Errata for:
Wavelet Radiance Transport for Interactive Indirect Lighting
This errata applies to the version of the paper published inRendering Techniques 2006 (Eurographics Sym- posium on Rendering)[KTHS06]. The versions currently available online should have been updated already.
• p. 4, equation 3
Correct form of the incident transport operator:
(TL)(x,x←y) = Z
ω
fr(ω,y,y→x)V(x,y)⌊ω·ny⌋L(y, ω)dω where fr(ω,y,y→x)V(x,y)⌊ω·ny⌋is the kernel,k(x,y, ω).
• p. 5, equation 4
Our 8-dimensional formulation is incorrect. 8-dimensional formulation is probably possible, but a correct 6-dimensional version is as follows:
Tr,s= Z
x,y,ω
k(x,y, ω)⌊x←y·ny⌋
rxy2 bss(y)bsa(ω)brs(x)bra(x←y)dωdxdy WhereK(x,y, ω) =k(x,y, ω)⌊x←y·nr2 y⌋
xy
.
• p. 6, section 4.3.2
’WhereK refers to the kernel’→’WithK as defined in equation 4.
Proof
Each transport coefficient is obtained by operating on the sending basis functionbss(y)bsa(ω) and projecting the result on the receiving onebrs(x)bra(α):
Tr,s =hbdrsbra|Tbssbsai
=hbdrsbra| Z
ω
k(x,y, ω)bss(y)bsa(ω)dωi
bdrsbra refers to the dual ofbrsbra, but since our basis is orthonormalbdrsbra=brsbra. The inner product is evaluated over positionxand directionx←yas follows:
= Z
x,y
brs(x)bra(x←y)⌊x←y·ny⌋ rxy2
Z
ω
k(x,y, ω)bss(y)bsa(ω)dωdxdy
Since we used area-based integration instead of hemispherical, we need to convert between the differential measures with ⌊x←y,nr2 y⌋
xy
. Technically a visibility term V(x, y) would be needed as well, but it is already included ink(x,y, ω).
So the final form:
Tr,s= Z
x,y,ω
k(x,y, ω)⌊x←y·ny⌋
r2xy bss(y)bsa(ω)brs(x)bra(x←y)dωdxdy
References
[KTHS06] Janne Kontkanen, Emmanuel Turquin, Nicolas Holzschuch, and Fran¸cois Sillion. Wavelet radiance trans- port for interactive indirect lighting. In Wolfgang Heidrich and Thomas Akenine-M¨oller, editors,Rendering Techniques 2006 (Eurographics Symposium on Rendering). Eurographics, jun 2006.
