Ati ene ƒe ŋgɔdonya si me wowɔa nu aduadu le

Nusitae Ati Eneawo Le Vevie Wu Wu alesi Nèsusu

| Quadtrees nye nyatakaka ƒe ɖoɖo dzeani mawo dometɔ ɖeka si ŋu ame akpa gãtɔ mesea nu tsoe gbeɖe o, ke hã wonaa ŋusẽ kpoo le ɖoɖo siwo le vevie wu le dɔwɔwɔ me le egbegbe kɔmpiutadziɖoɖowo me — tso videofefewo ƒe gododo didi dzi va ɖo anyigbaŋutinunya ƒe nyatakakaɖoɖo siwo wɔa dɔ tso teƒe ŋuti nyabiase miliɔn geɖe ŋu le sɛkɛnd ɖeka me. Menye ɖeko alesi wowɔa dɔe gɔmesese nana nèzu dɔwɔla nyuitɔ o; etrɔa alesi nèbua ɖoɖowɔwɔ kple didi to teƒe ŋuti nyatakakawo me vevie. Eɖanye be èle nyatakakaɖoɖoɖa ƒe mɔnu tum, numekuku ƒe mɔnu si wotu ɖe teƒe si nèle dzi, alo nèle agbagba dzem ko be yeaɖe nyatakaka teƒe 50,000 afia le canvas dzi evɔ màgbã web-browser o, quadtrees naa egbɔkpɔnu si gɔme sese le bɔbɔe eye wòwɔa dɔ ɖedzesi aɖe.

Nuka Tututue Nye Ati Ene?

Ati ene nye ati ƒe nyatakaka ƒe ɖoɖo si me vi ene pɛpɛpɛ le ememe node ɖesiaɖe si, wo dometɔ ɖesiaɖe tsi tre ɖi na teƒe si le akpa eve ƒe akpa enelia ɖeka. Kpɔe ɖa le susu me be yexɔ nuto si le dzogoe ene me eye yemae ɖe dzogoe ene me siwo sɔ me — dzieheɣetoɖoƒe, dzieheɣedzeƒe, dzieheɣetoɖoƒe, kple dzieheɣedzeƒe. Woate ŋu ama dzogoe ene mawo dometɔ ɖesiaɖe ɖe dzogoe ene bubu me, eye nenemae woawɔe, zi gbɔ zi geɖe, vaseɖe esime nàɖo nɔnɔme aɖe si me nàtɔ ɖo gbɔ. Zi geɖe la, tɔtrɔ ƒe nɔnɔme ma nyea goglome si sɔ gbɔ wu alo dzidzenu na nyatakaka teƒe agbɔsɔsɔme si node ɖeka ateŋu alé hafi wòahiã be wòama.

Mɔnu sia ƒe atsyɔ̃ le eƒe tɔtrɔ ɖe nɔnɔmewo ŋu me. Nuto siwo me nyatakakawo ƒe teƒewo sɔ gbɔ ɖo la ma ɖe lãmenugbagbevi siwo le nyuie wu me, evɔ teƒe siwo mebɔ o ya gakpɔtɔ nye nuto gã siwo womema o. Ati ene si adzra kɔfidzraƒe 10,000 ƒe teƒewo ɖo le dukɔ aɖe me godoo ana mamã goglo siwo me kɔ nyuie ɖe Manhattan dzi — afisi fiase 300 ate ŋu anɔ le kilometa sq ʋee aɖewo me — esime wòalé Wyoming kɔƒenutome ƒe akpa gã aɖewo ɖe te abe nuto ɖeka si me mã o si me zero alo teƒe ɖeka le ene. Tameɖoɖo kplikpaa sia si trɔna ɖe nɔnɔmewo ŋue nye nusi na ati eneawo ŋu ŋusẽ le ale gbegbe ne wotsɔe sɔ kple grid gbadza, si agblẽ ŋkuɖodzinu gbogbo aɖewo ɖe lãmenugbagbevi ƒuƒluwo dzi.

| Vovototo ɖesiaɖe wɔa dɔ nyuie wu na zazã ƒe nɔnɔme vovovowo, gake gɔmeɖose vevi si nye recursive subdivision la gakpɔtɔ le ɖeka le wo katã me.

Alesi Dede kple Nyabiase Dɔwɔna

Be nàtsɔ teƒe aɖe ade ati ene me la, èdzea egɔme tso ke ƒe nugbɔ eye nèkpɔa teƒe eneawo dometɔ si me teƒea ge ɖo. Emegbe ègatrɔna yia akpa enelia ma ƒe vi node me eye nègawɔa dɔa ake. Ne èɖo aŋgba ƒe nugbɔ si mewu eƒe ŋutete o (zi geɖe la, woɖonɛ ɖe teƒe 1 alo 4) gbɔ la, ɖeko nèdzraa teƒea ɖo ɖe afima. Ne aŋgba la le eƒe ŋutete nu xoxo la, ema ɖe vi ene me, gbugbɔ maa eƒe teƒe siwo li xoxo la ɖe wo dome, eye emegbe wòtsɔa teƒe yeyea dea ɖevi si sɔ la me. Zi geɖe la, dɔwɔwɔ sia wua enu le O(log n) ɣeyiɣi me hena mama si da sɔ, togbɔ be nɔnɔme vɔ̃ɖitɔ kekeake siwo me nyatakaka siwo woƒo ƒu ŋutɔ le ateŋu agblẽ dɔwɔwɔ me hã.

Range querying — teƒewo katã didi le dzogoe ene me nuto si wona me — nye afisi ati eneawo klẽna le vavã. Le esi teƒe be nàlé ŋku ɖe teƒe ɖesiaɖe ɖesiaɖe ŋu le wò nyatakakadzraɖoƒe (O(n) dɔwɔwɔ) la, èdzea egɔme tso ke gbɔ eye nèbiaa nya bɔbɔe aɖe le node ɖesiaɖe ŋu: ɖe node sia ƒe liƒo do go kple nye didi ƒe dzogoe ene mea? Ne menye nenema o la, ke ètso ati sue bliboa — si ate ŋu aɖe nya akpe geɖe ɖa le wo ŋu bubu me le tsɔtsɔ sɔ kple wo nɔewo zi ɖeka me. Ne mɔdodo aɖe li la, ègatrɔna yia ɖevi siwo ŋu nya ku ɖo la me. Teƒe siwo wokpɔ le aŋgba ƒe nugbɔ siwo dze le didi ƒe dzogoe ene me la xɔa kpe ɖe emetsonu ƒe hatsotso ŋu.

Bu kpɔɖeŋu nyui aɖe ŋu kpɔ: nyatakakadzraɖoƒe si me asisiwo ƒe teƒe 100,000 le le asiwò eye ehiã be nàdi amesiame le kilometa 5 ƒe didime me tso fiase yeye ʋuʋu gbɔ. Mɔnu si wozãna le ŋutasẽnuwɔwɔ me bia be woabu akɔnta le didiƒe 100,000 ŋu. Ati ene si wotu nyuie ate ŋu aɖe ema dzi akpɔtɔ va ɖo ɖaseɖigbalẽ 200-500 pɛ ko to anyigba ƒe nɔnɔme ƒe nuto blibo siwo dze ƒã be womewɔ ɖeka kple wò didiƒe o la ɖeɖeɖa kabakaba me. Ema nye dɔwɔwɔ ƒe nyonyo si nye 200x alo esi wu nenema — vovototo si le biabia si xɔa milisekɔnd 800 kple milisekɔnd 4 dome.

Xexeme Nyateƒetɔ Dɔwɔɖoɖo Siwo Ƒoa Dɔ Le Quadtrees

Ati ene ƒe dɔwɔwɔ keke ta yi ŋgɔ sasasã wu kɔmpiutaŋutinunya si wozãna le suku. Wonye gɔmeɖoanyi na ɖoɖo siwo ame biliɔn geɖe zãna gbesiagbe, zi geɖe la, womenya o.

ƒe nyawo
• Anyigbatata kple mɔzɔzɔ: Dɔwɔƒewo abe Google Maps kple Mapbox zãa tile ɖoɖo siwo le abe ati ene tsɔ subɔa anyigbatata ƒe nɔnɔmetatawo. Zoom ƒe ɖoɖo ɖesiaɖe ma tilewo ɖe vi ene me, si tae anyigbatata tile ƒe nɔnɔmetatawo zɔna ɖe z/x/y ƒe nɔnɔme si ɖea quadtree adrɛswɔwɔ fiana. Ne èdzi dugã ƒe xɔtunu ɖe edzi la, tile siwo ƒe nɔnɔme deŋgɔ siwo sɔ koe xɔa agba — xexeame ƒe akpa mamlɛa nɔa nɔnɔmetata si le gbadzaa me.
• Dzesidede nuwo ƒe gododo le fefewo me: Fefe ƒe mɔ̃wo zãa ati ene (kple wo hati 3D, octrees) tsɔ dea dzesii nyuie ne nuwo do go. Le esi teƒe be wòado nu eve ɖesiaɖe kpɔ — O(n2) drɔ̃e baɖa aɖe si me nu 1,000 le le screen dzi — nusiwo me quadtree cell ɖeka le koe mɔ̃a léa ŋku ɖe, si ɖea ɖaseɖiɖiwo dzi kpɔtɔna va ɖoa xexlẽme si dzi woate ŋu akpɔ.
• Nɔnɔmetata ƒe nutete: Nutome ƒe ati ene ateŋu aƒo nɔnɔmetatawo nu ƒu to piksel siwo te ɖe wo nɔewo ŋu siwo ma amadede ɖeka tɔgbewo ƒoƒo ƒu ɖe blɔ gãwo me. Esia nye gɔmeɖoanyi na nutete ƒe akɔntabubu aɖewo siwo ɖoa nutete ƒe xexlẽme 10:1 gbɔ esime woléa nukpɔkpɔ ƒe nuteƒewɔwɔ me ɖe asi le teƒe siwo me mekɔ tututu o.
• Ʋuʋuwo dzikpɔkpɔ kple ɖoɖowɔwɔ: Dɔwɔƒe siwo tsɔa ʋuwo yia teƒe bubuwo zãa teƒe ƒe xexlẽdzesiwo tsɔ sɔ kple ʋukulawo kple nudɔdɔ siwo te ɖe wo ŋu le ɣeyiɣi ŋutɔŋutɔ me. Quadtree na dispatch system ɖoa biabia si nye "ʋukula 5 kawoe te ɖe pickup teƒe sia ŋu wu?" le ʋu akpe geɖe siwo le woƒe GPS teƒewo ɖɔlim le sɛkɛnd ʋee aɖewo ɖesiaɖe me.
• Anyigba ƒe teƒe ŋuti numekuku: Mɔ̃ siwo ƒoa asitsanyatakaka siwo wotu ɖe teƒe si wole dzi nu ƒu — asisiwo ƒe agbɔsɔsɔme ƒe nɔnɔmetatawo, nudzadzra ƒe anyigbamama ƒe nyonyome, fiasewo ƒe ɖoɖowɔwɔ me dzodzro — ɖoa ŋu ɖe teƒe ŋuti nyatakakawo ƒe ɖoɖowo ŋu be woana biabia siawo nawɔ nu aduadu tsɔ wu be woawɔ dɔ le hatsotsowo me.

ƒe nyawo

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Nu vevi si le megbe na quadtrees enye be teƒe ƒe biabia akpa gãtɔ mehiã be woalé ŋku ɖe nyatakaka akpa gãtɔ ŋu o. To ɖoɖowɔwɔ ɖe teƒe ŋu le ɖoɖo nu la, ètrɔa brute-force didiwo wozua mɔzɔzɔ siwo woɖo taɖodzinu na — ètrɔa sɛkɛndwo wozua milisekɔndwo eye nènana ɣeyiɣi ŋutɔŋutɔ me kadodo nanya wɔ kple nyatakakadzraɖoƒe gãwo gɔ̃ hã.

ƒe nyawo

Ati ene Tutu Tso Gɔme

Basic quadtree ƒe dɔwɔwɔ nye nusi ŋu woate ŋu ate ɖo nukutɔe, na domedome dɔwɔlawo gɔ̃ hã. Nu vevi ƒe wɔwɔme hiã akpa ʋee aɖewo ko: liƒo (teƒe si le dzogoe ene me si node la xɔ), ŋutete (teƒe gãtɔ hafi mamã), teƒewo ƒe ƒuƒoƒo, kple nuƒoƒo tso vi node ene ŋu (le gɔmedzedzea me nye nu dzodzro). Woateŋu aŋlɔ insert dɔwɔwɔ bliboa ɖe kɔda ƒe fli 30 teti me le gbegbɔgblɔ akpa gãtɔ me.

Dɔwɔwɔ si me mama la wɔa vi ƒe node yeye ene, siwo dometɔ ɖesiaɖe xɔa dzila ƒe liƒo ƒe akpa enelia ɖeka. Le dzila si si liƒo le (x, y, kekeme, kɔkɔme) gome la, dzieheɣedzeƒe vi la xɔa (x + kekeme/2, y, kekeme/2, kɔkɔme/2), dzieheɣetoɖoƒe xɔa (x, y, kekeme/2, kɔkɔme/2), kple bubuawo. Ne woma wo me vɔ la, wogbugbɔ maa teƒe siwo li xoxo la ɖe ɖevi siwo sɔ me. Vodada si bɔ enye be woaŋlɔ be be yewoakɔ dzila ƒe dzesiwo ƒe ƒuƒoƒoa ŋu le gbugbɔmamã megbe, si wɔnɛ be emetsonuwo gbugbɔna le biabiawo me.

Le nuwɔwɔ zazã gome la, nyonyo geɖewo le vevie. Zi geɖe la, ne èɖo node ƒe ŋutete ɖe teƒe 4-8 la, ewɔa dɔ wu ŋutete si nye 1, elabena eɖea ati ƒe goglome kple node ƒe nuwo ƒe ta dzi kpɔtɔna. goglome ƒe seɖoƒe si sɔ gbɔ wu (zi geɖe la, dzidzenu 8-12) tsɔtsɔ kpee xea mɔ na dɔléle ƒe dɔléle siwo me teƒe geɖe ma kɔordinate ɖeka tɔgbe le be woagawɔ ati siwo goglo seɖoƒe meli na o. Eye le nyatakakadzraɖoƒe siwo le ŋusẽ kpɔm afisi teƒewo ʋãna le — abe ʋu ƒe kplɔkplɔ ene — àdi be yeawɔ mɔ̃ aɖe si woatsɔ aɖe ati la ɖa alo aɖaŋu aɖe si dzi woato agbugbɔ ati la atu ɣeaɖewoɣi, elabena ati eneawo medaa asɔ le wo ɖokui si abe alesi ati dzĩ-yibɔwo wɔnɛ ene o.

Quadtrees le Asitsatsa ƒe Dɔwɔƒewo kple Numekukuwo me

ƒe nyawo

Egbegbe asitsamɔnuwo le dɔ wɔm kple teƒe ŋuti nyatakakawo geɖe wu, eɖanye asisiwo ƒe teƒewo, nudɔdɔ ƒe teƒewo, nudzadzra ƒe anyigbamamawo, alo nunɔamesiwo yometiti o. Kuxia menye nyatakaka sia dzadzraɖo ko o — ke boŋ ele ewɔm be woate ŋu abiae le ɣeyiɣi ŋutɔŋutɔ me le dzidzenu nu. Ne ehiã be asitsaha aɖe si le dɔ wɔm le du 50 me nakpɔ asisiwo ƒe agbɔsɔsɔ le susu me, atsɔ mɔ si dzi woatsɔ nuawo ayi na amewo, alo adzro nutome ƒe nudzadzra ƒe dɔwɔwɔ me la, teƒe ƒe dzesidemɔnu si le ete lae afia nenye be dashboard la atsɔ agba le milisekɔnd 200 alo sɛkɛnd 20 me.

Esia nye susu ɖeka si ta mɔ̃wo abe Mewayz — si ƒoa modules 207 siwo xɔ CRM, invoicing, fleet management, booking, kple analytics nu ƒu ɖe asitsa OS ɖeka me — kpɔa viɖe tso teƒe ŋuti nyatakakawo gbɔ kpɔkpɔ nyuie me le hood te. Ne ehiã be ʋuwo dzikpɔkpɔ ƒe mɔ̃ aɖe naɖe ʋu 500 siwo le dɔ wɔm afia le anyigbatata dzi, alo ne CRM mɔ̃ aɖe kpɔ teƒe 138,000+ siwo zãlawo le le susu me hena anyigbamama ƒe ɖoɖowɔwɔ la, ɖeko mɔnu siwo me susu mele o medzidzea nu o. Teƒe ƒe xexlẽdzesiwo ƒe ɖoɖowo abe quadtrees (alo woƒe nyatakakadzraɖoƒe si sɔ kple wo nɔewo, abe PostGIS R-trees kple MySQL teƒe ƒe dzesiwo ene) na wònya wɔ be woatsɔ nɔnɔme siawo ana evɔ mehiã be woana dɔwɔƒe ƒe xɔtunu si sɔ kple wo nɔewo o.

Le asitsaha siwo le mɔ̃wo me tom gome la, nusi woatsɔ ayi teƒe bubuwo la wɔa dɔ: dɔwɔnu siwo kpɔa teƒe kple teƒe ŋuti nyatakakawo gbɔ nyuie la mele aɖaŋunu dzeaniwo zãm ɖe eta ko o. Wole vovototo wɔm le agbalẽŋɔŋlɔ ƒe ɖoɖo si ate ŋu aɖe dɔwɔƒe siwo li enumake afia le kilometa 10 me kple esi xɔa sɛkɛnd 8 hafi tsɔa nusiwo do tso eme mawo ke la dome. Dɔwɔwɔ le ɖoƒe sia ɖea egɔme tẽ ɖe zãla ƒe nuteƒekpɔkpɔ me eye, mlɔeba la, gakpɔkpɔ.

Quadtrees vs. Teƒe ƒe Nyatakaka ƒe Dɔwɔɖoɖo Bubuwo

Menye ati ene koe nye tiatia na teƒe ƒe xexlẽdzesiwo o, eye mɔnu bubuawo gɔmesese kpena ɖe ŋuwò be nàtia dɔwɔnu nyuitɔ. R-trees, si wozãna ŋutɔ le nyatakakadzraɖoƒewo abe PostGIS kple SQLite ƒe R*Tree module ene, ɖoa nyatakakawo ɖe ɖoɖo nu ɖe ​​dzogoe ene me liƒo suetɔ kekeake me eye wokpɔa didiƒe ƒe biabiawo kple aƒelika siwo te ɖe wo ŋu didiwo gbɔ nyuie. Zi geɖe la, wowɔa dɔ wu quadtrees na disk-dzi nudzraɖoƒe elabena woɖea I/O dɔwɔwɔwo dzi kpɔtɔna, si tae teƒe ƒe nyatakakadzraɖoƒe akpa gãtɔ zãa R-tree ƒe tɔtrɔwo le ememe tsɔ wu quadtrees.

K-d atiwo ma teƒea to mama siwo trɔna ɖe axis ŋu zazã me (gbã to x, emegbe to y, emegbe to x ake) eye wonyo ŋutɔ na aƒelika siwo te ɖe wo ŋu didi le didime si sɔ me. Wodina be yewoawɔ dɔ wu quadtrees ne didime le sue eye nyatakakadzraɖoƒea le teƒe ɖeka, gake esesẽna be woawɔ yeyee le mɔ si trɔna nu. Geohashes tsɔa mɔnu bubu kura, ŋlɔa latitude kple longitude ɖe ka ɖeka me afisi ŋgɔdonya siwo woama fia teƒe ƒe tete ɖe wo nɔewo ŋu — si wɔe be wosɔ nyuie na nyatakakadzraɖoƒe ƒe indexing kple caching gake womete ŋu trɔna bɔbɔe na didiƒe ƒe biabiawo o.

| Le ŋgɔgbe dɔwɔnu si ɖea nyatakaka teƒe 10,000 ɖe canvas dzi kple pan-and-zoom gome la, quadtree si wowɔ le JavaScript ƒe fli 100 me awɔ dɔ wu egbɔkpɔnu ɖesiaɖe si nyatakakadzraɖoƒe da megbe na to network latency ɖeɖeɖa ko me.

Gɔmedzedze: Afɔɖeɖe siwo kplɔe ɖo siwo ŋudɔ woate ŋu awɔ

Ne èdi be yeana yeƒe gɔmesese le ati ene ŋu nade to wu nuxexlẽ tso wo ŋu la, mɔnu si wɔa dɔ wue nye be nàtu ɖeka le nukpɔkpɔ me. Wɔ canvas dɔwɔnu bɔbɔe aɖe si me ne èzi edzi tsɔa dzesiwo kpenɛ, eye nàkpɔ ati la ƒe mama suewo le ɣeyiɣi ŋutɔŋutɔ me. Tsɔ range-query rectangle si nàte ŋu ahe aƒo xlãe eye nàhe susu ayi teƒe siwo wòke ɖo la kpee. Asiwɔwɔ ɖe nu dzi sia tua nukpɔsusu si nuxexlẽ agbɔsɔsɔme aɖeke mateŋu asɔ o — àkpɔ nusita nyatakaka siwo woƒo ƒu wɔa ati siwo goglo wu kple alesi atitsotso ƒe nuwɔna le nyabiasewo me ɖea teƒe gãwo ɖa.

enumake

Le nuwɔwɔ ƒe dɔwɔwɔwo gome la, bu mɔfiame siawo ŋu: ne wò nyatakakawo le nyatakakadzraɖoƒe la, zã teƒe ƒe xexlẽdzesi si wò nyatakakadzraɖoƒea naa (PostGIS, MySQL Spatial, MongoDB 2dsphere indexes) tsɔ wu be nàwɔ quadtrees le dɔwɔwɔ ƒe kɔpi me. Ne èle asitsalawo ƒe akpa ƒe nukpɔkpɔ alo ŋkuɖodzinu me dɔwɔwɔ wɔm la, agbalẽdzraɖoƒewo abe d3-quadtree na JavaScript alo pyquadtree na Python naa dɔwɔwɔ siwo wodo kpɔ le aʋawɔwɔ me. Eye ne èle mɔ̃ aɖe tum si kpɔa teƒe ŋuti nyatakaka ƒomevi ɖesiaɖe gbɔ — tso asisiwo ƒe adrɛs dzi va ɖo dɔdɔ ƒe mɔfiame dzi va ɖo anyigbamama dzikpɔkpɔ dzi — de ɣeyiɣia eme be nàse teƒe ƒe xexlẽdzesiwo gɔme, elabena atrɔ asi le nusi wò dɔwɔɖoɖo ateŋu awɔ le agbɔsɔsɔ me ŋu le gɔmedzedzea me.

Ati eneawo tsi tre ɖi na gɔmeɖose si keke ta wu le kɔmpiutaŋutinunya me: be ɖoɖo si nètia na wò nyatakakawoe afia biabia siwo ŋu nàte ŋu aɖo nyuie. Kɔordinate ƒe xexlẽdzesi gbadzaa ateŋu aɖo eŋu be "na teƒeawo katãm," gake quadtree ateŋu aɖo eŋu be "na teƒe siwo katã te ɖe afisia ŋu" — eye ateŋu awɔe kabakaba ale gbegbe be wòase le eɖokui me enumake. Le xexe si me asitsatsa ŋuti nyatakakawo ƒe 73% ƒe akpa aɖe le teƒe aɖe le dɔwɔƒewo ƒe akɔntabubu nu la, ŋutete ma menye sukudede ɖeɖeko o. Enye hoʋiʋli ƒe viɖe.

Nyabiase Siwo Wobiana Enuenu

Nukae nye ati ene eye aleke wòwɔa dɔe?

Ati ene nye nyatakaka ƒe ɖoɖo si wotu ɖe ati dzi si ma teƒe si le akpa eve me ɖe akpa ene siwo sɔ me gbugbɔgagblɔ. Node ɖesiaɖe ateŋu alé nyatakaka teƒe xexlẽme aɖe si seɖoƒe li na hafi ama ɖe ɖevi node ene me. Mamã sia si le ɖoɖo nu nana be teƒe ƒe biabiawo — abe teƒewo katã didi le nuto aɖe me ene — kabakaba ŋutɔ, si ɖea didiɣi dzi kpɔtɔna tso fli dzi va ɖo logarithmic dzi le nɔnɔme ŋutɔŋutɔ akpa gãtɔ me.

Afikae wozãa ati ene zi geɖe le xexeame ŋutɔŋutɔ ƒe dɔwɔwɔwo me?

| Dɔwɔwɔ ɖesiaɖe si hiã be wòadi, ade eme, alo akpɔ nusiwo woma ɖe akpa eve ƒe teƒe dzi nyuie la ateŋu akpɔ viɖe tso quadtree indexing me.

Aleke ati eneawo sɔ kple teƒe ŋuti nyatakaka ƒe ɖoɖo bubuwo?

To vovo na grid gbadzawo la, ati eneawo trɔa woƒe vovototodedeameme ɖe nyatakakawo ƒe tsɔtsɔme nu — teƒe siwo mebɔ o nɔa ƒuƒlu esime nuto siwo me amewo sɔ gbɔ ɖo la ma ɖe akpa suewo me yi ŋgɔe. Ne wotsɔe sɔ kple k-d-tiwo la, ati eneawo zazã le bɔbɔe wu eye wosɔ nyuie wu na 2D nyatakaka siwo woma ɖekae. R-tiwo kpɔa nuto siwo ƒo xlã wo nɔewo gbɔ nyuie wu, gake quadtrees ɖua dzi le edede ƒe duƒuƒu me eye wòle bɔbɔe be woatsɔ wo asɔ kple wo nɔewo na ɣeyiɣi ŋutɔŋutɔ ƒe dɔwɔwɔ.

Ðe quadtrees ateŋu akpeɖe dɔwɔwɔ nyuie wu le asitsatsa ƒe kɔmpiuta dɔwɔɖoɖowo mea?

Kakaɖedzitɔe. Asitsadɔwɔnu ɖesiaɖe si kpɔa teƒe ŋuti nyatakakawo, teƒe ŋuti numekuku, alo interactive dashboards gbɔ kpɔa viɖe tso quadtree optimization me. Mɔ̃wo abe Mewayz, si nye 207-module business OS si dzea egɔme tso $19/mo, wɔa nyatakaka ƒe ɖoɖo nyui siwo le megbe ŋudɔ tsɔ naa nuteƒekpɔkpɔ siwo le kabakaba, siwo wɔa dɔ nyuie — tso fiase didi ƒe anyigbatatawo dzi va ɖo ɣeyiɣi ŋutɔŋutɔ me numekuku dzi le nyatakaka teƒe akpe geɖewo dzi.