# A Model of Islamic Rectilinear
Interlaced Lattices

## MODELLING A RIGE

To understand and code a rige implies finding out the following:

- The lattice to which it belongs.
- The particular use of this lattice by this particular Rige, that is, what segments are included in it.
- This use can be simplified when, as usual, a smaller part of the form can be found, which engenders
the rest by simple geometric operations, as symmetries (axial, central) -the GE-, and/or displacements -the
TE-.

Those operations are not always simple to find out, especially in large orders, such as 24, 36, and so on; in these
cases the angles are not easily discriminated (see Lattice Orders,
above).
In any case a segment is defined by the straight line to which it belongs, and by its two extremes, determined
respectively by two other straights. Thus a segment is defined by three straights. A straight in our model is
defined by two elements: the angle of the main direction of the straight, and its distance to the centre. Both
parameters are determined by two integer indexes, that of the angle, between 0 and N-1 (order), and that of the
distance, an integer between 0 (straight passing on the centre) and D, the maximum number of distances which
the form uses which is always limited and finite.

A simpler method for defining segments could be found: the Cartesian coordinates of their extremes. However,
this would not allow either the perception of symmetries, or the use of the inner limitations of the lines position,
which simplifies greatly the selection for human users: they will introduce the straight index of distance
(1,2,3...) and the index of basic angles (1,2,3,..). It is much simpler to see two straight segments in cross, gyrated
30 degrees, than list their end coordinates (see Computer Implementation, in Apendix.2).

The symmetries of the system allow an easy definition, but by limiting the possibilities, as in any form of
art.

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09-June-95