
reeb graph

oru reeb graph (reena thom georges reebinte peril) oru yadhaartha moolyamulla functionte level settukalude parinaamatthe prathifalippikkunna oru ganithashaasthra vasthuvaan.
samanamaaya oru ashayam jii avatharippichu.emm. adelson-velsky eiii.ezz. cronroad cheyth hilbertinte pathimoonnaamatthe prashnatthinte vishakalanathin prayogichu. jii. nirddeshichu. mozhs sidhaanthathile oru upakaranamenna nilayil, 2 dii scaler feeldukal formula _ 1, formula _ 2, formula _ 3 enniva thammilulla multy valued functional bandhangal padikkunnathinulla swaabhaavika upakaranamaan reeb graafukal.
formula _ 4 umm formula _ 5 umm, kaaranam reeb graafinte oru vyakthigatha arikumaayi bandhapetta oru pradeshathu parimithappedutthumbol eee bandhangal eaka moolyamullathaanu. samudrashaasthrathile nishpaksha prathalangalekkurichu padikkaanaanu eee pothuvaaya thathwam aadyamaayi upayogichathu.
computer aided jyaamitheeya roopakalppana, topology adisthaanamaakkiyulla aakruthi poruthappedutthal, topological daatta vishakalanam, topological lalithavalkkaranam, vrithiyaakkal, uparithala vibhajanavum parameterisation, level settukalude kaaryakshamamaya kanakkukoottal, neuro sayans, jyaamitheeya thermodynamics ennivayulppede computational jyaamithiyilum computer graphixilum reeb graafukal vaividhyamaarnna prayogangal kandethiyittundu.
oru paranna sthalathulla oru functionte oru prathyeka saahacharyathil (saankethikamaayi lalithamaayi bandhippicha domaine), reeb graph oru poolii trea roopappeduthunnu, ithine kondoor trea ennum vilikkunnu.
level settu graafukal probability density functionukalum regression functionukalum kanakkaakkunnathumaayi bandhapetta stattistikkal anumaanathe sahayikkunnu, avaa mattu karyangalkkoppam klasttar vishakalanathilum function opttimaiseshanilum upayogikkaam. 
aupachaarika nirvachanam.
oru topological space "x" umm oru thudarchayaaya function "f": "x" → r nalkumbol, "x" ll oru thulyatha bandham nirvachikkuka, avide "p" umm "q" umm oru single level settil "f" −1 ("c") nte ore connectucheytha gadakathil ulppedumbozhellaam "p" ̃ "q" chila yadhaartha "c". x"/̃ enna kwashant topology ulla koshyant space aanu reeb graph.
mozhs functionukalkulla vivaranam.
f" ennathu vyathyasthamaaya nirnaayaka moolyangalulla oru mozhs functionaanengil, reeb graph kooduthal vyakthamaayi vivarikkanaakum. athinte nodukal allengil vertisukal "f" −1 ("c") enna critical level settukalumaayi poruthappedunnu. nodukal/konukalil aarkkukal allengil arikukal kandumuttunna paatten "t" nirnaayaka moolyamaaya "c" yiloode kadannupokumbol "f" −1 ("t") level settinte topologyile maattathe prathifalippikkunnu. udaaharanathinu, "c" ennathu "f"-nte ettavum kuranjatho paramavadhi aayathaanengil, oru ghadakam srishtikkukayo nasippikkukayo cheiyunnu; thalphalamaayi, digri 1 ulla anubandha nodil oru arck uthbhavikkukayo avasaanikkukayo cheiyunnu. "c" ennathu soochika 1-nte oru saddle pooyintum "f"-1 ("t")-nte rund gadakangalum "t" vardhikkumbol "t" = "c"-ll layippikkukayaanenkil, reeb graafinte anubandha sheershakathin digri 3 undu, koodaathe "y" enna aksharam pole kaanapedunnu; "c"-nte soochika mangiya "x"-1 "umm" f "-1 (" c ")-nte oru gadakavum randaayi vibhajikkappedumbol athe nyaayavaadam baadhakamaan.

