Fast iterative circles (and ellipses, and other figures).

Fast iterative circles (and ellipses, and other figures).

Here’s the entire algorithm to compute points on an elliptical arc, very quickly:

    while(true)
    {
        x += d * y;
        y -= d * x;
    }

Attributed to Marvin Minsky, 1972: HAKMEM, MIT AI Memo 239 (HTML version here). Also on a PDP-1, David Mapes talks about finding it independently. I’ve been using this to make circles since I found it by accident in the early 1980s (using a BBC Micro). Nowadays I’m using it to make music synthesizers (running on ARM Cortex M4).

Source: https://cabezal.com/misc/minsky-circles.html