Reciprocal formulation for heterogeneous non-exponential transport

Develop a reciprocal formulation for general heterogeneous non-exponential transport in participating media.

Background

The paper introduces a unified scene representation using anisotropic 3D Gaussian primitives combined with a non-exponential, linear transmittance model inspired by Vicini et al. (2021). While effective for modeling both hard surfaces and aggregated elements, the authors note that such non-exponential transmittance models may violate physical constraints related to reciprocity.

Reciprocity—such as the weak reciprocity proposed by d’Eon (2018)—is a foundational physical property for radiative transfer formulations. The authors state that their current transmittance model shares this limitation and highlight the need for a reciprocal formulation that applies broadly to heterogeneous non-exponential media.