Qhia cov duab ntawm lub dav hlau (txhais lus)

2024 Tus sau: Leah Sherlock | [email protected]. Kawg hloov kho: 2023-12-17 05:37

Kev muaj peev xwm ua kom pom cov duab sib txawv ntawm lub dav hlau ntawm daim ntawv, canvas thiab lwm qhov chaw yog qhov txuj ci tseem ceeb. Thiab qhov tseem ceeb tshaj plaws, nws yog ib qho tseem ceeb rau cov neeg ua yeeb yam: cov neeg pleev kob, sculptors, cov duab kos duab, cov neeg tsim qauv (ntawm cov chaw sab hauv thiab cov chaw tsim vaj tsev), thiab rau cov neeg ntawm kev tshawb fawb: lej, physicists, designers, inventors.

Tab sis kuj yog ib qho tseem ceeb rau tus neeg uas nyob deb ntawm cov spheres no kom kawm paub yuav ua li cas thiaj paub thiab pom lub ntiaj teb nyob ib puag ncig nws. Qhov no yuav pab kom nkag siab ntau ntxiv rau tag nrho nws cov versatility. Yog tias koj tsis muaj lub tswv yim txaus ntawm yuav ua li cas kom raug, ces koj feem ntau yuav tsis ua tiav hauv ib qhov project, duab lossis kos duab ntawm ib qho invention. Ntawd yog, qhov txuj ci no tseem ceeb ob qho tib si rau kev daws cov haujlwm yooj yim, txhua hnub, thiab rau cov uas muaj lub ntiaj teb, qhov tseem ceeb thoob ntiaj teb.

keeb kwm me ntsis

Txij thaum ub, tib neeg tau sim piav txog qhov lawv pom nyob ib puag ncig lawv: lwm tus neeg, qee lub tsev qub qub ntawm lub sijhawm ntawd, lub ntiaj teb zoo nkauj zoo nkauj ntawm cov nroj tsuag thiab tsiaj txhu, roob majestic, thiab tej yam yooj yim, khoom siv hauv tsev. Qhov ntawd yog, lub ntiaj teb nyob rau hauv tag nrho nws ntau haiv neeg thiab grandeur.

Tab sis tom qab ntawd lawv tseem tsis tau paub yuav ua li cas nws thiaj li ua tau kom raug thiab muaj peev xwm, kom pom ntau yam khoom peb sab hauv lub dav hlau yog qhov tseeb tiag, ciaj sia. Tus neeg ntawd tsis muaj kev paub txog thiab, tsis tas li ntawd, tsis muaj kev txawj tshwj xeeb, tshwj tsis yog tej zaum rau cov qib qis tshaj plaws.

Nws tau hais nyob rau hauv qhov chaw ua ntej tias thawj daim duab hauv ntiaj teb muaj tsuas yog ib txoj kab uas mus raws tus duab ntxoov ntxoo ntawm ib tug neeg los ntawm lub hnub rau ntawm phab ntsa. Ntawd yog, xwm nws tus kheej tau hais qhia nyob rau hauv qhov kev taw qhia nws tsim nyog txav mus rau hauv kev tshawb nrhiav qhov kev daws teeb meem rau qhov teeb meem no.

Thiab cov lus nug no txhawj xeeb tus txiv neej ntawm lub sijhawm ntawd kuj yog vim li no: nws tsis yog xav qhuas lub silhouette nyob voluminous, tus thawj, yog li hais, tab sis nrhiav kom ntes ib qho khoom siv dav hlau. Thiab nws ua li no kom nws thiaj li kho tau nws lub tsev lossis qhov chaw dawb huv rau nws, lossis nqa ib lub nras nrog nws thiab txav mus rau qhov deb.

Pattern geometry

Thiab txhua yam koj hais, tab sis xyoo dhau los, ntau pua xyoo dhau los, thiab qee yam, raws li kev vam meej tau tsim, tib neeg maj mam kawm kom pom cov duab nyuaj hauv qhov chaw ob sab, uas yog, ntawm lub dav hlau. Tsuas yog tam sim no qhov tseeb ntawm qhov ntau thiab tsawg ntawm cov khoom piav qhia pib zoo li kwv yees.

Tab sis cov lus nug ntawm yuav ua li cas kom raug cov duab ntawm daim duab ntawm lub dav hlau thiab ntau npaum li cas lawv sib haum rau lub ntim ntawm cov khoom qub, ib zaug dhau los ua qhov tseem ceeb heev. Nyob rau hauv ib txoj kev, ib tug tshiab science hu uageometry. Ntau precisely, nws seem yog piav geometry.

Ntawm no nws tsuas yog kawm cov duab thiab dav hlau, kab thiab cov ntsiab lus, nrog rau lawv txoj kev sib raug zoo ntawm ib leeg - ob qho tib si hauv qhov chaw peb sab thiab ob sab.

Kev hloov pauv txoj hauv kev

Ib qho tseem ceeb hauv kev kos duab kos duab yog kev nthuav qhia cov duab ntawm lub dav hlau duab. Tom qab tag nrho, qhov tseeb, qhov no yog kev ntes ntawm peb-dimensional spatial khoom nyob rau hauv ob-dimensionality. Namely: lub complex yuav tsum tau hloov dua siab tshiab rau hauv ib qho yooj yim, uas yog, ib yam khoom uas muaj ib tug ntev, dav, qhov siab yuav tsum tau pauv mus rau ib tug dav hlau.

Thiab piav qhia txog geometry ua rau "kev hloov pauv" ua tsaug rau qee txoj hauv kev. Muaj txog rau ntawm lawv nyob rau hauv tag nrho. Nov yog peb qhov tseem ceeb thiab nrov tshaj plaws thoob ntiaj teb:

• kev pom (thaum cov khoom piav qhia raug tshem tawm hauv qhov chaw);
• orthogonal projection (kev kwv yees nyob rau hauv parallel, qhov twg cov rays yog perpendicular rau lub dav hlau);
• oblique projection (projection in parallel, where the rays are tilted relative to the dav hlau).

Cov duab kos pom pom meej meej hauv axonometric projection (uas suav nrog orthogonal thiab oblique). Tab sis nws yog kwv yees kom meej meej thiab tiag tiag thaum nws pom nyob rau hauv foundations. Thiab nws yog txoj hauv kev saum toj no uas daws cov lus nug ntawm yuav ua li cas tso cov duab ntawm lub dav hlau.

Kev xav

Kev pom yog qhov chaw muaj koob meej tshaj plaws ntawm lwm txoj hauv kev ntawm cov duab. Vim tib neeg qhov muagzoo li lub koob yees duab lens, nws pom qhov chaw nyob ib puag ncig zoo ib yam. Tej yam uas nyob deb ntawm tus neeg soj ntsuam tshwm sim me me, thiab qee zaum me dua, dua li thaum lawv nyob ze.

Piv txwv li, muab cov duab ntawm lub voos xwmfab hauv qhov chaw. Yog hais tias, qhov tseeb, tag nrho nws cov npoo yog sib npaug rau ib leeg, ces thaum koj saib cov khoom no nyob rau hauv qhov kev ncua deb, nws yuav zoo li tias cov npoo converge (los yog yuav tsum converge) ntawm ib qho chaw. Thiab, dab tsi yog qhov nthuav tshaj plaws, lawv yuav tsum tsis yog sib koom ua ke ntawm ib qho chaw, tab sis muaj ib qho kev sib tshuam taw tes.

Ua tsaug rau cov tswv ntawm Renaissance: Albrecht Dürer, Piero Della Francesca, Andrea Mantegna, Leon Batista Alberti, niaj hnub painting paub dab tsi ncaj linear foundations yog, yuav ua li cas txiav txim siab qhov siab ntawm lub qab ntug thiab vanishing cov ntsiab lus.

Thiab lub ntiaj teb nto moo txawj ntse - Leonardo da Vinci - thawj zaug sib cav txog lub tswv yim ntawm huab cua. Qhov no suav nrog kev hloov ntawm cov xim, lub suab ntawm cov khoom, kev hloov pauv ntawm nws cov yam ntxwv sib txawv (tso zuj zus raws li cov khoom txav mus deb).

kev ua yeeb yam

Orthogonal yog hu ua parallel projection, uas yog coj mus rau ib txoj kab ncaj nraim, uas yog perpendicular rau lub dav hlau. Nyob rau hauv tus txheej txheem ntawm nws daim ntawv thov, qhov ntev ntawm lub contours ntawm cov khoom nyob twj ywm unchanged. Ntawd yog, cov khoom raug nthuav tawm yam tsis muaj kev cuam tshuam.

Lub phiaj xwm peb-dimensional yog, raws li nws tau, decomposed rau hauv peb qhov kev pom: los ntawm sab, sab xub ntiag thiab sab saud. Thiab saib txhua qhov no tib lub sijhawm, koj tuaj yeem ntxivib tug sawv cev ntawm yam khoom zoo li hauv ntim. Tib lub sijhawm, qhov ntev ntawm daim duab tseem tsis hloov pauv ob qho tib si hauv daim duab peb sab thiab hauv ob sab ib.

Oblique projection

qhov kev kwv yees no tau muab faib ua ntau yam ntxiv, xws li:

• isometric saib;
• dimetric projection;
• trimetric projection.

Isometric muaj qhov sib txawv ntawm txhua 3 axes (ntev, dav, qhov siab). Ntawd yog, lub kaum sab xis ntawm qhov sib npaug ntawm cov axes yog sib npaug li 120 degrees. Nyob rau hauv lub dimetric ib, qhov distortions raws 2 axes yog sib npaug, thiab qhov thib peb yog txawv. Thiab nyob rau hauv lub trimetric projection, tag nrho cov distortion coefficients (uas yog, nrog rau tag nrho cov 3 axes) txawv.

Zoo ntawm kev sib hloov

Thaum ib daim duab peb sab sab xis tig raws lub axis ntawm ib qho ntawm ob txhais ceg, nws sab thib peb (hypotenuse) yuav piav qhia txog daim duab tshiab hu ua lub khob hliav qab. Thiab yog tias koj tig lub duab plaub (square) raws ib qho ntawm nws sab, koj tau txais lub tog raj kheej. Thaum lub semicircle tig, ib tug kheej kheej yuav tawm.

Nws ua raws li los ntawm kev tig lub dav hlau raws qee qhov axis, peb tau txais qhov hu ua cov lej ntawm kev sib hloov.

Cov duab no muaj qhov axis ntawm kev sib hloov. Yuav ua li cas lawv saib nyob rau hauv lub dav hlau nyob ntawm lawv qhov kev tso kawm txheeb ze rau qhov muag. Piv txwv li, sab saum toj thiab hauv qab ntawm lub tog raj kheej yog qhov tseem ceeb ntawm lub voj voog. Thiab yog tias koj saib lawv hauv lub dav hlau, lawv zoo li ellipses.

Tab sis txoj haujlwm yuav nyuaj dua yog tias, thaum tso tawmspatial cov duab ntawm lub dav hlau, lawv muaj ib tug inclined axis. Nyob rau hauv cov ntaub ntawv no, nws yog ib qho tseem ceeb uas lub contours ntawm lub cev ntawm kiv puag ncig yog equidistant los ntawm lub axis ntawm lub tom kawg.

Ib me ntsis txog chiaroscuro

Chiaroscuro ua lub luag haujlwm tseem ceeb hauv kev nthuav tawm cov duab ntawm lub dav hlau. Vim hais tias lub ntim ntawm cov duab piav qhia yog tsim tsis tsuas yog vim cov kab, tab sis kuj yog vim qhov tseeb tis ntawm lub teeb thiab duab ntxoov ntxoo ntawm nws sab. Thiab ces nws zoo nkaus li voluminous nyob rau hauv lub dav hlau ntawm ib tug ob-dimensional nto.

Yog li, cov duab ntawm cov duab ntawm lub dav hlau, txiav txim siab lawv qhov ntau thiab tsawg, cov yam ntxwv ntawm qhov tseeb overlay ntawm lightness thiab tsaus me ntsis yog ua tau heev ua tsaug rau cov saum toj no txoj kev. Thiab, qhov tseem ceeb tshaj, cov no yog cov txheej txheem pov thawj tiag tiag hauv kev xyaum, uas yog siv los ntawm cov kws tshaj lij ntawm peb lub sijhawm.