Curve ray tracing on parallel processors (e.g. GPUs)

Question

Some modern GPU raytracing APIs (e.g. Nvidia's OPTIX and now Apple's Metal since 3.1) support curves of various types as basic geometric primitives. I was wondering how curve ray intersection tests (with curve 'thickness' specified per control point) an be done efficiently on a parallel processor such as a GPU? I tried looking up some newer papers and articles, but many of them do triangulation, which is something is not happening here. What is the state of the art in this domain as of 2023?

Answer 1

I am doing 2D cubics with thickness in parallel on GPU like this:

• Is it possible to express "t" variable from Cubic Bezier Curve equation?

porting to 3D raytrace is relatively easy just create transformation that converts the ray into one of the axises (for example z) and voala you have 2D case again this is also very useful for other primitives like cones, cylinders, boxes ... where analytical solution in arbitrary 3D pose would complicate (even slow) things down