  Embedding polygonal mesh assets within photorealistic Neural Radience Fields
(NeRF) volumes, such that they can be rendered and their dynamics simulated in
a physically consistent manner with the NeRF, is under-explored from the system
perspective of integrating NeRF into the traditional graphics pipeline. This
paper designs a two-way coupling between mesh and NeRF during rendering and
simulation. We first review the light transport equations for both mesh and
NeRF, then distill them into an efficient algorithm for updating radiance and
throughput along a cast ray with an arbitrary number of bounces. To resolve the
discrepancy between the linear color space that the path tracer assumes and the
sRGB color space that standard NeRF uses, we train NeRF with High Dynamic Range
(HDR) images. We also present a strategy to estimate light sources and cast
shadows on the NeRF. Finally, we consider how the hybrid surface-volumetric
formulation can be efficiently integrated with a high-performance physics
simulator that supports cloth, rigid and soft bodies. The full rendering and
simulation system can be run on a GPU at interactive rates. We show that a
hybrid system approach outperforms alternatives in visual realism for mesh
insertion, because it allows realistic light transport from volumetric NeRF
media onto surfaces, which affects the appearance of reflective/refractive
surfaces and illumination of diffuse surfaces informed by the dynamic scene.
