# The Universe of Discourse

Wed, 17 Jan 2007

Linogram development: 20070117 Update
The array feature is almost complete, perhaps entirely complete. Fully nontrivial tests are passing. For example, here is test polygon002 from the distribution:

        require "polygon";

polygon t1(N=3), t2(N=3);

constraints {
t1.v[0] = (0, 0);
t1.v[1] = (1, 1);
t1.v[2] = (2, 3);
t2.v[i] = t1.v[i-1];
}

This defines two polygons, t1 and t2, each with three sides. The three vertices of t1 are specified explicitly. Triangle t2 is the same, but with the vertices numbered differently: t2.v0 = t1.v2, t2.v1 = t1.v0, and t2.v2 = t1.v1. Each of the triangles also has three edges, defined implicitly by the definition in polygon.lino:

        require "point";
require "line";

define polygon {
param index N;
point v[N];
line e[N];
constraints {
e[i].start = v[i];
e[i].end = v[i+1];
}
}

All together, there are 38 values here: 2 coordinates for each of three vertices of each of the two triangles makes 12; 2 coordinates for each of two endpoints of each of three edges of each of the two triangles is another 24, and the two N values themselves makes a total of 12 + 24 + 2 = 38.

All of the equations are rather trivial. All the difficulty is in generating the equations in the first place. The program must recognize that the variable i in the polygon definition is a dummy iterator variable, and that it is associatated with the parameter N in the polygon definition. It must propagate the specification of N to the right place, and then iterate the equations appropriately, producing something like:

e0.end = v0+1
e1.end = v1+1
e2.end = v2+1
Then it must fold the constants in the subscripts and apply the appropriate overflow semantics—in this case, 2+1=0.

Open figures still don't work properly. I don't think this will take too long to fix.

The code is very messy. For example, all the Type classes are in a file whose name is not Type.pm but Chunk.pm. I plan to have a round of cleanup and consolidation after the 2.0 release, which I hope will be soon.