Over at Fractal Forums, DarkBeam came up with a Distance Estimator for a trefoil knot in this thread. Here are a few samples, created using the new ‘soft’ raytracer, I’m working on in Fragmentarium:
These kinds of knots are easy to describe by a parametrized curve, but making a distance estimator for them is impressive – I wouldn’t have guessed it was possible at all.
It is also possible to create several variations:
In the same thread, Knighty came up with an impressive figure-8 knot distance estimator:
In another thread at Fractal Forums, Knighty also published an interesting technique (“Fold and Cuts”) for creating a large variety of distance estimated polyhedra:
(If you wonder about the materials, I’ve added some 3D Perlin noise to the distance estimate – this is simple way to creature a structural texture, and it creates true displacements, not just surface normal perturbations).
The threads linked to above contains Fragmentarium scripts with the relevant distance estimators.
4 thoughts on “Knots and Polyhedra”
Those renders are starting to look super real now, great stuff!
Wow! they look as photography. Are you planning to do bidirectional path tracing?
Thanks, Knighty and Subblue.
I don’t think my raytracer necessarily need to be more sophisticated: I’m not aiming for photorealism – what I hope to achieve is something more dreamy, with strong contrasts and shadows. But I will try out some different techniques, and see what works.