The Universe of Discourse

Sat, 20 Jan 2007

Another Linogram success story
I've been saying for a while that a well-designed system surprises even the designer with its power and expressiveness. Every time linogram surprises me, I feel a flush of satisfaction because this is evidence that I designed it well. I'm beginning to think that linogram may be the best single piece of design I've ever done.

Here was today's surprise. For a long time, my demo diagram has been a rough rendering of one of the figures from Higher-Order Perl:

(It's big, so this is a reduced version; click to expand it.)

I wanted component k in the middle of the diagram to be a curved line, but since I didn't have curved lines yet, I used two straight lines instead, as shown below:

As of today, I have working curves, so I went to replace k with a curved line instead. I went into the demo.lino file, which I wrote a couple of years ago, to see what changes would be required. The definition of k was much more complicated than I remembered. Here is the relevant extract:

        define bentline {
          line upper, lower;
          param number depth = 0.2;
          point start, end, center;
          constraints {
            center = upper.end = lower.start;
            start = upper.start;  end = lower.end;
            start.x = end.x = center.x + depth;
            center.y = (start.y + end.y)/2;


        bentline k;
        label klbl(text="k") = - (0.1, 0);
        constraints {
          k.start = plus.sw; k.end = times.nw;
So I had defined a thing called a bentline, which is a line with a slight angle in it. Or more precisely, it's two approximately-vertical lines joined end-to-end. It has three important reference points: start, which is the top point, end, the bottom point, which is directly under the top point, and center, halfway in between, but displaced leftward by depth.

I now needed to replace this with a curved line. This meant removing all the references to start, end, upper and so forth, since curves don't have any of those things. A significant rewrite, in other words.

But then I had a happy thought. I added the following definition to the file:

        require "curve";
        define bentline_curved extends bentline {
          curve c(N=3);
          constraints {
            c.control[0] = start;
            c.control[1] = center;
            c.control[2] = end;
          draw { c; }

A bentline_curved is now the same as a bentline, but with an extra curved line, called c, which has three control points, defined to be identical with start, center, and end. These three points inherit all the same constraints as before, and so are constrained in the same way and positioned in the same way. But instead of drawing the two lines, the bentline_curved draws only the curve.

I then replaced:

        bentline k;
        bentline_curved k;
and recompiled the diagram. The result is below:

This diagram is identical, except that arc k has changed from a bent line to a curve. Compare:

To make this change, I didn't have to edit or understand the definition of bentline, except to understand a bit about its interface: begin, end, and center. I could build a new definition atop it that allowed the rest of the program to use it in exactly the same way, although it was drawn in a completely different way.

I didn't foresee this when I designed the linogram language. Sometimes when you try a new kind of program for the first time, you keep getting unpleasant surprises. You find things you realize you didn't think through, or that have unexpected consequences, or features that turn out not to be as powerful as you need, or that mesh badly with other features. Then you have to go back and revisit your design, fix problems, try to patch up mismatches, and so forth. In contrast, the appearance of the sort of pleasant surprise like the one in this article is exactly the opposite sort of situation, and makes me really happy.

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