fold reference lines particularly close to the edge, this setting allows you to exclude references within a certain distance of the edge.

This setting restricts the available reference lines to those having at least one vertex laying either on the edges of the square or the easy-to-fold 22.5° aux lines. These vertices are shown in blue on the crease pattern.

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Upload a 22.5° crease pattern as a .fold or .cp file. The crease pattern will be rendered on the left side of the screen. The engine will analyze all the vertices within the crease pattern and sort them approximately (the ranking system needs some work) by difficulty. The first-ranked reference will be highlighted in green on the crease pattern, and the steps to develop it will be displayed on the right side of the screen.

To move through the list of references in order of difficulty, use the left + and - buttons at the bottom of the screen. Alternatively, select directly on the crease pattern which line you would like to solve. Cycle through the various solutions to each ref using the right + and - buttons.

The right side of the header has a field for input of custom a, b, c values. The values correspond to a pair of sums, having the form (a+b√2)/c. In the image to the right, (a_x+b_x√2)/c_x is shown in red, and (a_y+b_y√2)/c_y in green. The larger value is scaled to the side-length of the square, making the reference to be found the ratio of the smaller value to the larger.

Unless the desired reference is simply a binary fraction of the edge length, the first step will involve folding a few 22.5° lines as foundation for the following steps. Those creases not laying at 22.5° degrees (the "Kamiya reference") are constructed by making a crease through a pair of existing points. In certain cases there are creases which appear to follow neither of these conventions - they lay perpendicular to an existing line.

In the following steps, black dots indicate important landmarks used to construct creases. Binary fractions are also used. The fraction itself is printed, the line along which the fraction is taken is highlighted. The crease emanating from the fraction lays perpendicular to the highlighted line.

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