Piav txog kev daim nyob rau hauv ib tug dav hlau (nrhiav kom tau)

Cov muaj peev xwm kom zoo zoo tso saib ntau daim nyob rau hauv lub dav hlau daim ntawv, canvas, thiab lwm yam nto yog sufficiently tseem ceeb kev txawj. Thiab saum toj no tag nrho, nws yog ib qho tseem ceeb rau cov neeg nyob rau hauv lub kos duab: painters, sculptors, graphic ntxias, designers (sab hauv tej qhov chaw ntawm cov vaj tse thiab architectural ib puag ncig) thiab rau cov txiv neej ntawm kev kawm: mathematicians, physicists, designers thiab inventors.

Tab sis tus txiv neej deb ntawm cov chaw no rau kawm tau li cas rau perceive thiab muaj kev cuam tshuam lub ntiaj teb no nyob ib ncig ntawm peb yog tseem ceeb heev. Qhov no yuav pab npaum li cas ntxaum tsuab tag nrho nws cov versatility. Yog hais tias koj tsis muaj txaus cov tswv yim hais txog yuav ua li cas yuav ua rau nws kom raug, ces koj feem ntau yuav yuav tsis tau qhov zoo tshaj plaws tsim, daim duab los yog kos duab ntawm tej invention. Hais tias yog, qhov no muaj kev txawj yog ib qho tseem ceeb ob leeg rau tej yam yooj yim, txhua hnub paub tab thiab muaj ib lub ntiaj teb no, universal tseem ceeb.

Ib me ntsis keeb kwm

Los ntawm ancient sij hawm tus neeg tau sim depict dab tsi lawv pom ib ncig ntawm lawv: lwm tus neeg, tej yam txheej thaum ub qauv ntawm cov sij hawm, cov amazingly zoo nkauj ntiaj teb no ntawm cov nroj tsuag thiab tsiaj txhu, majestic roob, thiab cia li yam, tsev neeg cov khoom. Qhov ntawd yog lub ntiaj teb no nyob rau hauv tag nrho nws cov ntau haiv neeg thiab grandeur.

Tab sis, ces lawv tsis muaj ib tug clue txog yuav ua li cas nws yog ua tau mus nqa tawm meej thiab raug los tso saib sib txawv seem rau lub dav hlau twb yeej muaj tiag, ciaj sia. Muaj ib tug neeg ntawm cov txuj ci thiab tshwj xeeb tshaj yog tsis muaj kev txawj, tsuas yog, tej zaum, cov yooj yim tshaj plaws.

Hais lus ua ntej lawm qhov chaw uas lub ntiaj teb no tus thawj painting tsuas yog ib tug kab, uas khiav raws tus tib neeg ntxoov ntxoo nrum los ntawm lub hnub nyob rau hauv lub phab ntsa. Qhov ntawd yog qhov xwm heev pom tias, yuav tsum mus nyob rau hauv kev tshawb fawb ntawm txoj cai tshuaj rau qhov no qhov teeb meem nyob rau hauv cov kev taw qhia.

Thiab rau lo lus nug hais tias kev kub ntxhov tus neeg ces kuj rau no yog vim li cas: nws tsis xav kom cia li txaus siab rau cov surround ciaj sia silhouette, thawj, thiaj li mus hais lus, thiab sim mus ntes tus peb-dimensional khoom rau lub dav hlau. Thiab nws ua li ntawd no nyob rau hauv thiaj li yuav tau nyob rau hauv no txoj kev los sis rau decorate koj lub tsev los yog qhov chaw dawb ceev rau nws, los yog coj ib tug parcel nrog ib daim duab thiab txav ntawd mus rau ib ncua deb.

Lub geometry ntawm daim duab

Thiab txawm koj hais, tab sis lub xyoo dhau lawm, centuries dhau los, thiab ua cas nyob rau hauv txoj kev loj hlob ntawm kev vam meej, cov neeg tau kawm los maj mam qhia txoj rho nyob rau hauv ob qhov ntev, uas yog, nyob rau lub dav hlau. Tshwj tias seem raug thiab proportions ntawm lub xwm khoom tshwm sim los ua heev approximate.

Tab sis cov nqe lus nug ntawm yuav ua li cas zoo cov zaub ntawm cov nuj nqis nyob rau hauv lub dav hlau thiab yuav ua li cas lawv sib haum mus rau lub ib thooj ntawm cov thawj kwv, kuj yog ib qho tseem ceeb heev. Nyob rau hauv ib txoj kev nyob rau hauv hais no qhov teeb meem tau pab tshiab science hu ua Geometry. Los yog es, nws seem - uas piav txog geometry.

Ntawm no nws yog cia li kawm nrhiav thiab dav hlau, cov kab ncaj nraim thiab cov ntsiab lus, raws li tau zoo raws li lawv cov kev sib raug zoo rau txhua tus lwm yam - ob yam tib si nyob rau hauv peb qhov ntev thiab nyob rau hauv ob-seem qhov chaw.

hloov dua siab tshiab txoj kev

Ib qho tseem ceeb feature nyob rau hauv kos duab yog muab los tso rau cov nuj nqis ntawm daim duab dav hlau. Tom qab tag nrho cov, nyob rau hauv qhov tseeb, yog lub imprint ntawm peb seem nyob rau hauv ob-seem. Namely, ib tug complex yuav tsum tau hloov dua siab tshiab mus rau ib tug yooj yim, uas yog, ib tug kwv uas muaj ib tug ntev, dav, qhov siab, yuav tsum tau txhais mus rau hauv lub dav hlau.

Thiab yuav piav txog geometry ce xws "zaus", ua tsaug rau ib co kev. Lawv tag nrho, muaj txog rau. Ntawm no yog cov peb lub ntsiab sawv daws yuav, thiab feem ntau nrov nyob rau hauv lub ntiaj teb no:

• Pem taub (thaum cov duab kwv yog tshem nyob rau hauv qhov chaw);
• orthogonal projection (projection nyob rau hauv parallel, qhov twg lub rays yog perpendicular mus rau lub dav hlau);
• oblique projection (projection nyob rau hauv thaum uas tig mus, qhov twg beams tau ris txheeb ze mus rau ib tug dav hlau).

Suffice nws zoo nkaus li kom meej meej duab yam khoom nyob rau ntawm ib axonometric saib (uas muaj xws li orthogonal thiab oblique). Tab sis lub meej tshaj plaws thiab muaj tseeb, nws yog npaj raws li ib tug kev xav. Thiab nws yog saum toj no txoj kev lom zem ntau daws tau qhov teeb meem ntawm yuav ua li cas yuav ua rau cov zaub ntawm cov nuj nqis rau lub dav hlau.

foundations

Pem taub cov lwm txoj kev rau cov duab yuav siv sij hawm qhov chaw ntawm yawm. Vim hais tias cov tib neeg qhov muag raws li ib tug lub koob yees duab lens pom surrounding chaw nyob rau hauv ib txoj kev zoo. Tej yam uas yog deb ntawm lub observer, nyob rau hauv nws me me saib me me, thiab tej zaum kuj tsawg npaum li cas, dua li thaum lawv nyob ze.

Piv txwv li, muab ib daim duab ntawm ib lub voos xwmfab nyob rau hauv qhov chaw. Yog hais tias, nyob rau hauv qhov tseeb, tag nrho cov ntawm cov npoo yog thaum uas tig mus rau txhua lwm yam, ces thaum koj saib nyob rau ntawm no kwv nyob rau hauv qhov kev ncua deb, tej zaum nws yuav zoo li hais tias tus sawv los sib (los yog yuav tsum los sib) nyob rau hauv ib tug taw tes. Thiab, yog dab tsi feem ntau nthuav, tsis yog muaj tuaj ua ke nyob rau ib tug taw tes thiab muaj ib tug taw tes ntawm kev tshuam.

Tsaug rau cov masters ntawm lub Renaissance: Albrecht Dürer, Piero della Francesca, Andrea Mantegna, Leon Battista Alberti, niaj hnub kos duab paub hais tias xws li ib tug tib neeg linear foundations, yuav ua li cas los mus txiav txim rau qhov siab ntawm lub qab ntug thiab vanishing cov ntsiab lus.

Ib lub ntiaj teb no-nrov ntse heev - Leonardo da Vinci - sib cav rau thawj lub sij hawm lub tswvyim ntawm sim saum nruab ntug foundations. Qhov no hloov xim tus kwv xim, txawv kev hloov nyob rau hauv nws tus yam ntxwv (txo raws li qhov kev ncua deb ntawm tus kwv).

orthogonal projection

Orthogonal hu ua thaum uas tig mus projection, uas yog raws kev coj kom lub kab, uas yog perpendicular txheeb ze rau lub dav hlau. Thaum lub sij hawm nws daim ntawv thov tus kwv nkhaus qhov ntev nyob twj ywm unchanged. Hais tias yog, tus kwv yog tso tawm tsis muaj distortion.

Lub pob peb-dimensional kwv li nws yog decomposed rau hauv peb hom: sab, pem hauv ntej thiab sab saum toj. Thiab saib nws tag nrho cov nyob rau tib lub sij hawm, nws yog ua tau rau nteg cia ib lub tswv yim yuav ua li cas tus kwv zoo nyob rau hauv volume. Lub qhov ntev ntawm cov nuj nqis nyob twj ywm unchanged nyob rau hauv lub peb-dimensional duab, thiab tus ob-seem.

oblique projection

Qhov no projection subdivided rau hauv ob peb subspecies, namely:

• isometric saib;
• dimetric projection;
• Trimetric.

Nyob rau hauv isometric distortion coefficients nyob rau hauv tag nrho cov 3 axes (qhov ntev, dav, qhov siab). Piv txwv li lub ces kaum ntawm lub axes yog npaum li cas nyob rau hauv officers 120 degrees. Nyob rau hauv dimetric - 2-axis distortion sib npaug thiab qhov peb yog sib txawv. Thiab Trimetric tag nrho distortion coefficients (i.e., rau tag nrho 3 axes) yog cov sib txawv.

cov nuj nqis kev sib hloov

Thaum rotating ib txoj cai daim duab peb sab nrog ib tug axis ntawm ib tug ntawm ob txhais ceg ntawm nws thib peb tog (lub hypotenuse) piav ib tug tshiab zoo, uas yog hu ua ib tug lub khob hliav qab. Thiab yog hais tias koj tig tus duab plaub (square) nyob rau ib qho ntawm nws sab, peb tau txais ib tug lub tog raj kheej. Thaum rotating cov voj voog yuav Kheej.

Nws hais ntxiv hais tias lub rotating dav hlau nrog ib tug axis, peb muab tau cov thiaj li hu ua kev sib hloov daim duab.

Cov nuj nqis muaj ib tug muab axis. Txoj kev uas lawv saib nyob rau hauv lub dav hlau nyob rau qhov kev tso kawm txheeb ze rau qib qhov muag. Piv txwv li, lub Upper thiab qis sab ntawm tus kheej kheej, nyob rau hauv qhov tseeb, sawv cev rau cov nram qab no. Thiab yog hais tias koj saib nyob rau ntawm lawv nyob rau hauv ib tug dav hlau, lawv zoo li ellipses.

Tab sis neeg ua hauj lwm yuav txawm nyuab dua yog hais tias tus kuas ntawm spatial nuj nqis uas lawv tau ris axis dav hlau. Nws yog ib qho tseem ceeb tias cov muab nkhaus ntawm lub cev twb equidistant los ntawm lub axis ntawm lub yav tas.

Ib me ntsis ntawm lub teeb thiab ntxoov ntxoo

Ib qho tseem ceeb luag hauj lwm nyob rau hauv displaying rau daim nyob rau lub dav hlau ua si chiaroscuro. Vim hais tias lub ib thooj ntawm cov xwm kwv yog tsim tsis tsuas los ntawm cov kab, tab sis kuj los ntawm ib tug muab faib rau ntawm lub teeb thiab duab ntxoov ntxoo nyob rau hauv nws cov sab. Thiab ces nws zoo nkaus li kuj voluminous nyob rau hauv lub dav hlau ntawm ob-dimensional nto.

Yog li, cov nuj nqis ntawm cov zaub dav hlau, lub ntsiab txhais ntawm lawv loj, tshwj xeeb yog muaj tseeb overlay lightness thiab tsaus me ntsis nws yog tau mus nqa tawm vim yog lub saum toj no txoj kev. Thiab, tseem ceeb tshaj, nws tau tiag tiag pov thawj txoj kev uas yog siv los ntawm ua tshwj xeeb ntawm peb lub sij hawm.