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An efficient ray tracing method is presented for calculating interreflections between surfaces with both diffuse and specular components. A Monte Carlo technique computes the indirect contributions to illuminance at locations chosen by the rendering process. The indirect illuminance values are averaged over surfaces and used in place of a constant "ambient" term. Illuminance calculations are made only for those areas participating in the selected view, and the results are stored so that subsequent views can reuse common values. The density of the calculation is adjusted to maintain a constant accuracy, permitting less populated portions of the scene to be computed quickly. Successive reflections use proportionally fewer samples, which speeds the process and provides a natural limit to recursion. The technique can also model diffuse transmission and illumination from large area sources, such as the sky.

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Cre gory J. Ward Franc" M. Rdin , ft,1 'n Rob ert D. Clt arLigAting S1, tem, R u tGrcA Lawr enee Ber keley L aboratory 1 e ye/atrllft Rd ., 9().3111 B erl:t.lt,1 , CA 94 7£0 ( / 15) , S6 -, 757 Abs tn .ct An efficient. ray tr acing met hod is pre se nted for calcul ating inte rrefleerions betw een s ur faces wit h bot h diffuse an d spec ulai' co mpone nts. A Mont e Car lo t echn ique co mp utes t he indi rect co nt r ibutions to illum inan ce a.t locat ions chosen by th e rendering proc ess. Th e ind irect illu m inan ce values ar e a verage d ove r surfac es and used in place of a cOM ta n t " amb ient." te rm . Illumin an ce calculations are mad e only (or th ose are as par t icipati ng in t he selec ted vi ew, an d the results are sto red so t hat subse quent views can re use co mmon valu es . Th e den sity of th e cal culati on is ad ju ste d to m aintain a cons tan t. ac cu racy , perm ittin g less popu lated po rt icna of t he sce ne to be co mpute d quickly . Succ essive reflections use pro por tional ly fewer sa mples , whi ch spe eds t he process and pro vides a natur al lim it to recurs ion . Th e tec hni que can also mode l diffuse t rans mission and illumina t ion fro m lar ge aru $()U fCe8, such as t he sky .Ge neral T erms : Algorithm , com plexity .Add it ion al K eyword s a nd Ph rases : Cac hing, diffuse, illu minan ce, int erre ftectio n , lu minan ce, Mo nte Car lo tec hnique , rad iosity , ray t rac ing, rend erin g, spec ular . 1. In tr oduc.tion © 1988 ACM .(}.. 89191·275-6/ 88/008/0085 $00. 75 85 R o =. "average"distanceto surfaces at PoTh e ch~ge in % becom es th e di stance betw een two pointe, and t he chan ge In ebecomes th e angl e betw een two eurfeee norm als. Th is equation is use d to est imate t he rela t ive change in illuminance for any geometry . Bo t h th e po ints and t he surface nor mals~determin ed by t.he ray interse ct-i on calcu latio n . R 0 is the harm on ic mean (reciprocal mean reciproca l) of distance!l to visible surfaces, which can be computed (rom ray lengt hs during prim ary eval uat ion . 87 10 . NI8bit.a, TOmoyuD and Eihacbiro Nakamae , uCoatlo\lOUl TOIle Repneentatioo. 01 Tbree--Dimenaioaal Objectc Taki.a.1 A«ount 01 SbadOWfland Iaterre 8ectioD," 0 0".

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