i ▁+ ▁ 2 ) nd ▁vertices ▁of ▁the ▁sequ ential ▁strip . ▁Such ▁a ▁sequ ential ▁strip ▁can ▁reduce ▁the ▁cost ▁to ▁transmit ▁n ▁tri angles ▁from ▁ 3 n ▁to ▁n ▁+ ▁ 2 ▁vert ic ies . ▁ ▁Sim pl ification ▁en velop es ▁Var sh ney ▁proposed ▁the ▁idea ▁of ▁simpl ification ▁en velop es ▁as ▁a ▁method ▁of ▁simultaneously ▁pres erving ▁both ▁global ▁and ▁local ▁topology . ▁A ▁surface ' s ▁en velope ▁is ▁a ▁shell - like ▁structure ▁consisting ▁of ▁a ▁pair ▁of ▁surfaces ▁a ▁distance ▁ ε ▁on ▁either ▁side ▁of ▁the ▁original ▁surface . ▁Each ▁surface ▁has ▁its ▁own ▁level ▁of ▁detail , ▁often ▁referred ▁to ▁as ▁the ▁' h ier archy ▁of ▁LO D '. ▁Many ▁consider ▁the ▁main ▁draw back ▁of ▁simpl ification ▁en velop es ▁to ▁be ▁that ▁the ▁algorithms ▁for ▁their ▁calculation ▁are ▁difficult ▁to ▁program . ▁ ▁Level ▁of ▁detail ▁for ▁ 3 D ▁graphics ▁In ▁ 2 0 0 2 , ▁Var sh ney ▁published ▁the ▁first ▁edition ▁of ▁" Level ▁of ▁Det ail ▁for ▁ 3 D ▁Graphics ". ▁The ▁book ▁details ▁several ▁principles ▁for ▁optim izing ▁ 3 D ▁rendering ▁including : ▁The ▁use ▁of ▁multiple ▁discrete ▁levels ▁of ▁detail ▁( LO D s ) ▁in ▁lieu ▁of ▁a ▁single ▁view - dependent ▁LO D ▁Top ology - pres erving ▁and ▁topology - sens itive ▁simpl ification ▁algorithms ▁to ▁maxim ize ▁f idel ity ▁The ▁use ▁of ▁multiple ▁LO D s ▁in ▁multiple ▁instanti ations ▁in ▁g