Line Integration for Rendering Heterogeneous Emissive Volumes

Emissive media are often challenging to render: in thin regions where only few scattering events occur the emission is poorly sampled, while sampling events for emission can be disadvantageous due to absorption in dense regions. We extend the standard path space measurement contribution to also collect emission along path segments, not only at vertices. We apply this extension to two estimators: extending paths via scattering and distance sampling, and next event estimation. In order to do so, we unify the two approaches and derive the corresponding Monte Carlo estimators to interpret next event estimation as a solid angle sampling technique. We avoid connecting paths to vertices hidden behind dense absorbing layers of smoke by also including transmittance sampling into next event estimation. We demonstrate the advantages of our line integration approach which generates estimators with lower variance since entire segments are accounted for. Also, our novel forward next event estimation technique yields faster run times compared to previous next event estimation as it penetrates less deeply into dense volumes.