One of the key in­gredi­ents of any phys­ic­ally based ren­der­ing sys­tem is a de­tailed spe­cific­a­tion char­ac­ter­iz­ing the in­ter­ac­tion of light and mat­ter of all ma­ter­i­als present in a scene, typ­ic­ally via the Bi­d­irec­tion­al Re­flect­ance Dis­tri­bu­tion Func­tion (BRDF). Des­pite their util­ity, ac­cess to real-world BRDF data­sets re­mains lim­ited: this is be­cause meas­ure­ments in­volve scan­ning a four-di­men­sion­al do­main at suf­fi­cient res­ol­u­tion, a te­di­ous and of­ten in­feas­ibly time-con­sum­ing pro­cess.

We pro­pose a new para­met­er­iz­a­tion that auto­mat­ic­ally ad­apts to the be­ha­vi­or of a ma­ter­i­al, warp­ing the un­der­ly­ing 4D do­main so that most of the volume maps to re­gions where the BRDF takes on non-neg­li­gible val­ues, while ir­rel­ev­ant re­gions are strongly com­pressed. This ad­apt­a­tion only re­quires a brief 1D or 2D meas­ure­ment of the ma­ter­i­al's retro-re­flect­ive prop­er­ties. Our para­met­er­iz­a­tion is uni­fied in the sense that it com­bines sev­er­al steps that pre­vi­ously re­quired in­ter­me­di­ate data con­ver­sions: the same map­ping can sim­ul­tan­eously be used for BRDF ac­quis­i­tion, stor­age, and it sup­ports ef­fi­cient Monte Carlo sample gen­er­a­tion.

We ob­serve that the above de­sid­erata are sat­is­fied by a core op­er­a­tion present in mod­ern ren­der­ing sys­tems, which maps uni­form vari­ates to dir­ec­tions samples that are pro­por­tion­al to an ana­lyt­ic BRDF. Based on this in­sight, we define our ad­apt­ive para­met­er­iz­a­tion as an in­vert­ible, retro-re­flect­ively driv­en map­ping between the para­met­ric and dir­ec­tion­al do­mains. We are able to cre­ate noise-free ren­der­ings of ex­ist­ing BRDF data­sets after con­ver­sion in­to our rep­res­ent­a­tion with the ad­ded be­ne­fit that the warped data is sig­ni­fic­antly more com­pact, re­quir­ing 16KiB and 544KiB per spec­tral chan­nel for iso­trop­ic and an­iso­trop­ic spe­ci­mens, re­spect­ively.

Fi­nally, we show how to modi­fy an ex­ist­ing go­nio-pho­to­met­er to provide the needed retro-re­flec­tion meas­ure­ments. Ac­quis­i­tion then pro­ceeds with­in a 4D space that is warped by our para­met­er­iz­a­tion. We demon­strate the ef­fic­acy of this scheme by ac­quir­ing the first set of spec­tral BRD­Fs of sur­faces ex­hib­it­ing ar­bit­rary rough­ness, in­clud­ing an­iso­tropy.