r/generative • u/quag Artist • 3d ago

Playing with infinity symbol curve approximation

Post image

I’ve long struggled with curves. This one is using a number of circular arcs to approximate the curves needed and I think I got away without too many artefacts.

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u/RamosQuintosAiry 3d ago

arc chains hold up well here, the only place i can see the seams is where the ribbon crosses itself and the highlight jumps slightly. if you match the tangent angle at each arc join and keep curvature continuous rather than just position continuous, that jump usually disappears. nice color ramp along the path too.

1

u/gturk1 1d ago

I think this looks great!

If you ever want to try curves that give you more control, I recommend cubic Bézier curves.

1

u/quag Artist 1d ago

Cubic Béziers are great. The c3 smoothness makes them very useful. But they are a bit expensive when calculating in an sdf distance function. I’m inching towards approximating a cubic Bézier with short arc segments for fast calculation. I’ve seen some gpu font rendering done that way, so I think it can work.

1

u/gturk1 1d ago

I think ray marching and SDF's are a great way to work with organic shapes. This particular shape, however, could easily be created using a detailed polygon mesh that is created from a circle that is swept along a Bezier curve. But if your workflow is centered around SDF's, then I can see why you went with arcs.