References
The method
The fundamental method is presented in Bielefeld (2026).
The zone method
For reciprocal exchange factors, the method reproduces the zone method of Hottel (Hottel and Cohen 1958; Hottel and Sarofim 1967), in the explicit matrix form of Noble (Noble 1975).
The exchange factor method
The method builds on the exchange factor method of Larsen and Howell (Larsen 1983; Larsen and Howell 1985).
View factors and ray tracing
Analytical view factors are evaluated from the expression of Narayanaswamy (2015), in a translation of the implementation by Kerkhoff and Wagner (Kerkhoff and Wagner 2021a, 2021b). Rays are intersected with triangles by the method of Möller and Trumbore (1997), accelerated by bounding volume hierarchies built after Wald (2007).
Sampling
Ray emission is sampled from Sobol sequences (Sobol’ 1967; Joe and Kuo 2008), as provided by Sobol.jl (Johnson, n.d.).
Smoothing
Ray-traced exchange factors are smoothed by projection onto reciprocity and energy conservation, using Dykstra’s algorithm (Dykstra 1983); least-squares smoothing of direct exchange areas goes back to Larsen and Howell (1986).
Physics and validation
The examples are validated against Crosbie and Schrenker (1984), Heaslet and Warming (1965) and the Henyey–Greenstein phase function (Henyey and Greenstein 1941), with background from Howell et al. (2021) and Modest and Mazumder (2022).
Software
The package is written in Julia (Bezanson et al. 2017) and uses ConvolutionInterpolations.jl (Bielefeld 2025) for spectral binning and the Planck tables; figures are drawn with Makie.jl (Danisch and Krumbiegel 2021) and Plots.jl (Christ et al. 2023).
Bibliography
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