It is a long-stand­ing prob­lem in un­biased Monte Carlo meth­ods for ren­der­ing that cer­tain dif­fi­cult types of light trans­port paths, par­tic­u­larly those in­volving view­ing and il­lu­min­a­tion along paths con­tain­ing spec­u­lar or glossy sur­faces, cause un­us­ably slow con­ver­gence. In this pa­per we in­tro­duce Man­i­fold Ex­plor­a­tion, a new way of hand­ling spec­u­lar paths in ren­der­ing. It is based on the idea that sets of paths con­trib­ut­ing to the im­age nat­ur­ally form man­i­folds in path space, which can be ex­plored loc­ally by a simple equa­tion-solv­ing it­er­a­tion. This pa­per shows how to for­mu­late and solve the re­quired equa­tions us­ing only geo­met­ric in­form­a­tion that is already gen­er­ally avail­able in ray tra­cing sys­tems, and how to use this meth­od in in two dif­fer­ent Markov Chain Monte Carlo frame­works to ac­cur­ately com­pute il­lu­min­a­tion from gen­er­al fam­il­ies of paths. The res­ult­ing ren­der­ing al­gorithms handle spec­u­lar, near-spec­u­lar, glossy, and dif­fuse sur­face in­ter­ac­tions as well as iso­trop­ic or highly an­iso­trop­ic volume scat­ter­ing in­ter­ac­tions, all us­ing the same fun­da­ment­al al­gorithm. An im­ple­ment­a­tion is demon­strated on a range of chal­len­ging scenes and eval­u­ated against pre­vi­ous meth­ods.

Sup­ple­ment­al re­port

The ex­pan­ded tech­nic­al re­port (43 pages) in the list of re­sources above fol­lows the same struc­ture as the pa­per and provides a range of ad­di­tion­al de­riv­a­tions and res­ults. Note: since the ori­gin­al pub­lic­a­tion, the sup­ple­ment­al re­port has been su­per­seded by Wen­zel Jakob's Ph. D. dis­ser­ta­tion.