1.0 Point Identification
It is vital to be able to identify exactly any point either in the flat plane of the model itself or outside it. This could, of course, be done by assuming a standardised grid of lines which is superimposed over the model (or using Cartesian co-ordinates) as suggested by Mr. Palacios). There are considerable difficulties in such an approach, however. It is complex to define the 0, 0 point of the grid relative to the model, many distances necessarily involve ~ dimensions which cannot be exactly specified as a measurement except in a limiting case, it is difficult to identify the points of a model on a grid and much of our folding In any case naturally uses the existing edges and folds already present. I came to the conclusion, therefore, that it was simpler to let the model be its own "grid" and to define points by using the system of lines and points which already exist at that stage of the model. Let us now look at Some more powerful ways of Identifying points.1.1 Identification by Coincidence
Here is a simple example: The point K is defined as the coincidence or intersection of two lines (1--4) & (3--B) In O.I.L. this appears as:-
1.2 Identification by angular rotation
In many models we find it necessary to reverse fold a point or extension to suggest a head or foot etc. Such a fold is difficult to locate using the method so far defined but we can solve the problem completely by identifying a point which is to be the axis and then giving the degrees of rotation to define the new point. In its general form we shall be writing: -
T = (r-K ) ± q K
where T is the new point we are defining,q is the angle in degrees, + is clockwise, - anticlockwise,
K is the axis point
(r-K) is the line or radius to be rotated on K for q degrees.
Here we have a typical triangular projection. We require to identify point Q and this is given by the line (1-P) rotating on P so that at 45deg. anticlockwise, 1 will reach Q and thus identify it. In O.I.L. this reads:-
1.3.This example has introduced three other concepts of point identification which now must be spelt out.
1.3.1 Hierarchical definitionTo identify a point it may be necessary to define one or more previous points, but in the end all identification is achieved by a reference to points identifiable on the boundary or fold lines of the model itself. In other words, all point identification can be achieved by a hierachial structure. In our previous example we defined P in terms of points 1 & 2, and then Q in terms of P. 1.3.2. External points
Notice how in our previous example Q is defined as outside the boundary of the model and clearly any adequate notation system must be able to achieve this.
1.3.3 CombinationsI believe that it will be evident that we can define points by combinations of the methods indicated.
Here is a rather artificial example:
We require K to be halfway along 1 - 2 ; P is to be above K by 2/3 of the distance from K - 3 and lastly Q is 45deg. rotation of P -K , radius on K.
In O.I.L. this reads
We can also define or locate points by the coincidence of lines whether rotated or interpolated.
In general we will seek from the many ways open to us of identifying a point for that which is the most simple and compact and which naturally follows the sequence of folding.