Euripus-3 and Daedalus--Monte Carlo Density Codes for the Ibm-704

Abstract

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A Position‐Free Path Integral for Homogeneous Slabs and Multiple Scattering on Smith Microfacets

“…These numerical issues were also noted in earlier works, and mitigation strategies to reduce the equal‐cosine case to gamma distributions and/or clamping heuristics have been proposed [BD56; AKS60; AT64]. Although we do not use the clamping strategy currently, it shows promising results, and poses an interesting avenue for future work.…”

“…These derivations can be viewed as an expected‐value transform of the previously mentioned spatially‐1D Monte Carlo estimators, by analytically pre‐integrating over the distances between collisions. For the case of an infinite medium, these relations were derived in a number of ways [BD56; AKS60; Dra61; CJT69]. The approach was applied to several problems by predetermining a fixed truncation of the Neumann series ahead of time based on known properties of the volume and then integrating over the directional dimensions of the reduced integral equation using Monte Carlo.…”

“…This type of simplification is common in slab problems, having been used extensively outside [AKS60] and within graphics [HK93; HHdD16; DHd16; GHZ18; XWHM20; GGN20]. We briefly review it here before deriving our position‐free formulation.…”

A Position-Free Path Integral for Homogeneous Slabs and Multiple Scattering on Smith Microfacets

“…This type of simplification is common in slab problems, having been used extensively outside [AKS60] and within graphics [HK93; HHdD16; DHd16; GHZ18; XWHM20; GGN20]. We briefly review it here before deriving our position-free formulation.…”