2.3.2.1 Creating a Formex using coordinates

The first and most useful way to create a Formex is by specifying it's nodes and elements in a 3D-list.

	F=Formex([[[0,0],[1,0],[1,1],[0,1]]])

Figure 2.3: A very simple Formex
 
square.png

This creates a Formex F, which has the nodes (0,0), (1,0), (1,1) and (0,1). These nodes are all part of a single element, thus creating a square plane. This element is also the entire Formex. On the other hand, if you would change the position of the square brackets like in the following example, then you'd create a Formex F which is different from the previous. The nodes are the same, but the connection is different. The nodes (0,0) and (1,0) are linked together by an element, and so are the nodes (1,1) and (0,1). The Formex is now a set of 2 parallel bars, instead of a single square plane.

	F=Formex([[[0,0],[1,0]],[[1,1],[0,1]]])

Figure 2.4: Same nodes, different Formex
 
parallel.png

If we want to define a Formex, similar to the square plane, but consisting of the 4 edges instead of the actual plane, we have to define four elements and combine them in a Formex. This is not the same Formex as fig 2.3, although it looks exactly the same.

	F=Formex([[[0,0],[0,1]], [[0,1],[1,1]], [[1,1],[1,0]], [[1,0],[0,0]]])

The previous examples were limited to a 2-D environment for simplicity's sake. Of course, we could add a third dimension. For instance, it's no problem defining a pyramid consisting of 8 elements ('bars').

	F=Formex([[[0,0,0],[0,1,0]], [[0,1,0],[1,1,0]], [[1,1,0],[1,0,0]], [[1,0,0], 
		[0,0,0]], [[0,0,0],[0,1,0]], [[0,0,0],[0.5,0.5,1]], [[1,0,0],[0.5,0.5,1]], 
		[[1,1,0], [0.5,0.5,1]], [[0,1,0],[0.5,0.5,1]]])

Figure 2.5: A pyramid
 
pyramide.png

However, as you can see, even in this very small example the number of nodes, elements and coordinates you have to declare becomes rather large. Defining large Formices using this method would not be practical. This problem is easily overcome by copying, translating, rotating,... a smaller Formex -- as will be explained in 2.3.7 -- or by using patterns.