How it was supposed to look like in the first place: rounded with Bezier curves.
I've used Bezier curves and Hermite splines quite a lot to smooth out progressions of discrete points, such as Hamiltonian circuits. The challenge with this Hilbert curve is that there are tens of thousands of points, so drawing a nice OpenGL shape for each edge gets rather slow. Of course, this isn't a deal breaker for still images, but I like making my code efficient.
I've now constructed the Bezier curves in geometry shaders. I've used those for some time to draw simpler shapes more efficiently, such as line segments with rounded ends; the idea is to do more work on the GPU, while moving as little data as possible there. These line segments only need the endpoint coordinates, as well as thickness and colour. The curves seemed more challenging due to the number of parameters, but in the end there weren't really any issues.
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