I’ve made some great strides since my last update a day and a half ago. It turns out that having someone around to re-frame your problem can make the solutions to problems more readily apparent. I suspect this is how psychiatrists stay in business, I’m just glad it carries over into the world of mathematics
Rather than going through conforming Delaunay triangulations or by attempting to cut up triangles and create keystones, I’ve gotten another way to do it. Given a center-line, quads can be created by thinking of the left and right sides as ‘tracing’ along the path of the center, but offset by some distance on either side. In the case of turns, subtle and sharp angles can be handled in the same way. By getting the azimuth between the prior point and the next point (we can think of them as i-1 and i+1), a constant distance from i can be maintained by simply getting the positive and negative perpendicular vectors with respect to the azimuth from i-1 to i+1. It turned out to be a pretty good solution as you can see in the video below.