Curve Rendering for Fur and Hair

I’ve implemented Curve primitive ray intersection in Imagine based off Koji Nakamaru and Yoshio Ohno’s 2002 paper “Ray Tracing For Curves Primitive”. Basically, it involves projecting each curve’s ControlPoint positions into orthographic ray-space, so that the main intersection test can be done as a curve width test in two dimensions down the ray, and then the depth t-test can be worked out.

For straight curve primitives, this is sufficient, but for actual curves with any curvature down the length, splitting the projected curve recursively and performing the intersection test on these split curves is necessary. The recursion level needed to ensure accurate intersection depends on the curvature of each curve.

This recursive splitting obviously has an effect on the performance of the algorithm, so while intersecting straight curves is fairly fast, for a curve that curves gently at around 45 degrees from the root to the tip, a recursive splitting depth of six is needed, which results in 32 recursive splits, and a total of 64 intersections on both the original curve and the recursively split curves. Which is unfortunate, as to some extent it makes rendering non-straight curves unpractical for reasonable levels (+100,000) of curves.

For the moment, I’m setting the resultant geometric and shader normals from any intersection as facing back along the original camera ray, so that the normal always faces the camera. This is sufficient for very thin curves.

I’ve also implemented a set of Hair BSDFs for Diffuse and Specular, based on the 1989 Kajiya and Kay paper, which is commonly used. This is optimised for very thin curves, with no effective normal change across the curve, but with a tangent value which can be calculated from the intersection position on the ray.

For the moment, I’m storing curves in an acceleration structure, which works well for very short curves or longer curves which are axis-aligned, but for anything else (long curves going diagonally across dimensions) is bordering on ineffectual, as the resulting axis-aligned boundary boxes for each curve are extraordinarily large, with multiple curves often overlapping each other. I had hoped that spatial partitioning (with curve clipping to boundary boxes) would improve this considerably (it’s fairly useful for triangles), but the improvement for using curve clipping with spatial partitioning is not anywhere near as good as I would have hoped (it provides a slight intersection speedup though compared to object partitioning).

So for longer hairs, I’m going to have to think about how to speed this up considerably, as currently rendering long curved curves is orders of magnitude more expensive than I would have liked. It’s also going to either involve work to model and simulate hair strand interaction more, or import curves from elsewhere, as the method of generating hairs around meshes (importance sampling positions on each triangle for the root positions) and giving a random tilt or curve only really works with fur-type curves.