Optix has OPTIX_BUILD_INPUT_TYPE_CURVES to model splines. The SDK comes with an example named optixHair.
I could not find something like this under Vulkan RayTracing Extension, how could one implement this in Vulkan?
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I don't think vulkan has any way of natively doing curves.
I think you will need to program it yourself using VK_RAY_TRACING_SHADER_GROUP_TYPE_PROCEDURAL_HIT_GROUP_KHR, by providing your own bounding boxes for the curves and writing your own intersection shader for them.
I think this is an example of what you want. https://github.com/nvpro-samples/vk_raytracing_tutorial_KHR/tree/master/ray_tracing_intersection