Skip to content

Commit

Permalink
Replace transitive with associative (#122)
Browse files Browse the repository at this point in the history
  • Loading branch information
portsmouth authored Oct 13, 2023
1 parent 83e29c3 commit ecc46fb
Showing 1 changed file with 1 addition and 1 deletion.
2 changes: 1 addition & 1 deletion index.html
Original file line number Diff line number Diff line change
Expand Up @@ -154,7 +154,7 @@

It is understood that the BSDF $f^\prime_\mathrm{sub}$ at the new internal interface formed from the joining of the coat and substrate slabs is not necessarily the same as $f_\mathrm{sub}$, but would be derivable from it by considering the physics and geometry of the bond. Physically this BSDF should be consistent with the adjacent media $V_\mathrm{coat}$ and $V_\mathrm{sub}$, and it is assumed that the bond does not significantly alter the geometry of the substrate interface (i.e. the coat conforms to the substrate geometry). It is then reasonably unambiguous how the BSDF of the internal interface should be implemented, taking into account the known BSDFs and media of the component slabs being bonded in the layering and the final suite of parameters which is supposed to describe the resultant interface. For example bringing two dielectric slabs together produces well-understood Fresnel effects at the interface according to the ratio of the IORs of the dielectric media.

Technically the $\mathrm{\mathbf{layer}}$ operator is transitive, i.e.
Note that technically, the $\mathrm{\mathbf{layer}}$ operator is associative, i.e.
\begin{equation}
\mathrm{\mathbf{layer}}(S_a, \mathrm{\mathbf{layer}}(S_b, S_c)) = \mathrm{\mathbf{layer}}(\mathrm{\mathbf{layer}}(S_a, S_b), S_c)
\end{equation}
Expand Down

0 comments on commit ecc46fb

Please sign in to comment.