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2.0 Definition matrix

In our work so far only the most compact and simplified definition matrix has been used. On occasions it may be necessary to extend this

2.1 Diagonals

It has already been made clear in the previous article that the rows and columns are coincidental with lines at 90deg. to each other, i.e. the horizontal and vertical points of the model. If two points are in the same row on the matrix then they are on the same horizontal line on the model. The rows and columns are at right angles to each other.

It may be desirable to indicate where 3 or more points be on the same line which is other than vertical or horizontal and this has been called Diagonals

The general form is ; D (i - j - k - 1 - ...) ( p - q - r - ) etc, written immediately after the definition matrix where D indicates diagonals and i,j ,k... & p,q,r... are points identified in the matrix, thus ( i - j - k...) are on one "diagonal" line and (p - q - r ....) on another. An example will demonstrate the technique fully :

 

Thus the complete topology of the model in the plan view is now defined.

2.2 Layers

O.I.L. lays stress on the precise identification of the layers which are to be Involved in a fold - only in this way can we make absolutely clear how a fold Is to be made. Usually it is adequate to define the layers Involved in the actual folding but is some cases it may be desirable to add the layer count to the definition matrix.

Above is an example of the method - thus at A we have 4 layers of paper while at 1 we have only 1, shown by A(4) and 1(1).

2

A more complex shape - notice it is the maximum layers at a point that are counted, thus B has 3.

Closed and open boundaries

Most complex folding occurs because one or more of the boundary edges involved in the fold are closed. Where all edges involved in a fold are open (or where two or more layers are treated as one), then only valley and mountain folds are involved.

Compare diagram X with Y.

Diagram X

In X, the top boundary 1-2 is closed - layers 1 & 2 are joined along this edge = closed.

Diagram Y

In Y, the boundary has been cut to K, thus we now have two edges , closed to K and open to 2, instead of one closed edge.

2.4 Location of the model relative to the definition matrix

The position shown in each definition matrix is exactly that arrived at as a result of the previous folds(s). If we wish to turn the model over or rotate it, we must Indicate this by redefining the matrix.

after a definition matrix means turn the whole model over -there must now be a new definition matrix.

D 90deg.

means rotate the whole model through 90deg. ( a clockwise right angle ) or whatever angle is desired. Once again there must be a new definition matrix

The two moves can be combined thus :

D180 deg.

i.e. rotate through 180deg. clockwise, then turn over.
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