Ukwanda Kwezibalo: Ukushintsha Usayizi Ngaphandle Kokushintsha Isimo
I-Pendahuluan
Kumathematika, umqondo wokwanda udlala indima ebalulekile, ikakhulukazi ku-geometry. Ukwanda, noma ukuguqulwa okulinganayo, inqubo yokukhulisa noma ukunciphisa into ngaphandle kokushintsha isimo sayo sokuqala. Le nqubo ihilela ukusebenzisa isikali esithile ukukhulisa noma ukunciphisa yonke into ngokulinganayo. Lesi sihloko sizohlola umqondo, ukusetshenziswa, kanye nezibonelo zokwanda kwezibalo ngokujulile.
Izincazelo kanye Nemiqondo Eyinhloko
Ukwanda kobukhulu kuwuhlobo lokuguqulwa kwejiyometri olushintsha usayizi wesimo ngokusekelwe kusici sesikali, kuyilapho kugcinwa ukufana kwesimo. Ngamagama alula, ukwanda kobukhulu kubhekisela ekuguqulweni lapho usayizi wento ukhuliswa noma uncishiswa, kodwa isimo kanye nokuma kwento kuhlala kungashintshi.
Uma sichaza into ngama-coordinates endizeni enezinhlangothi ezimbili (2D), khona-ke ukuguqulwa kobubanzi kungavezwa ngefomula elula yezibalo. Ake sithi sinephuzu eline-coordinates (x, y) esifuna ukuyiguqula nge-scale factor k. Ama-coordinates amasha ephuzu yi-(kx, ky).
Uma u-k > 1, into izokhuliswa. Uma u-0 < k < 1, into izoncishiswa. Isibonelo, uma sinonxantathu onamaphuzu u-A(2, 3), u-B(4, 6), no-C(6, 5), futhi sifuna ukwandisa unxantathu ngesilinganiso esingu-2, khona-ke amaphuzu amasha kanxantathu yi-A'(4, 6), u-B'(8, 12), no-C'(12, 10).
Indlela Ukwanda Okusebenza Ngayo Ukuze siqonde ukuthi ukwanda kusebenza kanjani, kumelwe sicabangele izinto ezimbili ezibalulekile: 1. Isikhungo Sokwanda: Iphuzu eliqondile lapho amabanga awo wonke amaphuzu entweni ephindaphindwa khona ngesici sesikali. Lesi sikhungo singaba ngaphakathi, ngaphandle, noma ngqo kwelinye lamaphuzu ento. 2. Isici Sesilinganiso (k): Inani elisetshenziselwa ukuphindaphinda amabanga ukusuka enkabeni yokwanda kuya kuwo wonke amaphuzu entweni. Isibonelo, uma isici sesikali singu-2, khona-ke wonke amabanga ukusuka enkabeni yokwanda kuya emaphuzwini ento azophindwa kabili. Ake sithi isikhungo sokwanda sisekuqaleni (0,0). Uma iphuzu A(x, y) entweni yokuqala likhuliswa yisici sesikali k, khona-ke izixhumanisi ezintsha ze-A' zizoba (kx, ky). Kulesi simo, umugqa oxhumanisa isikhungo sokwanda kuya ephuzwini entweni yokuqala kanye nephuzu entweni ekhulisiwe lizohlala liqondile, okubonisa ukuthi into ikhulisiwe noma incishisiwe ngokulinganayo. Ukusetshenziswa Kokunwebeka Empilweni Yansuku Zonke 1. Ukudweba Nokunwebeka: Ukudweba kuvame ukusebenzisa umqondo wokwelulwa. Isibonelo, imephu yedolobha noma yezwe. Imephu enjalo iwukwelulwa kwendawo yangempela ngesici esithile sesikali, okuvumela ukwethulwa kwedatha yendawo ngendlela egayeka kalula. 2. Ukuthwebula Izithombe Nokuklama Imidwebo: Ezweni lokuthwebula izithombe nokuklama imidwebo, ukunwebeka kusetshenziswa kakhulu ekushintsheni usayizi wezithombe nemifanekiso. Le nqubo idinga ukwenziwa ngaphandle kokushintsha isilinganiso sesici (izilinganiso) sesithombe ukuze kugwenywe ukuphambuka. 3. Ukumodela Kwezibalo: Ekumodeleni kwezibalo, ikakhulukazi ku-physics nobunjiniyela, ukunwebeka kusetshenziswa ukulingisa izimo ezahlukene ngaphandle kokushintsha isimo esiyisisekelo semodeli. Isibonelo, ekulingiseni izakhiwo zokwakha, ukusetshenziswa kokunwebeka kungasiza ekuboneni umphumela wokwandisa isikali ngaphandle kokushintsha izilinganiso zezingxenye ngazinye. Izibonelo Zezinkinga Nezixazululo Inkinga 1: Cabanga ngephuzu P(3, 4) endizeni yokuhlela. Nweba leli phuzu ngesikhungo ku-(0,0) usebenzisa i-scale factor engu-3. Isixazululo: Iphuzu P line-coordinates (3,4). Uma sisebenzisa i-scale factor engu-3, siphindaphinda i-coordinates ngo-3: \[ P'(x', y') = (3 3, 3 4) = (9, 12) \] Ngakho-ke, iphuzu elisha P' ngemva kokunwebeka lingu-(9,12). Umbuzo 2: Unxantathu unamaphuzu A(1, 2), B(3, 4), kanye no-C(5, 6). Faka ukunwetshwa okunesikhungo ku-(0,0) kanye nesilinganiso se-0.5. Isixazululo: Iphuzu A(1,2): \[ A'(x', y') = (0.5 1, 0.5 2) = (0.5, 1) \] Iphuzu B(3,4): \[ B'(x', y') = (0.5 3, 0.5 4) = (1.5, 2) \] Iphuzu C(5,6): \[ C'(x', y') = (0.5 5, 0.5 6) = (2.5, 3) \] Ngakho-ke, ukubalwa ngemva kokwelulwa konxantathu kuzoba namaphuzu A'(0.5,1), B'(1.5,2), kanye no-C'(2.5,3). Ubudlelwano Nezinye Izinguquko Ngaphandle kokwelulwa, ezinye izinguquko ezahlukahlukene zaziwa ngejiyometri njengokuhumusha, ukujikeleza, kanye nokuzindla. Kodwa yini ehlukanisa ukwelulwa kulezi zinguquko? - Ukuhumusha kuhambisa into kusuka endaweni eyodwa kuya kwenye endizeni yokuxhumanisa ngaphandle kokushintsha usayizi wayo, isimo, noma ukuma kwayo. - Ukujikeleza kujikeleza into ezungeze isikhungo sokujikeleza nge-engeli ethile, kugcina usayizi wayo nesimo sayo kodwa kushintsha ukuma kwayo. - Ukuzindla kushintsha indawo yento ngokusekelwe emgqeni wokuzindla, njengokubonisa into emgqeni ukukhiqiza isimo esilinganayo. Okwamanje, ukwelulwa, ikakhulukazi, kushintsha usayizi kuphela ngenkathi kugcina isimo sayo nokuma kwayo. Isiphetho Ukwelulwa kungumqondo obalulekile wezibalo ekuqondeni ukuthi izinto zingashintshwa kanjani ngokulingana. Ukukhulisa noma ukunciphisa into ngaphandle kokushintsha isimo sayo esiyisisekelo kuyisisekelo sezinhlelo zokusebenza ezahlukahlukene emikhakheni ehlukahlukene, kusukela ekumepheni kuya ekwakhiweni kwezithombe, kanye nokulingisa kobunjiniyela. Ukuqonda nokusebenzisa ukunwebeka kuvula umnyango wezinhlobo eziyinkimbinkimbi kakhulu zokuguqulwa kwejometri kanye nokusetshenziswa kwazo okungokoqobo empilweni yangempela. Njengenye yamathuluzi amaningi asetshenziswa kwizibalo nesayensi, lo mqondo usikhumbuza iqiniso elibalulekile: usayizi ungashintsha, kodwa isimo kanye nomongo kuhlala kungaguquki.