Kuchinja muCartesian Plane
Ndege yeCartesian ipfungwa huru mumasvomhu nejometri, inozivikanwa zvikuru nevadzidzi nenyanzvi dzemasvomhu pasi rose. Ichishandisa sisitimu yekuwirirana yakatangwa naRené Descartes muzana remakore rechi17, ndege yeCartesian inobvumira girafu nekuongorora mabasa nemaumbirwo ejometri munzvimbo ine mativi maviri. Imwe pfungwa inokosha mukuongorora kwejometri yendege yeCartesian ndeyekushandura. Muchinyorwa chino, tichaongorora zvakadzama mhando dzakasiyana dzekuchinja mundege yeCartesian, kusanganisira shanduro, kutenderera, kufungisisa, uye kuwedzera.
1. Shanduro
Kushandura imhando yeshanduko inoshandura poindi yega yega yechinhu nedaro rakafanana uye nenzira imwe chete. MuCartesian plane, shanduro inogona kumirirwa nevector. Semuenzaniso, kana poindi P(x, y) ikashandurwa nevector (a, b), poindi itsva P' ichave pa coordinates (x + a, y + b). Kushandura kwakakosha mumhando dzakasiyana dzemashandisirwo, kubva pa computer graphics kusvika pakuongorora kufamba mu physics.
Semuenzaniso, kana poindi P(2, 3) yakashandurwa nevector (4, -1), ipapo poindi P' ichave pa coordinates (6, 2). Kuchinja uku kunochengetedza chimiro nehukuru hwechinhu, asi kunochinja nzvimbo yacho.
2. Kutenderera
Kutenderera kunotenderera poindi yega yega yechinhu ichi ichitenderedza poindi yepakati yakapihwa nekona chaiyo. MuCartesian plane, kutenderera kunowanzoitwa kutenderedza kwakabva (0, 0). Kutenderera kunogona kuratidzwa sekona inoyerwa mumaradians kana madhigirii.
Fomura yakajairika yekutenderera kwepoindi P(x, y) nekona θ nezvekwakabva (0, 0) ndeiyi:
\[P'(x', y') = (x \cos \theta – y \chivi \theta, x \chivi \theta + y \cos \theta)\]
Ngatitii tinoda kutenderedza poindi P(1, 0) nemadhigirii makumi mapfumbamwe nemana uchitenderera wachi. Nekushandisa fomura yekutenderedza:
\\[P'(x', y') = (1 \cos 90° – 0 \chivi 90°, 1 \chivi 90° + 0 \cos 90°)\]
Mhedzisiro yacho iP'(0, 1).
Kutenderera kushanduka kunochengetedza chimiro nehukuru hwechinhu asi kuchichinja nzira yacho.
3. Kufungisisa
Kufungisisa (Reflection) ishanduko inoratidza poindi yega yega yechinhu maererano nemutsetse wereferensi chaiwo. Mutsetse wereferensi unogona kuva mutsara we x, mutsara we y, kana mitsara ye y = x uye y = -x, kana mimwe mitsara.
Ngatitii mutsetse wekuratidzira uri x-axis, kuratidzwa kwepoindi P(x, y) pa x-axis kuchaburitsa poindi P' iri pama coordinates (x, -y).
Kana tikaratidza poindi Q(3, 4) mu-y-axis, ipapo ma coordinates e reflection inobuda Q' ndiwo (-3, 4). Reflection inochinja mafambiro echinhu asi inochengetedza chimiro nehukuru hwechinhu.
4. Kukura
Kuwedzeredza (dilation) ishanduko inowedzera kana kuderedza saizi yechinhu nechiyero chakati, maererano nenzvimbo yakati yepakati, kazhinji mavambo (0, 0). Kuwedzeredza kunotsanangurwa nechiyero k.
Kana chiyero chiri chikuru kupfuura 1, chinhu chinokura, nepo chiyero chiri pasi pe1, chinhu chinoderera. Fomura yakajairika ndeiyi:
\[ P'(x', y') = (kx, ky) \]
Semuenzaniso, kana tikaisa mutsetse papoindi R(2, 3) nechiyero che2:
\[ R'(x', y') = (2 \cdot 2, 2 \cdot 3) = (4, 6) \]
Kukura uku kunowedzera daro renzvimbo kubva pakabva chinhu chakatarwa uye kunochinja saizi yese yechinhu, asi kunochengetedza chimiro chechinhu chacho.
Kushandiswa kweShanduko
Kuchinja-chinja muCartesian plane kune mashandisirwo akapararira muzvikamu zvakasiyana-siyana zvesainzi neinjiniya. Mumifananidzo yemakombiyuta, kushanduka kwejometri kunoshandiswa kushandura mifananidzo nezvinhu zvine mativi matatu pachiratidziro chekombiyuta. Semuenzaniso, mumifananidzo, kushanduka kwakadai sekushandura nekutenderera kunoshandiswa kutevedzera kufamba.
Munyaya yefizikisi, shanduko dzinoshandiswa kuongorora kufamba kwezvinhu. Kuchinja kwakarongeka kunogona kuita kuti zvive nyore kuverenga nzira kana shanduko munzvimbo yezvinhu zviri muchadenga. Mumarobhoti, shanduko dzinobatsira mukugadzira mafambiro emarobhoti uye kufamba.
Muinjiniya yezvivakwa nekuvaka, shanduko dzejometri dzinobatsira mukugadzira nekuongorora zvivakwa, kusanganisira mukuita kwemifananidzo ye3D.
Nyanzvi dzemasvomhu nemainjiniya vanowanzo shandisa shanduko kuti vanzwisise zvakadzama hunhu husingachinji hwezvinhu zvejometri. Izvi zvinobatsira mukuratidza humwe hunhu hwejometri uye zvinobvumira vashandisi kugadzirisa matambudziko akaomarara mumasvomhu anoshandiswa.
Penutup
Kuchinja-chinja muCartesian plane kunopa maturusi ane simba ekuongorora nekushandura chimiro nenzvimbo yezvinhu zviri munzvimbo dzine mativi maviri. Nekunzwisisa pfungwa huru dzakadai sekushandura, kutenderera, kufungisisa, uye kuwedzera, tinogona kunzwisisa runako rwemasvomhu rwe geometry uye mashandisirwo aro muzvikamu zvakawanda zvesainzi netekinoroji. Kuchinja uku hakungopi nzira yekuona nyika yedu zvakarongeka, asiwo kunogonesa kushandiswa kweruzivo irworwo mumhando dzakasiyana-siyana dzehunyanzvi nesainzi.
