თამარ ბერიძე საინჟინრო გეომეტრიისა და სამრეწველო დიზაინის ზოგიერთი ერთობლივი ამოცანა და მათი გადაწყვეტის მაგალითები

Transcript

1 თამარ ბერიძე საინჟინრო გეომეტრიისა და სამრეწველო დიზაინის ზოგიერთი ერთობლივი ამოცანა და მათი გადაწყვეტის მაგალითები წარმოდგენილია დოქტორის აკადემიური ხარისხის მოსაპოვებლად საქართველოს ტექნიკური უნივერსიტეტი თბილისი, 0175, საქართველო 2012 წელი საავტორო უფლება თამარ ბერიძე, 2012 წელი i

2 საქართველოს ტექნიკური უნივერსიტეტი satransporto da manqanatmseneblobis fakulteti ჩვენ, ქვემორე ხელისმომწერნი ვადასტურებთ, რომ გავეცანით თამარ ბერიძის მიერ შესრულებულ სადისერტაციო ნაშრომს დასახელებით: sainjinro geometriisa da samrewvelo dizainis zogierti ertoblivi amocana da mati gadawyvetis magalitebi და ვაძლევთ რეკომენდაციას საქარველოს ტექნიკური უნივერსიტეტის satransporto da manqanatmseneblobis fakultetis სადისერტაციო საბჭოში მის განხილვას დოქტორის აკადემიური ხარისხის მოსაპოვებლად. თარიღი ხელმძღვანელი: პროფესორი: ანზორ შავგულიძე პროფესორი: ინესა ხატისკაცი რეცენზენტი: რეცენზენტი: ii

3 საქართველოს ტექნიკური უნივერსიტეტი 2012 წელი ავტორი: დასახელება: თამარ ბერიძე საინჟინრო გეომეტრიისა და სამრეწველო დიზაინის ზოგიერთი ერთობლივი ამოცანა და მათი გადაწყვეტის მაგალითები ფაკულტეტი : ხარისხი: სატრანსპორტო და მანქანათმშენებლობის დოქტორი სხდომა ჩატარდა: ინდივიდუალური პიროვნებების ან ინსტიტუტების მიერ ზემომოყვანილი დასახელების დისერტაციის გაცნობის მიზნით მოთხოვნის შემთხვევაში მისი არაკომერციული მიზნებით კოპირებისა და გავრცელების უფლება მინიჭებული აქვს საქართველოს ტექნიკურ უნივერსიტეტს. ავტორის ხელმოწერა ავტორი ინარჩუნებს დანარჩენ საგამომცემლო უფლებებს და არც მთლიანი ნაშრომის და არც მისი ცალკეული კომპონენტების გადაბეჭდვა ან სხვა რაიმე მეთოდით რეპროდუქცია დაუშვებელია ავტორის წერილობითი ნებართვის გარეშე. ავტორი ირწმუნება, რომ ნაშრომში გამოყენებული საავტორო უფლებებით დაცული მასალებზე მიღებულია შესაბამისი ნებართვა (გარდა ის მცირე ზომის ციტატებისა, რომლებიც მოითხოვენ მხოლოდ სპეციფიურ მიმართებას ლიტერატურის ციტირებაში, როგორც ეს მიღებულია სამეცნიერო ნაშრომების შესრულებისას) და ყველა მათგანზე იღებს პასუხისმგებლობას. iii

4 რეზიუმე sainjinro geometriis matematikuri da teqnikuri midgomebi da definaciebi Zalian axlos aris ertmanettan, magram pirveli problemis Teoriul mxareze aketebs aqcents, xolo meorekonkretuli teqnikuri amocanis realizaciaze. sadisertacio nasromsi SerCeuli da gamokvleulia sainjinro geometriis iseti midgomebi, romlebic, Cveni azrit, samrewvelo dizainis teqnikur amocanebsi SeiZleba iqnas gamoyenebuli. am TvalsazrisiT winamdebare nasromis konstruqciuli sqema asetia: sadisertacio nasromis standartuli Sesavlis Semdeg iwyeba ZiriTadi Sinaarsis ganxilva. saxeldobr, nasromis me-2 punqtsi (Sedegebi da mati gansja) mocemulia nasromis sami ZiriTadi nawili. pirvel nawilsi (2.1) gadmocemulia sakvlevi amocanisatvis specialurad SerCeuli Temebi: geometriuli gardaqmnebi, geoetriuli asaxvebi, evklides sivrce da misi Sevseba arasakutrivi elementebit, dezargis Teorema da misi Sedegebi, zogadi afinuri Sesabamisoba, afinurad Sesabamisi velebis mtavari mimartulebebi, sivrcis perspeqtiul-afinuri (natesauri) gardaqmna, dagegmilebis mimartulebis arceva natesaur sivrceebsi, natesauri sivrceebis asaxva ortogonalur gegmilebsi, zogadi saxis meore rigis zedapirebis kveta, meore rigis zedapirebis TanakveTis wiris ageba, elifsuri zedapirebi, sivrcis zogadi proeqciuli homologia. meore nawilsi (2.2) grzeldeba pirvel nawilsi dawyebuli kvleva, magram igi gamoyofilad ezrvneba mxazvelobiti geometriis ert-erti nawilis, gamoyenebiti perspeqtivis safuzvlebis, rogorc samrewvelo dizainis amocanebistvis gansakutrebit sawiro Temebis kvlevas. saxeldobr, aq ganxilulia Crdilebi ortogonalur gegmilebsi (geometriuli figurebidan gegmilta sibrtyeze dacemuli Crdilebi), Crdilebi ortogonalur gegmilebsi (geometriul zedapirebze dacemuli Crdilebi) da gamoyenebiti perspeqtivis safuzvlebi. aq mocemuli iv

5 yoveli Tema Seswavlilia samrewvelo dizainsi, saxeldobr, mxatvrul proeqtirebasi mati gamoyenebis TvalsazrisiT. mesame nawili (2.3) datmobili aqvs sadisertacio nasromis ZiriTadi amocanis-sainjinro geometriisa da samrewvelo dizainis ertoblivi amocanebis gamokvetas, am amocanebis saerto interesebis Seswavlas, mxatvrul proeqtirebasi axleburi grafikuli metodebis axsnas da mat gamoyenebas sainjinro praqtikis konkretul amocanebsi. arsanisnavia, rom yoveli teqnikuri amocanis amoxsna ganxorcielebulia kompiuteruli mxardawerit da rac mtavaria, am saqmesi intuiciuri algoritmis praqtikasi danergvis gzebis CvenebiT. am Tvalsazrisidan gamomdinare, mesame nawilsi ganxilulia: mxatvruli Semoqmedeba materialur warmoebasi, naketobis estetikuri Rirebuleba, sagnobrivi garemos gardaqmna da samrewvelo dizaini, teqnikuri estetikis motxovnebi farto moxmarebis sagnebi daproeqtebasi, daproeqtebis stadiebi, saproeqto amocanebis ZiriTadi tipebi, saproeqto grafika, modelireba, sainjinro geometriis gamoyeneba samrewvelo dizainis amocanebsi kompiuteruli mxardawerit. mesame nawilis bolo punqti (2.3.9) warmoadgens sadisertacio nasromis Semajamebel nawils da disertaciasi dasmuli amocanis pasuxs. winamdebare nasromis me-3 punqtsi Camoyalibebulia ZiriTadi Sedegebi. bolo punqti ki datmobili aqvs gamoyenebul literaturas. v

6 Abstract Mathematical and Technical Approaches and definition of Engineering Geometry are very close to each other, but the first represents theoretical side of problem, and the second - concrete technical realization of the task. In this dissertation work such geometrical and engineering approaches are selected and researched, which, in our opinion, may be used in the technical tasks of industrial design. In this respect, the present work s constructive scheme is as follows: the thesis begins with the standard introduction, then basic content review is discussed. In particular, in the thesis s 3 th paragraph (results and discussion) the three major parts of the work are given. In first part (2.1) research task s specially selected themes set out, such as geometrical transition, geometrical reflection, Euclidian space and its filling with nonbelonging elements, Desargues theorem and its consequences, the general affine compliance, main directions of affine respective fields, perspective affine transition of space, selection of main direction of related spaces, representation of related spaces in orthogonal projections, intersection of second-degree surfaces, construction of intersection lines of second degree surfaces, elliptical surfaces, general projective space homology. The second part of (2.2) continues the first part of the study, but it is dedicated to one of the parts of Descriptive Geometry- to fundamentals of perspective-.. In particular, there are considered shadows in orthogonal projections---- shadows, which fell from geometrical figures on projection plane, shadows, which fell on the surfaces, and fundamentals of applied perspective Each discussed theme is studied in terms of use in industrial design. The third part (2.3) is attached to the primary task of work research of joint task of engineering geometry and industrial design, study of common interests, explain of new methods in graphic design and their use in specific practical tasks. It should be noted that every technical problem solution is implemented by computer support and most importantly, by demonstration of introduction of this intuitive algorithm in the practice. According to this point of view in third part discusses: Artistic creation of material production, product aesthetic value, meaningful environmental transformation of industrial design, technical aesthetic requirements in vi

7 the planning of a broad consumer goods, project objectives, the main types of design graphics, modeling, use of engineering geometry in industrial design by computer support. The third part of the last paragraph of (2.3.9) is the concluding part of thesis and an answer of dissertation raised task. Industrial Design, In 3 th paragraph of present work main results established. In 5 th section used books has been attached. vii

8 Sinaarsi Sesavali 13 1 literaturis mimoxilva 17 2 Sedegebi da mati gansja; pirveli nawili geometriuli asaxvebi geometriuli gardaqmnebi evklides sivrce da misi Sevseba 23 arasakutrivi elementebit dezargis Teorema da misi Sedegebi zogadi afinuri Sesabamisoba afinurad Sesabamisi velebis mtavari 35 mimartulebebi sivrcis perspeqtiul-afinuri (natesauri) 37 gardaqmna dagegmilebis mimartulebebis arceva 38 natesaur sivrceebsi natesauri sivrceebis asaxva ortogonalur 40 gegmilebsi zogadi saxis meore rigis zedapirebi da 41 mati gardaqmna brunvis zedapirebsi meore rigis zedapirebis kveta meore rigis zedapirebis TaakveTis wiris ageba elifsuri zedapirebi sivrcis zogadi proeqciuli homologia meore nawili Crdilebi ortogonalur gegmilebsi(geometriuli figurebidan gegmilta sibrtyeebze dacemuli Crdilebi Crdilebi ortogonalur gegmilebsi (geometriul zedapirebze dacemuli Crdilebi gamoyenebiti perspeqtivis safuzvlebi mesame nawili mxatvruli Semoqmedeba materialur 70 warmoebasi naketobis estetikuri Rirebuleba sagnobrivi garemosgardaqmna dasamrewvelo 72 dizaini teqnikuri estetikis motxovnebi farto 73 moxmarebis sagnebis daproeqtebasi daproeqtebis stadiebi saproeqto amocanebis ZiriTadi tipebi viii

9 2.3.7 saproeqto grafika 80 modelireba sainjinro geometriis gamoyeneba samrewvelo 83 dizainis amocanebsi kompiuteruli mxardawerit 3 daskvna 103 gamoyenebuli literatura 106 ix

10 ნახაზების ნუსხა nax. 1 geometriuli asaxvis magaliti 21 nax. 2 geometriuli asaxvis magaliti 22 nax. 3 Seqcevadi asaxvis magaliti 22 nax. 4 wrewiris Tavis Tavze asaxva 23 nax. 5 evklides sivrce da misi Sevseba 24 arasakutrivi elementebit, ZiriTadi cnebebi da ganmartebebi nax. 6 evklides sivrce da misi Sevseba arasakutrivi elementebit, ZiriTadi cnebebi da ganmartebebi 24 nax. 7 evklides sivrce da misi Sevseba 25 arasakutrivi elementebit, ZiriTadi cnebebi da ganmartebebi nax. 8 evklides sivrce da misi Sevseba 26 arasakutrivi elementebit, ZiriTadi cnebebi da ganmartebebi nax. 9 evklides sivrce da misi Sevseba 27 arasakutrivi elementebit, ZiriTadi cnebebi da ganmartebebi nax. 10 evklides sivrce da misi Sevseba 28 arasakutrivi elementebit, ZiriTadi cnebebi da ganmartebebi nax. 11 dezargis Teorema sivrcisatvis 29 nax. 12 dezargis Teorema sibrtyisatvis 30 nax. 13 hiperboluri homologia arasakutrivi 31 RerZiT-msgavsebis gardaqmna nax. 14 paraboluri homologia arasakutrivi 31 RerZiT-paraleluri gadatana nax. 15 sibrtyis gawelva ormagi wrfeebis gaswvriv 31 gawelvis erti da igive koeficientit nax. 16 paraboluri homologia usasrulod Sors 32 mdebare centrit - Zvra nax. 17 afinuri Sesabamisoba 33 nax. 18 pespeqtiul-afinuri (natesauri) gardaqmnebi 33 sibrtyeze nax. 19 or sibrtyes Soris afinuri Sesabamisoba 34 gansazrvrulia Sesabamis wertilta sami wyvilit nax. 20 afinurad Sesabamisi velebis mtavari 35 mimartulebebi nax. 21 sivrcis perspeqtiul-afinuri (natesauri) 38 gardaqmna nax. 22 dagegmilebis mimartuleba natesaobis sibrtyis paraleluria 39 x

11 nax. 23 dagegmilebis mimartuleba natesaobis mimartulebis paraleluria nax. 24 natesauri sivrceebis asaxva ortogonalur gegmilebsi nax. 25 natesauri sivrceebis asaxva ortogonalur gegmilebsi naxazi 26 daxrili elifsuri cilindris gardaqmna magegmilebel cilindrad nax. 27 elifsuri hiperboloidis gardaqmna brunvis 43 hiperboloidad nax. 28 elifsuri paraboloidis kveta zogadi 45 mdebareobis sibrtyit nax. 29 samrerziani elifsoidisa da elifsuri 46 paraboloidis urtiertkveta nax. 30 samrerziani elifsoidi 47 nax. 31 sivrcis zogadi proeqciuli homologia 48 nax. 32 sivrcis zogadi proeqciuli homologia 49 ortogonalur gegmilebsi nax. 33 piramidis asaxva prizmaze sivrcis zogadi 50 proeqciuli homologiit nax. 34 donis wrfis Crdili 52 nax. 35 magegmilebeli wrfis Crdili 52 nax. 36 zogadi mdebareobis wrfis Crdili 52 nax. 37 mravalkutxedis Crdili 53 nax. 38 wrewiris Crdili wrewiria 53 nax. 39 wrewiris Crdili elifsia 34 nax. 40 marti prizmis Crdili 34 nax. 41 piramidis Crdili 34 nax. 42 brunvis cilindris Crdili 55 nax. 43 brunvis konusis Crdili 55 nax. 44 wrfis Crdili zedapirze 56 nax. 45 brtyeli figuris Crdili brunvis 56 cilindrze nax. 46 sxivuri kvetebis metodi 57 nax. 47 perspeqtiuli gamosaxulebis mirebis sqema 58 nax. 48 wrfis perspeqtivi 59 nax. 49 fuzeta sibrtyesi mdebare paralelur 60 wrfeta konis perspeqtivi nax. 50 fuzeta sibrtyis paraleluri wrfis 61 perspeqtivi nax. 51 fuzeta sibrtyis martobuli wrfis 61 perspeqtiva nax. 52 sasurate sibrtyis paraleluri wrfis 62 perspeqtivi nax. 53 suratis fuzis paraleluri wrfis 62 perspeqtivi nax. 54 sasurate sibrtyis martobuli wrfeebis perspeqtivi xi

12 nax. 55 sibrtyis perspeqtivi 63 nax. 56 sibrtyis arasakutrivi wrfis perspeqtivi 64 nax. 57 wrewiris perspeqtivis ageba Semoxazuli 65 kvadratis metodit nax. 58 fuzeta sibrtyis martobul sibrtyesi mdebare wrewiris perspeqtivi 66 nax. 59 ortogonalur gegmilebsi mocemuli 68 martkutxa paralelepipedis perspeqtivi nax. 60 cilindrultariani marti prizma 69 nax. 61 cilindrultariani marti prizmis 69 perspeqtivi nax. 62 elifsuri paraboloidis brtyeli kveti 89 Nnax. 63 litget (surti) 91 Nnax. 64 litget (modeli) 92 Nnax. 65 Elitget (saloni) 93 Nnax. 66 motogandola(naxazi) 94 Nnax. 67 motogandola (modeli) 95 Nnax. 68 Elitget is cxviri 96 Nnax. 69 memanqanis jixuri (modeli) 98 Nnax. 70 memanqanis jixuri (saamwyobo naxazi) 99 Nnax. 71 φ(m,t) zedapiris asaxva epiurze 100 Nnax.72 φ(m,t) zedapiris modeli 101 Nnax. 73 Nnax. 74 jixuris modeli elmavlis modeli xii

13 Sesavali sadisertacio Temis aqtualoba samrewvelo dizaini adamianta SemoqmedebiTi saqmianobis is ubania, romlis mizania industriuli wesit gamosvebuli gamoyenebiti sagnebis srulyofa. samrewvelo dizaini adamians optimalur da harmoniul sagnobriv garemos uqmnis. Aamis mirweva ki SesaZlebelia saganta kompleqsebis an calkeuli naketobebis funqciuri, estetikuri da saeqploatacio Tvisebebis ertianobit. konstruqciebis Sesaqmnelad sawiroa sxvadasxva sainjinro dargis specialistebis SemoqmedebiTi kontaqtebi, rac, erti mxriv, zrdis warmoebis efeqtianobas, meore mxriv, xels uwyobs momxmareblis motxovnilebebis maqsimalur dakmayofilebas. saqme isaa, rom samrewvelo dizaini organulad erwymis adamianta sazogadoebisatvis gankutvnil Tanamedrove samrewvelo produqciis Seqmnis process, romelsac warmartavs mrewvelobasi, teqnologiasa da ekonomikasi garkveuli dizaineri, romlis saqmianobac, proeqtis Sedgenis dros, mecnierebis sxvadasxva dargis mirwevebze da Tanamedrove teqnologiebzea damyarebuli. samrewvelo dizaini, rogorc praqtikuli saqme, dafuznebulia teqnikur estetikaze, ekonomikaze, sociologiaze, ergonomikaze. samrewvelo dizains axasiatebs sacdeli obieqtis modelireba, romelic naketobis saboloo optimaluri variantis dadgenamde mudmiv modifikacias ganicdis. samrewvelo dizainis metodi moicavs dasaproeqtebeli obieqtis kvlevas, funqciur ergonomiul da konstruqciul teqnologiur Ziebas naketobata mxatvruli konstruirebis TvalsazrisiT. samrewvelo dizaini XX saukunis pirmsod itvleba, Tumca misi Canasaxebi sazogadoebis ganvitarebis ufro adrindel periodebsic gvxvdeba. saxeldobr, im droidan, roca kustaruli warmoeba manqanurma warmoebam Secvala, ramac teqnikur gadatrialebas daudo safuzveli. daiwyo samrewvelo dizainis seriozuli ganvitareba. misi fuzemdeblebi iyvnen germanelebi: p. erensi, v. ropiusi, g. zemperi, g. metiziuri, belgieli van de 13

14 velde, frangi le-korpuzie da sxvebi. 30-iani wlebis Semdeg ki samrewvelo dizainis ganvitarebis centrma amerikis SeerTebul StatebSi gadainacvla, Tumca am dargis yvelaze warmatebul da mnisvnelovan kerad mxatvruli konstruirebis ulmis (germaniis) skola itvleba. saqartvelosi samrewvelo dizainis nimusebi adreuli xanidan gvxvdeba, magram misi ganvitarebis dasawyisad mainc 1899 wels Camoyalibebuli e.w. kavkasiis kustaruli komiteti da TbilisSi 1910 wels gaxsnili mxatvruli xelosnobis centris (ganatleba) samxatvro skola-saxelosnoa micneuli. Semdgom periodsi, roca qartul mrewvelobas da kulturas sakutari warmatebuli Sedegebi gaucnda, daiwyo ganvitarebis axali etapi: Seiqmna sxvadasxva danisnulebis samrewvelo da yofiti naketobebis mxatvruli konstruirebis proeqtebi, qarxnebsa (zugdidis faifuris qarxana) da fabrikebsi (mag. xasuris safeiqro-sagalanterio fabrika) Camoyalibda specialuri ganyofilebebi, romelta mtavar amocanad mxatvrul konstruirebastan dakavsirebuli programebis ganxorcieleba iyo dasaxuli. saqartvelosi samrewvelo dizainis ganvitarebasi kidev ertert win gadadgmul nabijad SeiZleba CaiTvalos saqartvelos teqnikur universitetsi dizainis katedris gaxsna (katedris gamge, prof. k. amirejibi). is, rac gamoyenebiti sagnebis garegan saxes gansazrvravs, pirvelad qaraldze ibadeba sainjinro grafikis metodebis gamoyenebit. imis gamo, rom sainjinro grafikis metodebis Teoriuli safuzveli sainjinro geometriaa, samrewvelo dizainic mwidro kavsirsia mastan da xsir SemTxvevaSi gamoyenebiti sagnebis garegnuli saxis optimaluri variantis mozieba damokidebulia im geometriul safuzvelze, romelsac maziebeli asagebi gamosaxulebistvis aircevs. terminologiis dazustebis miznit samrewvelo dizainis im ganstoebas, romelic gamoyenebiti sagnebis garegnuli saxis 14

15 asaxvas gulisxmobs, pirobit, samrewvelo grafika davarqvat da miznad davisaxot sainjinro geometriis metodebis samrewvelo grafikasi gamoyenebis problemata kvleva. Tu mivicnevt, rom Tanamedrove warmoebis mnisvnelovani maxasiatebelia gamosvebuli produqciis garegnuli saxe anu dizaini, masin iolad mivalt im daskvnamde, rom am maxasiateblis gaumjobesebistvis gadadgmuli yoveli nabiji da mat Soris Cvens mier arceuli problemis mecnieruli kvleva aqtualuria. sadisertacio Temis siaxle sainjinro grafikis sauniversiteto kursi Cveulebrivad gulisxmobs grafikul gamosaxulebata mirebis mxolod zogadi safuzvlebis Seswavlas. specialobata simravlis gamo, moqmed silabusebsi ar aris da arc SeiZleba iyos gatvaliswinebuli calkeuli viwro dargebis specifika. es garemoeba grafikuli metodebis fartod gamoyenebis SesaZleblobebs zrudavs. gamovyot erti konkretuli SemTxveva. magalitad, sauniversiteto kursi ar Seicavs sainjinro geometriis im specialur sakitxebs, romelta codnac sawiroa samrewvelo dizainis konkretuli amocanebis warmatebuli anu optimaluri gzebita da metodebit amosaxsnelad. swored am xarvezis armofxvras ezrvneba Cveni nasromi da ai, ratom: sainjinro geometriis Teoriisa da praqtikis zrva masalasi gabneuli specialuri, erti dargistvis sawiro sakitxebis mozieba da moziebulis sainjinro praqtikis amocanebisadmi misadageba mivicniet samecniero kvleviti samusaos ert-ert formad da zemotqmulidan gamomdinare, miznad davisaxet sainjinro geometriis im metodebis Sekreba, romlebic samrewvelo dizainis grafikuli amocanebis amoxsnis gamartivebasi dagvexmareboda. Cven vcadet amgvari samusaos Sesruleba da mopovebuli Sedegebis demonstrireba nisandobliv amocanebsi. 15

16 imis gamo, rom Cvens mier Catarebuli kvlevebis da Sedegebis analogi CvenTvis cnobil samecniero da saswavlo literaturasi ar moipoveba, sainjinro geometriisa da samrewvelo dizainis urtiertdakavsirebis Cveneuli varianti mecnierebistvis garkveul siaxled migvacnia da vtvlit, rom mirebuli Sedegebis praqtikasi danergva warmatebis momtani iqneba. nasromis mizani nasromis mizania, sainjinro geometriis sasualebata gamoyeneba mxatvrul proeqtirebasi (samrewvelo dizainsi) kompiuteruli mxardawerit. kvlevis obieqti sainjinro geometriisa da samrewvelo dizainis (naketobis mxatvruli proeqtireba) problematika da praqtikasi danergva. kvlevis metodebi winamdebare nasromsi dasmuli amocanebis gadasawyvetad gamoyenebulia sainjinro geometriis metodebi da naketobis mxatvrul proeqtirebasi gavrcelebuli samecniero-teqnikuri midgomebi. kvlevis Cvens mier arceul qargasi gatvaliswinebulia grafikuli amocanebis amoxsna kompiuteris mxardawerit. amdenad, garda zemoarnisnulisa, nasromsi kompiuteruli sainjinro grafikis metodikac xsirad aris gamoyenebuli. 16

17 1. literaturis mimoxilva nebismieri sameciniero-kvleviti nasromi iwyeba imis garkvevit, Tu saidan momdinareobs nasromsi dasmuli problema, ra aris cnobili am problemis Sesaxeb da arsebobs Tu ara alternatiuli gza mis gadasawrelad. amastan dakavsirebit kidev er- Txel gavixsenot Temis dasaxeleba,,sainjinro geometriisa da samrewvelo dizainis zogierti ertoblivi amocana da mati gadawyvetis magalitebi da CamovayaliboT am TemiT dainteresebis winmswrebi pirobebi arsebuli samecniero literaturis safuzvelze. rogorc Temis dasaxelebidan Cans, sakvlevi obieqtia sainjinro geometriisa da samrewvelo dizainis saerto amocanebi da mati gadawyveta ertoblivi sasualebebit. terminologiuri cdomilebebis Tavidan acilebisa da sakvlevi problemis uket warmocenis miznit gadavxedot Cven mier sabazisod micneul samecniero literaturas. sainjinro geometria aris geometriis dargi, romelic Seiswavlis figuris gegmiluri gardaqmnis mimart invariantul Tvisebebs. sivrcis an sibrtyis gardaqmnas gegmiluri ewodeba Tu igi wrfes asaxavs wrfesi. sainjinro geometriasi ganixileba gegmi-luri wrfis, sibrtyisa da sivrcis cnebebi. cnobilia, rom geg-milur sibrtyes mivirebt, Tu evklides Cveuleberiv sibrtyes davumatebt am sibrtyidan usasrulod dasorebul elemetebs. am SemTxvevaSi itvleba, rom sibrtyeze mocemuli wrfis yvela paraleluri wrfe ikveteba da amit ganisazrvreba e.w. arasakutrivi wrfe. sibrtyis yvela arasakutriv wertilta ertobliobas arasakutrivi wrfe ewodeba. analogiurad ganisazrvreba e.w. gegmiluri sivrce. yoveli wrfe mistvis arasakutrivi wertilis damatebis Semdeg gadaiqceva Sekrul wirad da mas gegmiluri wrfe ewodeba. Ggegmiluri sibrtye gansxvavebulia evklides sibrtyis agebulebisagan. gegmilur sibrtyeze wrfeta yoveli wyvili gadakvetilia. aseve gadakvetilia gegmilur sivrcesi sibrtyeta yoveli 17

18 wyvili. gegmiluri sibrtyisa da sivrcis SemoReba sasualebas izleva, ganisazrvros gegmiluri gardaqmna, rogorc urtier- Tcalsaxa wertilovani asaxva gegmiluri sibrtyisa an sivrcisa Tavis Tavze, romelic wrfes wrfed asaxavs. sainjinro geometriis ert-erti ZiriTadi debulebaa oradobis principi. oraduli winadadebebis magalitebia paskalis Teorema da briansonis Teo-rema. sainjinro geometriis ZiriTadi cnebebisa da wiandadebebis magalitebia ormagi fardoba da dezargis Teorema. sainjinro geometriis metodebi sasualebas izleva Rmad CavwvdeT sxvadasxva geotriul sakitxs da movaxerxot am sakitxebis gamoyeneba sainjinro praqtikis, mat Soris samrewvelo dizainis amocanebsi. sainjinro geometriis metodebis uket gasacnobad Cven Rmad SeviswavleT am dargis saswavlo da samecniero literatu-ra. mat Soris ZiriTadia qvemot CamoTvlili gamocemebi, damxmare ki mititebulia gamoyenebuli literaturis saerto siasi. 1. Глаголев Н. А. Проективная геометрия. М., `Высшая школа~, ст Глаголев Н. А. Начертательная геометрия. М., `Высшая школа~, ст Кокстер Х. С. М. Действительная проективная плоскость. М., Гос. Изд.-во Физико-математической литературы ст Юнг Дж. В. Проективная геометрия. М., Гос. Изд.-во Физико-математической литературы ст ა.შავგულიძე, ი.ხატისკაცი, ზ.კვინიკაძე, გ.ჩიტაიშვილი., ნ.ნიკვაშვილი საინჟინრო გრაფიკა მათემატიკოსებისათვის. `ტექნიკური უნივერსიტეტი~ I I I ნაწილი. გვ С. А. Фролов. Методы преобразования ортогональных проекций. Изд-во `Машиностроение~, М., ст ი. ხატისკაცი ზედაპირების თანაკვეთის წირის აგების თეორია და პრაქტიკული გამოყენება. თბილისი, `განათლება~,

19 sainjinro geometriasi gamocemuli literaturis paralelurad, Cven mxatvrul konstruirebasa da gamoyenebit perpeqtivsi gamoqveynebul Sromebsac gavecanit da SeviswavleT kidec isini. mati ZiriTadi nawili qvemotaa CamoTvlili, damxmare ki mititebulia gamoyenebuli literaturis saerto siasi. 1. Рынин Р. А. Линейная перспектива. Петроград გ. ვაჩნაძე. გამოყენებითი პერსპექტივის საფუძვლები. თბილისი, 3. Тимрот Е.С. Начертательная геометрия, Государственное Изд.-во Литературы по строительству, архитектуре и строиматериалам. М Кочегаров Б.Е., Промышленный дизаин, Владивосток, Изд.-во. ДВГТУ, Ковешников Н.А., Дизаин. История и теория, М. Изд.-во Омега-л, Сомов Ю., Композиция С в технике, М. Машиностроение, Ульрих К.У, Эппингер С, Промышленный дизаин, М. Вершина, Панеро Д., Зелник М., Основы эргономикы, человек, пространство, интериер. М. Изд.-во АСТ. mititebuli literaturis SeswavliT, gamovitanet daskvna, rom Cvens xelt arsebul nasromebsi calke sakitxad ar aris Seswavlili sainjinro geometriisa da samrewvelo dizainis ertoblivi amocanebi da bunebrivia, arc am amocanebis ertoblivi sasualebebis gamoyenebit amoxsnazea saubari, gansakutrebit masin, rodesac saqme kompiuteruli sainjinro grafikis axlad SeZenili metodebis praqtikasi danergvastan gvaqvs: Финкельштейн Э. Auto CAD 2007 и Auto CAD LT Библия пользователя. `диалектика~, М., 2007., Вернер Зоммер. Auto CAD Руководство 19

20 конструктора. Изд-во `Бином~, М., 2008., ა. შავგულიძე, გ. გარიშვილი. კომპიუტერული საინჟინრო გრაფიკა. გამomcemloბა `ტექნიკური უნივერსიტეტი~, თბილისი, 1997., ა. შავგულიძე, გ. გარიშვილი. საინჟინრო გრაფიკის ამოცანების გადაწყვეტა ავტომატიზირებული დაპროექტების სისტემის AutoCAD-ის საშუალებით. გამomcemloბა `ტექნიკური უნივერსიტეტი~, თბილისი, zemoarnisnuls SesaZloa davumatot isic, rom Cven miznad davisaxet sainjinro geometriisa da samrewvelo dizainis Seswavla axali realobis gatvaliswinebit, Zveli da axali masalebis Sejereba ert dargsi - samrewvelo dizainsi mati gamoyenebis TvalsazrisiT. Cven SevecadeT, praqtikasi fartod gavrcelebuli kompiuteruli naxazebis SedgenaSi Segvetana e.w. intuiciuri algoritmis cneba da amit kompiuteris yoveli moqmedeba (magaltad, zedapirebis warmoqmnisa da asaxvis amocanebsi) sainjinro geometriis metodebis gamoyenebit Segvevso. Cven mier Seswavlili da Cveni azrit ramdenadme gadawrili problema gulisxmobs mxatvrul daproeqtebasi siaxlis Setanis mcdelobas sainjinro amocanebis mecnierulad dasabutebis saxit. 20

21 2. Sedegebi da mati gansja 2.1 pirveli nawili 2.1.1Ggeometriuli asaxvebi sxvadasxva geometriuli amocanebis amoxsnisas xsirad gvixdeba gadasvla erti geometriuli figuridan mis garkveul saxecvlilebastan. magalitad, mxazvelobit geometriasi sivrcesi mdebare figurebis anasaxebs ganvixilavt da am anasaxebze moqmedebebis SesrulebiT vwyvett sivrcit amocanebs. or geometriul figuras, an mat nawilebs Soris SeiZleba damyarebuli iyos garkveuli Sesabamisoba. im wess an kanons, romlis mixedvitac Φ figuris TiToeul wertils Φ'figuris gansazrvruli wertili Seesabameba, Φ figuris figurasi asaxva ewodeba[14]. nax. 1 Tu Φ figuris A wertils figuris A' wertili Seesabameba, vambobt, rom A wertili A' wertilze aisaxa. A'-s A wertilis anasaxi ewodeba, xolo A wertili A'-is wina saxea (nax. 1). asaxvis gansazrvrebidan sulac ar gamomdinareobs, rom aucilebelia figuris yoveli wertili Φ figuris romelime wertilis anasaxs warmoadgendes. sxvanairad rom vtqvat, ar aris aucilebeli figuris yvela wertils hqondes wina saxe 21

22 (nax. 1). agretve, figuris wertils SeiZleba hqondes ertze meti wina saxe, anu Φ figuris ramdenime gansxvavebuli wertili SeiZleba figuris erti da igive wertilze aisaxos (nax. 2). nax. 2 nax. 3 Tu Φ figura figuraze ise aisaxa, rom Φ figuris nebismieri ori gansxvavebuli wertili figuris isev or gansxvavebul wertilzea asaxuli, asaxvas Seqcevadi ewodeba. Aam SemTxvevaSi Φ da figurebis wertilta Soris urtiert calsaxa Sesabamisobaa damyarebuli. rac imas nisnavs, rom ara marto Φ figuris nebismier A wertils Seesabameba. Tu Φ figura figuraze ise aisaxa, rom Φ figuris nebismieri ori gansxvavebuli wertili figuris isev or gansxvavebul wertilzea asaxuli, asaxvas Seqcevadi ewodeba. Aam SemTxvevaSi Φ da figurebis wertilta Soris urtiertcalsaxa Sesabamisobaa damyarebuli. rac imas nisnavs, rom ara marto Φ figuris nebismier A wertils Seesabameba A' figuris ertaderti A' wertili, aramed piriqitac, figuris nebismier A' wertilsac Φ figuris ertaderti A wertili Seesabameba (nax. 3) geometriuli gardaqmnebi iset urtiertcalsaxa asaxvas, roca Φ figura TavisTavze aisaxeba, Φ figuris gardaqmna ewodeba. sazogadod, gardaqmnis dros Φ figuris wertilebi amave figuris sxva wertilebze 22

23 aisaxeba. radgan Φ figuris gardaqmna urtiertcalsaxaa, amitom igi Seqcevadia. nax. 4 wrewiris Sesabamis wertilebs Soris damyarebuli Sesabamisoba wrewirs Tavis Tavze asaxavs (nax. 4). Uufro zustad Tu CamovayalibebT, Φ figuris Tavis Tavze iset asaxvas, romelsic or gansxvavebul wertils ori gansxvavebuli wertili Seesabameba, Φ figuris gardaqmna ewodeba. radgan sibrtye geometriuli figuraa, amitom sibrtyis gardaqmnis cneba figuris gardaqmnis cnebis analogiuria. sibrtyis gardaqmna ewodeba sibrtyis Tavis Tavze iset asaxvas, romelsic sibrtyis or gansxvavebul wertils isev ori gansxvavebuli wertili (anasaxi) Seeesabameba. asaxvas, romelsic Φ figuris nebismieri wertili Tavis Tavze aisaxeba, Φ figuris igivuri gardaqmna ewodeba. E evklides sivrce da misi Sevseba arasakutrivi elementebit Tu sibrtyes 'sibrtyeze davagegmilebt, a wrfis wertilebi a' wrfis wertilebze aisaxeba, magram a' wrfeze gveqneba erti wertili, romelic ar armocndeba a wrfis romelime wertilis gegmili. es aris wertili A',romelic a wrfis paralelur wrfeze Zevs. 23

24 nax. 5 e. i. a' wrfis yvela wertili a wrfis yvela wertilis gegmils warmoadgens, garda erti wertilisa. Aam danaklisis Sesavsebad CavTvaloT, rom A' wertili a wrfis,,usasrulod Sors mdebare wertilis gegmilia (nax. 5). avirot a wrfe da masze aramdebare P wertili. P wertilze gavatarot a wrfis mkveti wrfe. wrfeebis gadakvetis wertili nax. 6 arvnisnot M-iT. warmovidginot, rom mkveti wrfe Semobrundeba P wertilis irgvliv a wrfis paralelur b mdebareobasi. masin da a wrfeebis gadakvetis M wertili gadaadgildeba usasrulobasi a wrfis gaswvriv. Aamitom, roca 24

25 a da wrfeebi paraleluri gaxdeba, Cven mat mivawert,,usasrulod Sors mdebare gadakvetis wertils, anu vityvit, rom paraleluri wrfeebi usasrulod Sors mdebare wertilsi ikveteba (nax. 6). davakvirdet, rogor gadaadgildeba a da wrfeebis gadakvetis M wertili, roca mkveti wrfe srul bruns aketebs P wertilis irgvliv. Tavidan M wertili mozraobs garkveuli mimartulebit, roca wrfe miirebs b mdebareobas, M wertili miva a wrfis usasrulod Sors mdebare M mdebareobasi. vtqvat, wrfe agrzelebs brunvas. masin M wertili armocndeba zemot arnisnuli M mdebareobis sawinaarmdego mimartulebit da bolos, roca wrfe daamtavrebs brunvas, daubrundeba Tavis sawyis M mdebareobas. sxvanairad rom vtqvat, SemdgomSi wrfes ganvixilavt, rogorc Sekrul wirs[33]. Aaxla ukve a' wrfis yoveli wertili a wrfis romelime wertilis gegmils warmoadgens (Cveulebrivs an usasrulod Sors mdebares). piriqit, a wrfis yoveli wertili a' wrfis romelime gansazrvrul wertilze ( Cveulebrivze an usasrulod Sors mdebareze) gegmildeba (nax. 7 ). nax. 7 sibrtyis kutvnili da a wrfis paraleluri wrfeebi ' sibrtyeze gadakvetil wrfeebad gegmildeba. mati gadakvetis wertili swored is wertilia, romelic itvleba a wrfis usasrulod Sors mdebare wertilis gegmilad. Aamitom vtvlit, 25

26 rom ertmanetis paralelur yvela wrfes aqvs erti saerto usasrulod Sors mdebare wertili anu paraleluri wrfeebi ert wertilsi ikveteba (nax. 8). nax. 8 sibrtyis paraleluri yvela magegmilebeli wrfe ert sibrtyesi Zevs. es sibrtye gegmilta ' sibrtyes ' wrfeze kvets. am ' wrfis wertilebi sibrtyis usasrulod Sors mdebare wertilebis gegmilebs warmoadgens. sxvanairad rom vtqvat, ' wrfe sibrtyis usasrulod Sors mdebare wrfis gegmilia[33]. aqedan Semogvaqvs daskvna, rom ertmanetis yvela paraleluri sibrtye ikveteba ert usasrulod Sors mdebare (arasakutriv) wrfeze da piriqit, arasakutriv wrfeze gadakvetili sibrtyeebi ertmanetis paraleluri sibrtyeebia. Ee.i. ori araparaleluri sibrtyis arasakutrivi wrfeebi sxvadasxva wrfeebia. Ees nisnavs, rom arsebobs usasrulo raodenoba arasakutrivi wrfeebisa. sivrcis usasrulod Sors mdebare wrfeebis ertoblioba (igivea, rac usasrulod Sors mdebare wertilta ertoblioba) yovel sakutriv wrfestan ikveteba ert wertilsi da amitomac ewodeba mas arasakutrivi(usasrulod Sorsmdebare) sibrtye(nax.9). 26

27 nax. 9 Tu A masin A wertilze gamavali wrfeebi paraleluria wrfeze gamavali sibrtyeebis (nax. 10). evklides sibrtyeze arasakutrivi wrfis SemotaniT gafartoebul sivrcesi ganisazrvra erti romelime sibrtyis paralelur sibrtyeta ertoblioba, romelsac sibrtyeta Sekvra ewodeba da am Sekvris RerZs arasakutrivi wrfe warmoadgens. es arasakutrivi wrfe Sekvris yvela sibrtyis kutvnilia. Aamgvarad, sibrtyeta SekvrasTan ertad, romelsac gaacnia sakutrivi RerZi, gvaqvs paralelur sibrtyeta Sekvra arasakutrivi RerZiT. sivrcis yvela arasakutrivi elementebis ertobliobas unda gaacndes Semdegi Tvisebebi: TiToeul wrfestan ert wertilsi unda ikvetebodes (am wrfis arasakutriv wertilsi) da TiToeul sibrtyestan _ ert wrfeze (am sibrtyis arasakutriv wrfeze). Cans, am motxovnebis dakmayofileba SeiZleba, Tu evklides sivrces davumatebt arasakutriv sibrtyes, rogorc arasakutriv wrfeta da wertilta geometriul adgils. paralelur wrfeta TiToeul konas erti arasakutrivi wertili Seesabameba, paralelur sibrtyeta TiToeul Sekvras ki _ erti arasakutrivi wrfe. arasakutriv da sakutriv elementta urtiertkutvnileba Semdegnairad ganisazrvreba: arasakutrivi wrfe ekutvnis yvela 27

28 im sakutriv sibrtyes, romlebic Sedis am wrfeze gamaval paralelur sibrtyeta SekvraSi. Yyvela arasakutrivi wertili da arasakutrivi wrfe ekutvnis arasakutriv sibrtyes. evklides gafartoebul sivrces, Sevsebuls arasakutrivi elementebit, proeqciuli sivrce ewodeba. proeqciuli geometriis terminologiit Tu visargeblebt, sibrtyeze mdebare paraleluri wrfeebi qmnis wrfeta konas arasakutrivi centrit. vinaidan sibrtyis TiToeul wertilze gadis mocemuli wrfis paraleluri mxolod erti wrfe, amitom mocemul sibrtyeze mocemuli wrfis paralelurad mxolod erti wrfeta kona gaivlis. nax. 10 proeqciuli sivrce, evklides sivrcis msgavsad materialuri samyaros ert-ert geometriul modelad itvleba. amitom mizansewonilad CavTvaleT, Cveni samusaos pirveli nawili geometriuli figurebis proeqciuli Tvisebebis ganxilvas mivuzrvnat dezargis Teorema da misi Sedegebi geometriuli figurebis proeqciuli Tvisebebis Seswavla daviwyot dezargis TeoremiT. Aam Teoremis Sinaarsi da misgan gamomdinare Sedegebi mnisvnelovani nabijia elementaruli 28

29 geometriuli amocanebidan proeqciuli geometriis ufro rtul amocanebze gadasvlisas[14]. dezargis Teorema: Tu sivrcesi mdebare ori samkutxedis wveroebis SemaerTebeli wrfeebi ert wertilsi ikveteba, masin samkutxedebis Sesabamisi gverdebis sami wyvili ert wrfeze mdebare sam wertilsi gadaikveteba (nax. 11). nax. 11 martivad mtkicdeba Sebrunebuli Teoremac: Tu ori samkutxedi sivrcesi isea ganlagebuli, rom Sesabamisi gverdebis gadakvetis wertilebi ert wrfeze mdebareobs, masin samkutxedebis Sesabamisi wveroebis SemaerTebeli wrfeebi ert wertilsi gadaikveteba. dezargis Teirema (pirdapiri da Sebrunebuli) ZalaSia masinac, rodesac ABC da A'B'C' samkutxedebi ert sibrtyesi mdebareobs (nax. 12) 29

30 nax. 12 am SemTxvevaSi dezargis Teorema ase Camoyalibdeba: Tu sibrtyeze mdebare ori samkutxedis wveroebis SemaerTebeli wrfeebi ert wertilsi ikveteba, masin samkutxedebis Sesabamisi gverdebis sami wyvili ert wrfeze mdebare sam wertilsi gadaikveteba. ert sibrtyeze mdebare wertilovani velebis aset kolineacias homologia ewodeba. S o RerZs_homologiis RerZi. sxvadasxva velebis Sesabamisi wertilebis SemaerTebeli wrfeebis gadakvetis S wertils ki _ homologiis centri. homologiis RerZi ormagi wertilebis ertobliobas warmoadgens. aseve ormagia homologiis centri (romelic TavisTavze aisaxeba) da masze gamavali magegmilebeli wrfeebi (Tumca mat aqvs mxolod ori ormagi wertili: homologiis centri da RerZTan gadakvetis wertili). amrigad, homologia gansazrvrulia, Tu mocemulia homologiis S centri, S 0 RerZi da wertilovani velebis Sesabamis (A da A') wertilta wyvili. ganvixilot homologia, romlis centri sakutrivi wertilia, RerZi ki arasakutriv wrfes warmoadgens - hiperboluri 30

31 homologia arasakutrivi RerZiT metrul geometriasi kargad cnobili msgavsebis gardaqmnaa(nax.13). nax. 13 nax. 14 axla ganvixilot paraboluri homologia arasakutrivi RerZiT (igivea, rac paraleluri gadatana)[3], romelsac centric arasakutrivi aqvs(nax.14). zemot ukve ganvixilet pirveli tipis homologiebi: hiperboluri, rodesac centri RerZs ar ekutvnis (msgavsebis gardaqmna) da b) paraboluri, rodesac centri RerZze Zevs (paraleluri gadatana). axla ganvixilot meore tipis homologiebi usasrulod Sors mdebare centrit. homologiis yvela sakutriv-ormagi wrfe centrze gadis. Tu centri arasakutrivia, es wrfeebi ertmanetis paraleluria. nax.(15)-ze ganxiluli gardaqmna aris sibrtyis gawelva ormagi wrfeebis gaswvriv gawelvis erti da igive koeficientit nax

32 axla ganvixilot paraboluri homologia usasrulod Sors mdebare centrit. am SemTxvevaSi ara marto yvela sakutrivormagi wrfea ertmanetis paraleluri, aramed RerZic am wrfeebis paraleluria, anu ikveteba mattan arasakutriv wertilsi-centrsi. es iqneba paraboluri homologia usasrulod Sors mdebare centrit _ igive Zvra (nax. 16)[4]. nax. 16 arnisnuli daskvnebi da winadadebebi sasualebas gvazlevs praqtikuli amocanebis amoxsnisas warmatebit gamoviyenot proeqciuli geometriis metodebi zogadi afinuri Sesabamisoba or brtyel vels Soris perspeqtiul-afinuri Sesabamisoba paraleluri dagegmilebis Sedegad myardeba. A ganvixilot iseti Sesabamisoba, romelic SeiZleba mivirot paraleluri dagegmilebebis kompoziciit. sibrtyeze, Semdeg sibrtye S mimartulebit davagegmilot sibrtye S -ze, bolos ki mimartulebit sibrtye S mimartulebit -ze. Aamgvarad, da sibrtyeebs Soris damyarda damokidebuleba, rodesac sibrtyis A, B da C wertilebs sibrtyis A, B da C wertilebi Seesabameba. cxadia, A, B da C sazogadod ar warmoadgens A, B da C wertilebis paralelur gegmilebs. Tumca, mat SenarCunebuli eqneba perspeqtiul-afinuri Sesabamisobis zogierti Tviseba. 32

33 martlac, radgan da s Soris Sesabamisoba paraleluri dagegmilebis kompoziciit aris mirebuli, TiToeuli aseti dagegmileba ki inarcunebs kolinearobas da sami wertilis martiv fardobas, amitom da s sibrtyeebs Soris Sesabamisobasac igive Tvisebebi eqneba(nax.17). nax. 17 Sesabamisobas, romelic damyarda da sibrtyeebs Soris,afinuri ewodeba.[14]. axla ganvixilot perspeqtiul-afinuri (natesauri) gardaqmnebis ertoblioba sibrtyeze. TiToeuli gardaqmna gansazrvrulia RerZiTa da Sesabamis wertilta wyvilit: 1) S 0 da ). A 0 da (A 3) S ), A 0 da (A 2) S ), (A A nax

34 suratze nacvenebia B wertilis Sesabamisi B wertilis ageba. rogorc ganxiluli SemTxvevebidan Cans, paraleluri dagegmilebis an perspeqtiul-afinuri gardaqmnebis kompoziciebit mirebuli Sesabamisoba xasiatdeba kolinearobita da sami wertilis martivi fardobit(nax.18). ganvixilot ori wertilovani velis afinuri Sesabamisobis erti kerzo SemTxveva. Mmocemuli sibrtye msgavsebit gardavqmnat sibrtyesi. rogorc vicit, ori wertilovani veils msgavsebisas SenarCunebulia wrfeta kolinearoba da Sesabamis wrfeta paraleloba. Aam Tvisebebis safuzvelze SegviZlia davaskvnat, rom da velebs Soris afinuri Sesabamisobaa. sibrtyis sibrtyeze paraleluri dagegmileba da figurata gadaadgilebac afinuri Sesabamisobis magalitebia, radgan TiToeuli matgani kolinearobas, wrfeta paralelobas da sami wertilis martiv fardobas inarcunebs. cxadia, am gardaqmnebis kompoziciit mirebuli Sesabamisobac afinuri iqneba. nax. 19 C B sibrtyeze A vtqvat sibrtyeze mdebare ABC samkutxeds samkutxedi Seesabameba (nax.19), masin sibrtyeze arebuli nebismieri M wertilis Sesabamisi M wertils sibrtyeze Semdegnairad vipovit: M wertili ABC samkutxedis A wverostan SevaerToT da ganvsazrvrot (AM) da (BC) wrfeebis gadakvetis D wertili. sibrtyeze D wertili ganvsazrvrot (B C D )= (BCD) 34

35 tolobit, radgan afinur SesabamisobaSi sami wertilis martivi fardoba ucvlelia, xolo (AD) wrfis Sesabamis (A D ) wrfeze M wertili vipovot pirobit: (A D M )= (AMD). amrigad, sibrtyis nebismier M wertils sibrtyis erti garkveuli M wertili Seesabameba da piriqit afinurad Sesabamisi velebis mtavari mimartulebebi ganvixilot da afinurad Sesabamisi wertilovani velebi. rogorc vicit, sibrtyesi arebul urtiertmartobul wrfeta wyvils sibrtyesi yoveltvis urtiertmartobuli wrfeebi ar Seesabameba. davamtkicot, rom TiToeul wertilovan velsi moizebneba urtiertmartobul wrfeta erti wyvili mainc, romelsac meore velsi urtiertmartobuli wrfeebi Seesabameba. dasawyisisatvis ganvixilot is kerzo SemTxveva, rodesac mocemuli sibrtyeebi perspeqtiul-afinur (natesaur) SesabamisobaSia. natesaoba gansazrvrulia natesaobis S 0 RerZiTa da (MM ) Sesabamis wertilta wyvilit (nax.20). nax. 20 velis kutvnil M wertilze avagot da sibrtyeebis (MA) da (MB) wrfeebi. Aam wrfeebis sibrtyeze (M A) da (M B) wrfeebi Seesabameba. cxadia, Sesabamis wrfeta wyvilis gadakvetis A da B 35

36 wertilebi natesaobis S 0 RerZze Zevs. Tu M wertilze gamaval wrfeebs Soris kutxe marti armocndeba, masin mivirebt (AMBM ) otxkutxeds, romlis M da M mopirdapire wveroebtan Sedgenili kutxeebi martia. rogorc elementaruli geometriis kursidanaa cnobili, aset otxkutxedze SeiZleba wrewiris Semoxazva. M da M wverostan mdebare marti kutxeebi (AMBM ) OoTxkuTxedze Semoxazuli wrewiris diameters eyrdnoba. AB monakveti am wrewiris diametria, xolo C centri MM monakvetis SuamarTobisa da AB diametris gadakvetis wertili. A amrigad, Tu natesauri Sesabamisoba natesaobis S 0 RerZiTa da (MM ) Sesabamis wertilta wyvilitaa mocemuli, MM monakvetis SuamarTobisa da natesaobis S 0 RerZis gadakvetis C wertili saziebeli wrewiris centri iqneba. Aam wrewiris radiusi R=CM=CM. arvnisnot wrewirisa da natesaobis RerZis gadakvetis wertilebi A da B asoebit, masin sibrtyis kutvnil da urtiertmartobul MA da MB wrfeebs sibrtyeze isev M A da M B urtiertmartobuli wrfeebi Seesabameba. Aam mimartulebebs natesaobis mtavari mimartulebebi ewodeba. wertilovani velis yovel wertilze natesaobis mtavari mimartulebebis mxolod erti wyvili gadis, radgan damxmare wrewiris C centris gansazrvris ertaderti gza arsebobs[14]. rodesac natesaobis MM mimartuleba natesaobis S 0 RerZis martobulia, MM monakvetis SuamarTobi S 0 RerZis paraleluria da damxmare wrewiris C centri arasakutriv wertils warmoadgens. natesaobis mtavari mimartulebebidan erti emtxveva natesaobis MM mimartulebas, xolo meore natesaobis RerZis paraleluria. agretve (MA) da (MB) wrfeebis paraleluri wrfeebis nebismieri wyvilic mtavari mimartulebebs gansazrvravs. Tu monatesave wertilebi natesaobis RerZis mimart simetriuladaa ganlagebuli, MM monakvetis N Sua wertili natesaobis RerZs ekutvnis da damxmare wrewiris C centris mdebareoba gaurkvevelia. Aაm SemTxvevaSi ToToeul wertilovan 36

37 velze moiძebneba natesaobis mtavari mimartulebebis usasrulo raodenoba. arsanisnavia, rom da wertilovan velebs Soris afinuri Sesabamisoba SegviZlia warmovidginot rogorc ori gardaqmnis Sedegi. davusvat da velebs Soris Zogadi afinuri Sesabamisoba damyarebulia msgavsebis gardaqmnita da natesaobis kompoziciit ise, rom sibrtye msgavsebit gardaqmnilia 1 Si, xolo 1 natesaurad -Si. masin, rogorc vnaxet, 1 da sibrtyeebistvis SegviZlia ganvsazrvrot natesaobis mtavari mimartulebebi. Mmsgavsebis gardaqmna ki 1 sibrtyes sibrtyesi abrunebs. Aamave dros, msgavsebis gardaqmnisas mart kutxeebs isev marti kutxeebi Seesabameba. Aamitom, 1 sibrtyis mtavari mimartulebebi sibrtyis mtavar mimartulebebze aisaxeba. Ees nisnavs, rom afinurad Sesabamis or wertilovan velsi yoveltvis arsebobs erti wyvili mainc mtavari mimartulebebisa sivrcis perspeqtiul-afinuri (natesauri) gardaqmna G geometriuli gardaqmnebi, romelsac proeqciuli geometria Seiswavlis, mxolod brtyeli velebit ar Semifargleba. ganvixilot sivrcis perspeqtiul-afinuri gardaqmna, romelic xsirad mxazvelobiti geometriis rigi poziciuri da metruli amocanebis gadawyvetis ertadert mizansewonil metods warmoadgens. ori SeTavsebuli sivrcis natesauri Sesabamisoba gansazrvrulia, Tu mocemulia monatesave wertilta otxi wyvili. kavsiris wrfeebi urtiertparaleluria. natesaobis sibrtye rom ganisazrvros, sakmarisia SevaerToT mocemuli wertilebi. monatesave wrfeebis TiToeuli wyvilis gadakvetis 37

38 nax. 21 wertili natesaobis sibrtyes ekutvnis. rogorc vicit sibrtye sami wertilit ganisazrvreba. Aamitom, natesaobis sibrtyis gansazrvrisatvis sakmarisia monatesave wrfeta sami wyvilis gatareba (nax.21) dagegmilebis mimartulebis arceva natesaur sivrceebsi ganvixilot rogori unda iyos dagegmilebis mimartuleba, rom sivrcis natesaur gardaqmnastan dakavsirebuli agebebi rac SeiZleba martivad aisaxos gegmilta sibrtyeze.. Tu dagegmilebis mimartulebas SevirCevT ise, rom igi natesaobis a 0 sibrtyis paraleluri iyos, masin gegmilta sibrtyeze mirebul am natesaur Sesabamisobebs natesaobis mimartulebastan ertad natesaobis RerZic saerto eqneba(nax. 22). 38

39 nax. 22 axla ganvixilot SemTxveva, rodesac dagegmilebis mimartuleba natesaobis mimartulebis paraleluria (nax.23). am nax. 23 SemTxvevaSi, rogorc naxazidan Cans, natesaurad Sesabamisi wertilebis gegmilebi ertmanets daemtxveva. 39

40 2.1.9 natesauri sivrceebis asaxva ortogonalur gegmilebsi ert gegmilta sibrtyeze dagegmilebisas mizansewonilia, dagegmilebis mimartuleba natesaobis sibrtyis paralelurad avirot. rogorc vicit, ortogonaluri dagegmilebisas dagegmilebis mimartuleba gegmilta sibrtyeebis martobulia. amitom, Tu natesaobis sibrtyes am mimartulebis paralelurad avirebt, igi or pirobas unda akmayofilebdes: martobuli unda iyos rogorc horizontaluri, aseve frontaluri gegmilta sibrtyeebisa. Aam pirobas ki profilis sibrtye akmayofilebs (nax.24). nax. 24 naxazze natesaobis (profilis) sibrtye mocemulia Tavisi kvalebit. vtqvat, A wertilis monatesave wertilia A'(A' 1,A' 2 ). masin natesaobis mimartuleba ganisazrvreba Tavisi horizontaluri (A 1 A 1 ') da frontaluri (A 1 A 1 ') gegmilit. Mmocemuli B wertilis monatesave B' wertilis ageba sizneles ar warmoadgens. 40

41 nax. 25 axla ganvixilot SemTxveva, roca dagegmilebis mimartuleba natesaobis mimartulebis paraleluria. rogorc vicit, am dros sivrcis natesauri wertilebis nebismieri wyvilis gegmilebi ertmanets emtxveva. Oori gegmilta sibrtyis SemTxvevaSi ki gvezleva sasualeba, natesaobis sibrtye ise SevirCioT, rom igi paraleluri iyos ert-erti gegmilta sibrtyisa. natesaobis mimartuleba ki _ natesaobis sibrtyis martobuli (nax. 25). am SemTxvevaSi monatesave figurebis horizontaluri gegmilebi ertmanets emtxveva, xolo frontalur gegmilta sibrtyeze gegmilebs Soris myardeba natesauri Sesabamisoba, sadac natesaobis RerZs horizontaluri sibrtye warmoadgens zogadi saxis meore rigis zedapirebi da mati gardaqmna brunvis zedapirebsi formata mravalferovnebita da geometriuli figurebis warmoqmnasi Tavisi rolis mixedvit zedapirebs gansakutrebuli adgili uwiravs. 41

42 ganvixilot teqnikur formebsi fartod gavrcelebuli zogadi saxis meore rigis zedapirebi. aset zedapirebs miekutvneba elifsuri zedapirebi. Aam zedapirebis brtyeli kvetebi, Sesrulebuli simetriis RerZis martobuli sibrtyeebit, ertmanetis msgavs elifsebs warmoadgens. rogorc vicit, elifsi matematikuri wiria da wertil-wertil unda aigos. Aamitom, zogadi saxis meore rigis zedapirebis urtiertkvetis amocanebis gadawyveta rig sirtuleebtan aris dakavsirebuli. Aam SemTxvevaSi xsirad mivmartavt am zedapirebis gardaqmnas brunvis zedapirebsi. rogorc arvnisnet, sivrcis gardaqmnebis metodi mocemul figuras sxva iset figurad gardaqmnis, romlis Tvisebebi dasaxuli amocanebis amoxsnis gamartivebis sasualebas mogvcems. ganvixilot daxrili elifsuri cilindris gardaqmna nax

43 magegmilebel cilindrad, roca natesaobis sibrtye profiluri donis sibrtyea. natesauri Sesabamisobis dasamyareblad sawiroa monatesave wertilta wyvilic (nax 26). A wertilis monatesave wertilis SerCevisas unda gavitvaliswinot, rom A'B' da C'D' RerZebi ertmanetis toli iqneba. ganisazrvreba ra magegmilebeli cilindris horizontaluri gegmili, frontaluri gegmilis ageba sizneles arar warmoadgens. nax. 27 gardavqmnat elifsuri hiperboloidi brunvis hiperboloidad. Aamocanis gamartivebis miznit natesaobis 43

44 sibrtyed SevirCioT frontaluri sibrtye. natesaobis mimartuleba ki _ natesaobis sibrtyis martobulad (nax. 27). naxazze Sesrulebuli ageba uzrunvelyofs elifsis gardaqmnas iset wrewirsi, romlis diametric elifsis didi diametris tolia. Aam SemTxvevaSi brunvis hiperboloidis frontaluri gegmili emtxveva mocemuli elifsuri hiperboloidis frontalur gegmils. natesaobis sibrtyis ganxilulma SerCevam Tavidan agvacila is Sromatevadi samusao, romelic mocemuli zedapiris frontaluri gegmilis(lekaluri mrudis) agebastan iyo dakavsirebuli meore rigis zedapirebis kveta sivrcis natesauri gardaqmna, adre ganxiluli metodebisgan gansxvavebit, mnisvnelovnad amartivebs mxazvelobiti geometriis sakmaod rtul amocanebs. vtqvat, mocemuli gvaqvs elifsuri paraboloidi, romelic fuzit eyrdnoba frontalur gegmilta sibrtyes. vipovot am zedapiris kveta zogadi mdebareobis sibrtyit (nax. 28). cxadia, mkveti sibrtyeebis metodit am amocanis amoxsnisas sawiro gaxdeba didi raodenobit damxmare elifsebis ageba. Tu elifsur paraboloids natesauri SesabamisobiT brunvis paraboloidad gardavqmnit, elifsebis magivrad wrewirebs avagebt. natesaobis sibrtye SevirCioT horizontaluri gegmilta sibrtyis paralelurad. es sasualebas mogvcems, elifsi wrewirsi gardavqmnat, elifsuri zedapiri ki _ brunvis zedapirad. Ggardaqmnis Semdeg, Cvens winase dasmuli amocana mkveti sibrtyeebis daxmarebit SegviZlia gadavwyvitot. sakmarisi raodenobis sibrtyeebis gatarebit, SevZlebT avagot saziebeli wiri, romelic ra Tqma unda, elifss warmoadgens. 44

45 nax. 28 M meore rigis zedapirebis TanakveTis wiris ageba meore rigis zedapirebis TanakveTis wiris agebasi sivrcis natesauri gardaqmnis gamoyenebas masin aqvs azri, Tu kvetasi monawile orive zedapiri ertdroulad gardaiqmneba brunvis 45

46 zedapirsi (nax. 29). Ees ki mxolod masin aris SesaZlebeli, Tu orive zedapiris RerZebi urtiertparaleluria da RerZebis martobul kvetasi mirebuli brtyeli kvetebi ertmanetis msgavs da msgavsebulad ganlagebul elifsebs warmoadgens. ganvixilot samrerziani elifsoidisa da elifsuri paraboloidis kveta. natesaobis sibrtyed SevirCioT profilis sibrtye. Aam SemTxvevaSi natesaobis mimartuleba natesaobis sibrtyis martobulia. nax. 29 elifsuri zedapirebi meore rigis zedapirebia. Mmeore rigis zogadi saxis zedapirebidan mxolod cilindrebi (paraboluri da hiperboluri) da hiperboluri paraboloidi ar ekutvnis elifsur zedapirebs. 46

47 elifsuri zedapirebi miireba elifsis gadaadgilebit sivrcesi raime wiris gaswvriv ise, rom elifsis sibrtye yoveltvis paraleluri rceba paralelizmis sibrtyis. mimmartveli wiri brunavs sivrcesi nebismierad raime uzravi wertilis garsemo, Tanac elifsis didi da mcire diametrebi icvleba kanonzomierebit, romelic damokidebulia danarcen or mimmartvelze. amitom, elifsuri zedapirebi, sivrcis natesauri gardaqmnit advilad gardaiqmneba brunvis zedapirebad da piriqit. gardaqmnisas, Tu msaxveli elifsebidan ert-erts gardavqmnit wrewirad, masin yvela misi paraleluri da msgavsi elifsi wrewirad gardaiqmneba da SesaZlebeli gaxdeba urtiertparaleluri damxmare sibrtyeebis simravlis gamoyeneba, romlebic monatesave zedapirs wrewirze gadakvets. nax. 30 elifsur zedapirebs miekutvneba: a) elifsoidebi, romelta mimmartvelebi elifsebia (nax. 30) b) hiperboloidebi (nax. 27), romelta mimmartvelebi hiperbolebia g) paraboloidebi (nax. 29), romelta mimmartvelebi parabolebia d) konusi, romlis 47

48 mimmartvelebi daslili meore rigis wirebia (gadakvetili wrfeebis ori wyvili) e) elifsuri cilindri (nax.26), romelta mimmartvelebi daslili meore rigis wirebia (paraleluri wrfeebis ori wyvili) sivrcis zogadi proeqciuli homologiebi sivrcis proeqciuli homologia gardaqmnis ufro zogadi saxea, vidre natesauri gardaqmna. natesauri gardaqmnisas homologiis centri arasakutriv wertils warmoadgens da amitomac Sesabamis wertilta SemaerTebeli wrfeebi ertmanetis paraleluria. sivrcis zogadi proeqciuli homologia gansazrvrulia Sesabamisi wertilebis otxi wyvilit da perspeqtivis centrit. Sesabamis wertilta otxi wyvilidan sami wyvili gansazrvravs Sesabamisobis a 0 sibrtyes.asesabamisi wertilebis wyvili homologiis centrtan ertad ert wrfezez evs (nax.31) nax. 31 homologiurad Sesabamisi ori figura romelime gegmilta sibrtyeze homologiis sibrtyis paralelurad rom davagegmilot, masin gegmiltaa sibrtyeze mocemuli figurebis 48

49 gegmilebs Soris damyardeba brtyeli homologiuri Sesabamisoba, romlis RerZs homologiis sibrtyis gegmilta sibrtyestan gadakvetis wrfe warmoadgens, centrs homologiis centris gegmili[18]. rogorc vicit, ortogonaluri dagegmilebisas dagegmilebis mimartuleba gegmilta sibrtyeebis martobulia, amitom mizansewonilia, homologiis sibrtye martobuli iyos orive gegmilta sibrtyisa. am pirobas ki profilis sibrtye akmayofilebs (nax. 32). nax. 32 sivrcis homologia SegviZlia warmovidginot, rogorc sibrtyiti homologiebis usasrulo simravle. amitom sivrcis homologias yvela is Tviseba aqvs, rac sibrtyis homologias axasiatebs. Cven vicit, rom brtyeli homologiuri gardaqmnit elifsi, parabola da hiperbola wrewirze SeiZleba gardaiqmnas. Sesabamisad sivrcis homologiuri gardaqmna brunvis elifsoids, brunvis paraboloids da brunvis hiperboloids sferoze asaxavs, ritac poziciuri amocanebis amoxsnis dros garkveul gamartivebas mivarwevt (nax.33). sivrcis natesauri SesabamisobiT prizma SeiZleba mxolod prizmasi aisaxos. sivrcis zogadi proeqciuli homologiit ki 49

50 prizma SeiZleba piramidaze aisaxos da piriqit. es damokidebuli iqneba homologiis centris SerCevaze. kerzod, Tu piramidis D wveros SevusabamebT D ' wertils, masin piramidis Sesabamisi zedapiris wiboebi ertmanetis paraleluri armocndeba da mivirebt prizmul zedapirs. homologiis centri (SS ' ) wrfis romelime S(S 1,S 2 ) wertilia, homologiis P(Pº 1 Pº 2 ) sibrtye ki profilis sibrtyea. nax meore nawili Crdilebi ortogonalur gegmilebsi (geometriuli figurebidan gegmilta sibrtyeze dacemuli Crdilebi) teqnikur naxazebze Crdilebis ageba mxolod geometriuli TvalsazrisiT xdeba. Aamitom, sinatlis wyaros intensivoba da 50

51 fizikuri aspeqtebi mxedvelobasi ar miireba. sinatlis wyaros formisa da sivrcesi mdebareobis mixedvit sinatlis sxivebi SeiZleba iyos paraleluri (bunebrivi anu mzis ganateba) an gadakvetili (xelovnuri ganateba). Mmzes ganvixilavt, rogorc usasrulod Sors mdebare wertils da misgan gamomaval sxivebs urtiertparalelurebad vtvlit. Aaqedan gamomdinare, dacemuli Crdilebis ageba SeiZleba SevadaroT paralelur dagegmilebas, xolo Crdilebis sazrvris dadgenis principi_zedapiris moxazulobis agebas. Cveulebriv, teqnikur naxazebze, sinatlis sxivis mimartulebad im kubis diagonalis paralelur mimartulebas miicneven, romlis waxnagebi ZiriTadi gegmilta sibrtyeebis paraleluria. epiurze am ganatebis sxivebis gegmilebi X, Y da Z RerZebisadmi 45º-iT iqneba daxrili. ganatebisas, sinatlis sxivebi sivrcesi mdebare obieqtis zedapiris garkveul nawils anatebs, danarceni ki gaunatebeli (CrdilSi) rceba (nax. 40). Aam Crdils sakutar Crdils uwodeben. ganatebuli da gaunatebeli zedapiris gamyof sazrvars_sakutari Crdilis konturs, xolo Crdils, romelic sxva zedapirze ecema_dacemul Crdils (nax. 44). sinatlis sxivebma, romlebic geometriul figuras exeba, sivrcesi SeiZleba warmoqmnas cilindruli an waxnagovani zedapiri. Aam sxivuri zedapirisa da sxva zedapiris (an sibrtyis) kveta dacemuli Crdilis konturs gansazrvravs[18]. wertilis Crdili am wertilze gamavali ganatebis sxivis kvals warmoadgens gegmilta sibrtyeze.sxivebi, romlebic wrfeze gaivlis, sxivur sibrtyes warmoqmnis. wrfis (rogorc wertilta simravlis) Crdili am sxivuri sibrtyisa da gegmilta sibrtyis gadakvetit ganisazrvreba. Aaqedan gamomdinare, wrfidan dacemuli Crdili gegmilta sibrtyeze isev wrfes warmoadgens da misi agebistvis wrfis kutvnili ori wertilis Crdilis agebaa sakmarisi. 51

52 donis wrfis Crdilis agebisas (nax.34), paraleluri dagegmilebis Tvisebebidan gamomdinare, misi erti wertilis Crdilis ageba iqneba sakmarisi. nax. 34 nax. 35 magegmilebeli wrfis Crdilis ageba mocemulia nax.35-ze. nax.36-ze ganxilulia is SemTxveva, roca zogadi mdebareobis AB wrfis A wertilis Crdili horizontalur gegmilta sibrtyes ecema, xolo B wertilis Crdili _ frontalurs. nax. 36 mravalkutxedis Crdilis ageba misi kutvnili wertilebisa da wrfeebis Crdilebis agebaze daiyvaneba (nax.37). 52

53 nax. 37 imisda mixedvit, ra mdebareobasia wrewiris sibrtye gegmilta sibrtyeebis mimart, misi Crdili SeiZleba iyos wrewiri (nax.38) an elifsi (nax.39). nax. 38 nax.39-ze horizontaluri gegmilta sibrtyis martobul sibrtyesi mdebare wrewiris Crdili agebulia horizontalur gegmilta sibrtyeze 53

54 nax. 39 nebismieri zedapiris Crdilis asagebad, jer sakutari Crdilis konturi unda ganisazrvros (nax.40) da Semdeg am konturis dacemuli Crdili unda aigos. nax. 40 nax. 41 brunvis cilindris sakutari Crdilis konturis dasadgenad, cilindris mxebi da frontaluri gegmilta sibrtyis mimart 45º- 54

55 it daxrili horizontalurad magegmilebeli α da β sxivuri sibrtyeebi gavatarot (nax.42). cilindris zeda fuzis sakutari nax. 42 nax. 43 Crdili cnobili wesit avagot. mirebuli konturis dacemuli Crdili SemosazRvravs cilindris dacemul Crdils. frontalur gegmilze ki mirebuli msaxvelis marjvniv cilindri sakutar CrdilSi iqneba. Bbrunvis konusis dacemuli Crdilis asagebad, jer misi S wveros Crdili avagot. wveros Crdilis mirebul S 1 gegmilze konusis fuzis wrewiris mxebi da 1 B 1 wrfeebi gavatarot. Sexebis wertilebsi gamavali msaxvelebi da am wertilebs Soris moqceuli fuzis wrewiris rkali sakutari Crdilis konturs gansazrvravs (nax.43). 55

56 2.2.2 Crdilebi ortogonalur gegmilebsi (geometriul zedapireb ze dacemuli Crdilebi) wrfis Crdili mrud zedapirze am wrfeze gatarebuli sxivuri sibrtyisa da mocemuli zedapiris kvetas warmoadgens (nax.44). nax.45-ze brtyeli figuridan Crdili ecema brunvis cilindrze. Aagebebi ori zedapiris urtiertkvetis amocanis amoxsnis nax. 44 nax. 45 analogiuria. Crdilebis sazrvrebis dadgenis sxvadasxva metodi arsebobs. metods ki obieqtis formisa da mdebareobis mixedvit vircevt. sasurvelia, rom grafikuli operaciebis minimaluri raodenobit amonaxsnis rac SeiZleba meti sizuste iqnas mirweuli[30]. praqtikasi yvelaze metad gavrcelebulia zemot ganxiluli sxivuri kvetebis metodi, romelic Crdilebis agebis ZiriTad metods warmoadgens (nax.46). 56

57 nax gamoyenebiti perspeqtivis safuzvlebi figurata perspeqtiuli gamosaxuleba sasualebas gvazlevs proeqtis Seqmnis processive Semowmdes Cafiqrebuli kompozicia masstaburobis, proporciulobis, Semadgeneli nawilebis urtiertmdebareobis da sxva motxovnebis gatvaliswinebit[30]. centraluri dagegmilebis sqemit sibrtyeze mirebul gamosaxulebasa da samganzomilebian obieqts Soris garkveuli damokidebuleba arsebobs. Ggeometriuli figurebis proeqciuli Tvisebebis Seswavla dezargis TeoremiT daviwyet. im or samkurxeds, romlebic dezargis Teoremas akmayofilebs, perspeqtiuli samkutxedebi ewodeba. Sesabamisi wveroebis SemaerTebel wrfeta saerto S wertils_perspeqtivis centri, 57

58 xolo wrfes, romelic samkutxedebis Sesabamisi gverdebis gadakvetis wertilebit ganisazrvreba _ perspeqtivis RerZi. am terminebis gatvaliswinebit dezargis Teorema SeiZleba Semdegnairad CamovayaliboT: Tu or samkutxeds aqvs perspeqtivis centri, masin am samkutxedebs eqneba perspeqtivis RerZic da piriqit, Tu or samkutxeds aqvs perspeqtivis RerZi, masin iarsebebs perspeqtivis centric. perspeqtiuli gamosaxulebis misarebad centraluri dagegmilebis specialuri sistema gamoiyeneba. mocemul sqemasi sibrtye sibrtyis martobulia; rogorc naxazidan Cans, nebismieri A wertilisatvis sibrtyeze yoveltvis moizebneba ertaderti (A,A 1 ) wyvili da piriqit, am wesit agebuli (A,A 1 ) wyvili ertadert A wertils gansazrvravs sivrcesi[29]. axla ufro dawvrilebit ganvixilot am sqemis Semadgeneli elementebi da mirebuli terminebi (nax. 47). nax. 47 _ gegmilta vertikaluri sibrtye anu suratis sibrtye. _gegmilta horizontaluri sibrtye anu fuzeta sibrtye. X-suraTis fuze (X -horizontis sibrtye (S -horizontis sibrtye (S -neitraluri sibrtye (S S P -mtavari manzili. 58

59 P-mTavari wertili (SP PD 1 radiusiani wrewiri-mtavari wrewiri. D 1,D 2 -distanciis wertilebi ( SD 1 da SD 2 A 1, B 1 mocemuli wertilebi. A 1 1,B 1 1 wertilebis fuzeebi. A 1,B 1 meoreuli gegmilebi. A, B mocemuli wertilebis perspeqtivi[30]. wrfis perspeqtivis asagebad sakmarisia misi ori wertilis perspeqtiva avagot (nax.48). naxazze wrfis maxasiatebel wertilebad mocemuli wrfisa da sasurate sibrtyis gadakvetis B' wertili da am wrfis usasrulod Sors mdebare anu arasakutrivi A wertilia SerCeuli. sasurate sibrtyestan gadakvetis wertilis gegmili nax. 48 TavisTavs SeuTavsdeba (B' xolo arasakutrivi wertilis gegmilis asagebad mzeris S wertilze mocemuli wrfis paraleluri wrfe gavatarot da vipovot misi gadakveta (A sasurate sibrtyestan. Tu A wertils A wrfeze usasrulobisken gadavaadgilebt, misi A 1 fuzec A 1 1 wrfeze usasrulobisken gadaadgildeba. rodesac A 1 usasrulobasi gadava, misi magegmilebeli SA 1 sxivi A 1 1 wrfis da masasadame 59

60 fuzeta sibrtyis paraleluri gaxdeba. Aaqedan gamomdinare, igi nax. 49 sasurate sibrtyes horizontis xazze gadakvets. Aamave dros, A wertilis gadaadgilebis processi am wertilis da misi fuzis A da A 1 perspeqtivebi horizontis xazis mimart martobul kavsiris wrfeze iqneba ganlagebuli. e.i. Tu sasurate sibrtyeze mocemulia raime wrfis a perspeqtiva da agretve misi fuzis a 1 perspeqtiva, sawiroa a 1 gavagrzelot horizontis xazis gadakvetamde, mirebuli A wertilidan arvmartot martobi (vertikaluri kavsiris wrfe), romelic a wrfeze mogvcems arasakutrivi A wertilis A perspeqtivs[29]. ganvixilot fuzeta sibrtyesi mdebare paralelur wrfeta kona rogorc ' M'N ' C'D ' A'B zemot arvnisnet, A A,C' C, M M am wrfeta arasakutriv wertilta gegmilebis mosazebnad ki mzeris S wertilze TiToeuli matganis paraleluri wrfe gavatarot da am wrfeebis gadakvetis wertilebi sasurate sibrtyestan. Nnax. 49-dan Cans, rom es wertilebi ertmanets daemtxveva (B D N F ' A'B ganvixilot fuzeta sibrtyis paraleluri A'B' wrfe. A 1 'B' 1 da radgan paralelur wrfeebs erti Tavmoyris wertili aqvs, mat perspeqtivebsac Tavmoyris erti F wertili eqneba, romelic horizontis xazze mdebareobs (nax.50 60

61 nax. 50 nax. 51 fuzeta sibrtyis martobuli A'B' wrfis perspeqtivi suratis X fuzis martobuli iqneba (nax. 51), xolo fuzis A 1 B 1 perspeqtivi wertils warmoadgens. aseti wrfeebis Tavmoyris wertili arasakutrivia[29]. nax.52-ze sasurate sibrtyis paraleluri A'B' wrfis A'B' da A 1 B 1 AB perspeqtivia agebuli. rogorc naxazidan Cans, X;suraTis fuzis paraleluri A'B' wrfis perspeqtivi da 61

62 AB ) meoreuli A 1 B 1 gegmili (nax.53) suratis fuzis paraleluria A 1 B 1 X); sasurate sibrtyis martobuli wrfeebisa da mati fuzeebis Tavmoyris wertils mtavari P wertili warmoadgens (nax.54); nax. 52 perspeqtivsi sibrtyes ori gadakvetili wrfit gansazrvraven (nax.55), romeltagan erti fuzeta sibrtyestan, xolo meore surattan mocemuli sibrtyis TanakveTis wrfes warmoadgens (Sesabamisad, fuzeta da sasurate kvalebi)[29]. nax

63 Tu mzeris wertilze gamavali da mocemuli sibrtyis paraleluri sibrtyis surattan gadakvetas ganvixilavt, mivirebt wrfes, romelic mocemuli sibrtyis arasakutrivi wrfis gagmils warmoadgens (nax. 56). amgvarad, sibrtyis arasakutrivi wrfis perspeqtivi sibrtyis kvalis paraleluria. nax. 54 nax

64 nax. 56 rac Seexeba wrewiris perspeqtivs, igi miireba wrewiris TiToeul wertilze gamavali magegmilebeli sxivebisgan Seqmnili sxivuri konusisa da sasurate sibrtyis gadakvetasi. imisda mixedvit, Tu ra mdebareobasia sasurate sibrtye am am sxivuri konusis mimart, kvetasi mirebuli wiri ESeiZleba iyos elifsi, parabola an hiperbola. ganvixilot wrewiris perspeqtivis (elifsis) agebis ert-erti yvelaze gavrcelebuli metodi, romelsac Semoxazuli kvadratis metodi ewodeba[30]. nax. 57-ze mocemulia fuzeta sibrtyesi mdebare wrewiris ortogonaluri gegmilebi. wrewirze SemovxazoT kvadrati, SevirCioT mzeris wertili da sasurate sibrtye, romelic wrewiris centrze gadis. gavatarot x da h. suratis fuzeze P x wertilis sxvadasxva mxares gadavzomot mocemuli wrewiris radiusebi. Rogorc vicit, saturate sibrtyis martobuli wrfeebis Tavmoyris wertils mtavari P wertili warmoadgens. amitom, suratis fuzeze mirebuli 1 da 2 wertilebi SevaerToT P wertiltan. Ddistanciis D 1 da D 2 wertilebi SevaerToT P x wertiltan. miviret mocemuli kvadratis perspeqtivi. Kkvadratis qveda fuzeze, rogorc diametrze SemovxazoT naxevarwrewiri da 64

65 gavatarot horizontalur mimartulebastan 45º-iT daxrili radiusebi, romelta boloebi kvadratis diagonalebze gansazrvravs 5,6,7 da 8 wertilebs. mirebuli wertilebis momvlebi mrudi elifss warmoadgens. nax. 57 axla ganvixilot fuzeta sibrtyis martobul sibrtyesi mdebare wrewiri da avagot misi perspeqtivi. Aam SemTxvevaSic damxmare wrewirad sasurate sibrtyis paraleluri wrewiri gamoviyenot (nax. 58). avagot ortogonalur gegmilebsi mocemuli martkutxa paralelepipedis perspeqtivi (nax.59). SevirCioT mzeris (S 1, S 2 ) wertili da mtavari sxivis (S 1 P) mimartuleba. suratis sibrtye mzeris mimartulebis martobulad unda avirot, magram misi 65

66 nax. 58 dasoreba mzeris wertilidan mxolod imazea damokidebuli, Tu ra zomis perspeqtivi gvinda mivirot: rac ufro metadaa dasorebuli suratis sibrtye S wertilidan, mit ufro didi zomis perspeqtiul gamosaxulebas mivirebt. perspeqtivis asagebad horizonti da suratis fuze gavatarot. h da x wrfeta Soris manzili ortogonaluri gegmilebidan 66

67 unda avirot. davnisnot mtavari P wertili. Mmzeris S wertilze prizmis (1,2) da (2,3) wiboebis paraleluri wrfeebi gavatarot da vipovot am wrfeebis gadakvetis wertilebi sasurate sibrtyestan (F 1 da F 2 ), romlebic Sesabamisi mimartulebis paralelur wrfeta konebis Tavmoyris wertilebs warmoadgens. radgan (1,2) da (2,3) wrfeebi horizontaluri wrfeebia, mati Tavmoyris wertilebi horizontis xazze P wertilidan PF 1 da PF 2 manzilebit iqneba dasorebuli[30]. mocemuli figuris gamosaxulebis agebas ert_erti im (O) wertilidan daviwyebt, romelic usualod suratis sibrtyesia. suratis x fuzeze P wertilidan marjvniv movzomot P x O o monakveti. mirebuli O o wertili SevaerToT Tavmoyris F 2 wertiltan. radgan O wertili fuzeta sibrtyesia, O o wertilidan SegviZlia gadavzomot mocemuli figuris simarle ortogonaluri gegmilebidan da mirebuli O wertilic SevaerToT Tavmoyris F 2 wertiltan. axla ukve 1 da 2 wertilebis perspeqtivis ageba martivad SegviZlia: gavatarot (S ) da (S ) magegmilebeli wrfeebi. Aam wrfeebis gadakvetis wertilebi movnisnot suratis sibrtyeze da mirebuli 1 0 da 2 0 wertilebidan arvmartot martobebi (F 2 O o ) da(f 2 O) wrfeebtan gadakvetamde. miviret 5 da 6 wertilebi. 2 da 6 wertilebze gavatarot (2,3) da(67) paraleluri wrfeebi, romelta Tavmoyris wertilia F 1. rac Seexeba 3 da 7 wertilebs, aigeba ukve agebuli wertilebis analogiurad. 8 wertilis ageba sizneles arar warmoadgens. vtqvat, epiurze mocemulia marti prizma cilindruli TaRiT (nax. 60). avagot am figuris perspeqtivi zemot ganxiluli agebebis gatvaliswinebit (nax.61). 67

68 nax

69 nax. 60 nax

70 2.3 mesame nawili mxatvruli Semoqmedeba materialur warmoebasi materialuri warmoebis ganvitarebam moitxova iseti samrewvelo naketobebis daproeqteba da sagnobrivi garemos Seqmna, sadac am naketobebis teqnikur motxovnebtan ertad adamianuri faqtoric iqneboda gatvaliswinebuli. dizaineris mizani sazogadoebisatvis sasargeblo, saeqsploataciod mosaxerxebeli da lamazi sagnebis Seqmna gaxda[37]. samrewvelo dizaini samrewvelo naketobebis daproeqtebis SemoqmedebiTi procesia, romelic teqnikuri estetikis motxovnata Sesabamisad xorcieldeba. sasargeblo da lamazi naketobebis Seqmna am naketobebis konstruqciul-teqnikuri da ekonomiuri motxovnebis gatvaliswinebit unda xdebodes. formata Ziebisas dizainerma sworad unda gansazrvros teqnikursa da estetikurs, materialursa da suliers Soris arsebuli Tanafardoba mocemul sagnobriv garemosi. samrewvelo dizaini aramarto sagnobriv garemos gardaqmnis, aramed am garemos mimart adamianis damokidebulebasac ayalibebs. imdenad, ramdenadac eqsploataciis processi sagnebi garkveul zemoqmedebas axdens adamianze, iwvevs adamianis damokidebulebas am sagnobriv garemoze. adamianta gemovnebis ganvitarebastan ertad, samrewvelo dizains SeuZlia winaswar gansazrvros mosaxleobis motxovna Sesabamisi mimartulebit[40]. samrewvelo naketobebsi sasargeblo da lamazi ganuyofladaa dakavsirebuli. silamazes, rogorc damatebit maxasiatebels, ukve mza nawarms ver mivaniwebt. silamaze iqmneba daproeqtebis dasawyissive, roca formis SerCevisas vitvaliswinebt naketobis funqcionalur danisnulebas, kostruqcias, masalas da teqnologiurobas. amitom, mxatvruli konstruirebis metodi itvaliswinebs dizaineris musaobas mkvlevarebtan, konsruqtorebtan da teqnologebtan ertad, konstruirebis mosamzadebeli etapidanve. mxolod am SemTxvevaSi da aset 70

71 pirobebsi SeiZleba iyos dizaineris musaoba efeqturi axali naketobebis Seqmnisas[36] naketobis estetikuri Rirebuleba mxatvar-konstruqtorma proeqtirebis processi formata warmoqmnis obieqturi kanonzomierebebi unda gaitvaliswinos. man ara marto sagnebis sasargeblooba unda uzrunvelyos, aramed Seqmnas isini lamazi, Tanamedrove stilis, modis da estetikuri gemovnebis Sesabamisad, ert naketobasi SeuTanxmos sasargeblo da lamazi. swored es faqtori unda iyos gatvaliswinebuli proeqtirebis dros. im SemTxvevaSi, roca naketobis sargeblianobas ZiriTadi mnisvneloba aqvs (Carxebi, xelsawyoebi) proeqtirebasi unda Warbobdes funqvionaluri midgoma, magram aucileblad stilisa da kompoziciis motxovnata gatvaliswinebit. aseti naketobebis estetikuri Rirebulebebi da silamaze konstruqciebis daxvewisas ibadeba da mas ZiriTadad injiner-konstruqtori qmnis. roca wina planze naketobis silamazea wamoweuli (suvenirebi, bevri kulturulsayofacxovrebo nawarmi), izrdeba da xandaxan mtavaric xdeba formis mxatvruli Zieba, stilisa da modis ayola. ra Tqma unda, am SemTxvevaSic, proeqtirebisas formata warmoqmnis teqnikuri faqtorebis ugulvebelyofa ar SeiZleba. qmnis ra nawarms, mxatvar-konstruqtori aniwebs mas sazogadoebriv Sinarss, aketebs mas sasargeblos, mosaxerxebelsa da lamazs. mxatvruli proeqtirebis metodebit Seqmnili naketobebi aramarto teqnikurad sruyofili da ekonomiuria, aramed eqsploatacisas mosaxerxebeli, harmoniuli da garegnulad mimzidveli. aseti rezultati mxolod injinrebisa da mxatvar-konstruqtorebis mwidro TanamSromlobiT miirweva. mati ertoblivi musaobis Sedegad iqmneba samrewvelo produqcia 71

72 xarisxis marali macveneblit, romelic momxmareblis motxovnebs yovelmxriv daakmayofilebs[36]. yoveli axali naketoba, romelic seriul warmoebasi unda CaiSvas, winaswar saguldagulo mxatvrul damusavebas moitxovs. xelosnis warumatebloba aris cudi nawarmis erteuli egzemplari, xolo seriuli warmoebis warumateblobas ki mnisvnelovan danakargebamde mivyavart. amitom, axali samrewvelo nawarmis damproeqtebelta jgufs didi pasuxismgebloba akisria. Tavisi musaobis processi mxatvar-konstruqtors uxdeba gulmodgined gaitvaliswinos samrewvelo nawarmisatvis wayenebuli socialur-ekonomiuri da estetikuri motxovnebis farto wre. motxovnebs, romelsac seriuli samrewvelo produqciis momxmarebeli uyenebs mxatvar-konstruqtors, teqnikuri estetikis motxovnebi ewodeba. naketobisadmi teqnikuri estetikis motxovnebis gansazrvrisas sawiroa gatvaliswinebuli iyos rogorc misi moxmarebis, aseve Tanamedrove warmoebis pirobebi sagnobrivi garemos gardaqmna da samrewvelo dizaini warmoebis processi adamiani mudmivad qmnis da cvlis sagnobriv garemos. es garemo misi SromiTi saqmianobis produqts warmoadgens da im aucilebel cxovrebiseul sasualebas Seadgens, romlis garesec adamians arseboba ar SeuZlia. adamiani qmnis da iyenebs, sagnobrivi garemo formirdeba da funqcionirebs. samrewvelo nawarmi, romelic kargad pasuxobs Tavis danisnulebas da mocemul istoriul momentsi akmayofilebs adamians, ganixileba, rogorc funqcionalurad srulyofili, mosaxerxebeli da sasargeblo. 72

73 samrewvelo saqonlis xarisxis gaumjobesebasa da asortimentis srulyofasi did rols mxatvar-konstruqtorebi asruleben. mat mier daproeqtebuli naketobebi ertmanets unda Seesabamebodes zomebsi, formasi, fersi da garemomcvel saganta ertiani kompleqsebi warmoqmnas. damproeqteblebis winase dgas amocana _ adamianta SromisaTvis, yofacxovrebisa da dasvenebisatvis aucilebeli komfortuli garemos Seqmna. sawarmoo estetika teqnikuri estetikis ert-erti mnisvnelovani sakitxia. sawarmoo garemos estetikuri organizacia mwidro kavsirsia Sromis mecnierul organizaciastan da SromiTi saqmianobisa da dasvenebisatvis optimaluri pirobebis SeqmnasTan dakavsirebul problemebtan. igi agretve mnisvnelovan socialur faqtorsac warmoadgens, radgan xels uwyobs adamianis pirovnuli Tvisebebis ganvitarebas[40]. axali sawarmoebis daproeqtebisa da mseneblobis dros didi yuradreba etmoba samusao garemos Seqmnis problemebs, romlebic SromiTi pirobebis gaumjobesebasa da estetikuri Rirebulebebis dakmayofilebas emsaxureba. samrewvelo garemos estetikuri formireba unda ganixilebodes, rogorc RonisZiebaTa kompleqsi, mimartuli meqanizaciis, avtomatizaciis da srulyofili teqnologiebis danergvisaken, Sromis komfortuli pirobebis Seqmnisa da estetikuri gamomsaxvelobis mirwevisken. aseti garemo ki adamianebsi dadebit emocionalur da mxatvrul zemoqmedebas gamoiwvevs[36] teqnikuri estetikis motxovnebi farto moxmarebis sagnebis daproeqtebasi praqtikam gvicvena, rom roca saqme gvaqvs estetikurad srulyofil sagantan, roca Cven win martlac marali klasis 73

74 naketobaa, igi warmoadgens, rogorc wesi, injiner-konstruqtoris, mxatvar-konstruqtorisa da bevri sxva maralkvalificirebuli specialistis ertoblivi, SeTanxmebuli TanamSromlobis Sedegs. aseti Sedegis misarebad mxatvar-konstruqtorma winaswar kargad unda gaiazros da Seiswavlos teqnikuri estetikis is ZiriTadi motxovnebi, romelsad unda akmayofilebdes konkretuli dasaproeqtebeli naketoba. naketobis funqcia farto cnebaa da igi ucileblad adamianis morvaweobastan kavsirsi ganixileba. danisnulebis garda (ZiriTadi samusao funqcia), gatvaliswinebuli unda iyos iseti sakitxebi, rogoricaa momxmarebloba, simsubuqe da bolos momxmareblis usafrtxoeba eqsploataciis processi. aqedan gamomdinareobs mteli rigi motxovnebisa e.w. adamianur faqtortan dakavsirebit da ergonomikis sakitxebi. samrewvelo nawarmi lamazi rom iyos, massi srulad unda isaxebodes is mizani, romelsac adamiani ayenebs am nawarmis Seqmnisas. ramdenadac saqme gvaqvs materialur warmoebastan, srulyofilad unda gadaiwras teqnikuri sakitxebic, Tanac minimaluri sasualebebit. Tu es asea da sagnis formasic metnaklebad gamoixateba mizani da Sinaarsi, masin es forma ariqmeba, rogorc msvenieri[40]. dasaproeqtebeli sagnebisa da saganta kompleqsebis mimart wayenebuli teqnikuri estetikisa motxovnebi warmoadgens formata warmoqmnis ert-ert ZiriTad monacems. sxvadasxva faqtorebis gavlena da gatvaliswineba mxatvar-konstruqtors azlevs sasualebas winaswari warmodgena Seiqmnas funqcionaluri formis, konstruqciuli formisa da teqnologiuri formis Sesaxeb. magram srulyofili dizain-formis Sesaqmenlad es sakmarisi ar aris. garda amisa, sawiroa kompoziciis kanonzomierebebisa da sasualebebis codnac. teqnikuri estetikis zogadi motxovnebia[36]: 74

75 a)gamomsaxveloba, romelic warmoadgens naketobis Tvisebas, Tavisi garegnuli saxit TvalnaTliv asaxos xarisxi da Sesabamisi estetikuri zemoqmedeba moaxdinos. b)originaluroba-ertoblioba naketobis formis Taviseburi elementebisa da mati urtiertkavsirisa, romelic sasualebas gvazlevs, gavarciot igi sxva, amave tipis naketobisagan. originalurobis cneba ki ar gamoricxavs, piriqit xazs usvams da inarcunebs formistvis damaxasiatebel nacionalur, sawarmoo an safirmo nisans. g)harmoniuloba- naketobis formis Tvisebebi organulad unda erwymodes formis elementebs, rac am elementebis urtiertganlagebita da urtiertkavsirit miirweva. harmoniulobis motxovna vrceldeba agretve naketobis naketobis Sesabamisobaze im Senoba-nagebobasTan, sadac misi eqsploatacia unda moxdes. d)stilis ertianobis motxovna- naketobis stili im momentsi arsebul da istoriulad Camoyalibebul socialurekonomiur da ideur-estetikur principebs unda asaxavdes. e)stilis Tanamedroveoba naketoba SesabamisobaSi unda iyos saerto msoflio stiltan da ganvitarebis saerto donestan daproeqtebis stadiebi nebismieri samrewvelo naketobis daproeqtebis procesi SeiZleba stadiebad davyot. mxatvar-konsruqtoris roli TiToeul stadiaze sxvadasxva SeiZleba iyos[36]. proeqtirebis pirveli, mosamzadebeli stadia-kvlevis stadiaa. sxva specialistebtan ertad kvlevasi dizaineric irebs monawileobas, exeba formata warmoqmnis sakitxebs, swavlobs kavsirs adamiani-sagani-garemo. kvlevis processi grovdeba informacia dasaproeqtebel nawarmze im gamocdilebis gatvaliswinebit, Tu rogor mzaddeboda adre analogiuri naketobebi. mteli Segrovili informacia yovelmxriv analizdeba, 75

76 rac srul warmodgenas gviqmnis am naketobaze da efeqtur sasualebas warmoadgens misi Semdgomi srulyofisatvis. macveneblebi, romlis mixedvitac unda vawarmoot analizi, damokidebulia naketobis sirtuleze, mis urtiertkavsirze adamiantan da garemostan. naketobis nimusis Seswavlisas dgindeba misi damzadebistvis sawiro teqnologiuri da konstruqciuli metodebi, ganisazrvreba sawiro masalebi da daisaxeba mati gamoyenebis racionaluri gzebi, gamoikvleva naketobis Sesabamisoba danisnulebastan da eqsploataciis pirobebtan (Tu ramdenad mosaxerxebeli iqneba naketoba eqsploataciisas), gamoitvleba, ramdenad ekonomiuri gadawyvetilebebi iqna mirebuli. naketobis damzadebis Sefasebis zogadi macvenebeli gamoiyvaneba zemot CamoTvlil macveneblebze dayrdnobit. macveneblebis raodenoba da mati SedarebiTi analizi damokidebulia naketobis sirtulesa da danisnulebaze. kvlevis damamtavrebel stadiaze Sedgeba ZiriTadi motxovnebi axali naketobis daproeqtebaze da es motxovnebi gatvaliswinebuli iqneba momaval proeqtze musaobisas. daproeqtebis meore stadiaa mxatvrul-sakonstruqtoro winadadebebis stadia. es aris yvelaze ufro rtuli stadia mxatvrul konstruirebasi. am stadiaze warmoebs formata Zieba da damusaveba, ganisazrvreba kinematikuri da eleqtruli sqemebi, SeirCeva konstruqciuli masalebi, SesaZeni mza nawilebi da detalebi, dadgindeba kvanzebisa da calkeuli nawilebis gabarituli zomebi da misarebi konstruqciuli gadawyvetebi. am stadiaze ZiriTad Semsruleblebad gvevlinebian injinerkonstruqtori da mxatvar-konstruqtori, romlebic mwidro kontaqtsi musaoben mteli daproeqtebis processi. Tumca, es ar gamoricxavs teqnologis, ergonomistis, eqimis an sxva specialistis monawileobas proeqtirebis processi, magram am stadiaze isini ZiriTadad konsultatebis rols asruleben. 76

77 mxatvrul-sakonstruqtoro winadadebebs mohyveba dasaproeqtebeli naketobis eskizis damusaveba, romelic ZiriTadi damakavsirebeli rgolia injiner-konstruqtorsa da mxatvar-konstruqtors Soris. pirveli matgani wyvets proeqtirebis teqnikur sakitxebs, xolo mxatvar-konstruqtori am gadawyvetilebebis safuzvelze awarmoebs Ziebas. mxatvarkonstruqtoris mier winadadebebi da variantebi injinerkonstruqtors gadaecema dasamusaveblad. damusavebis am processi SeiZleba injiner-konstruqtors mxatvar-konstruqtoris sayuradrebod SeniSvnebi da winadadebebi daebados. Tavis mxriv, ukanasknels SeuZlia pasuxad axleburi konstruqciuli gadawyvetebi wamoayenos formisa da konstruqciuli gadawyvetebis Zieba SemoqmedebiTi procesia da optimaluri varianti mxolod masin SeiZleba SemuSavdes, Tu injiner- konstruqtorisa da mxatvarkonstruqtoris mier ertoblivad wamoyenebuli yvela motxovna da winadadeba iqneba gatvaliswinebuli. mxatvrul-sakonstruqtoro winadadebebis damusavebis stadiaze, rogorc wesi, ibadeba sakitxebis gadawyvetis sxvadasxva gzebi, naketobis eskizebi sruldeba naxatebisa da naxazebis saxit, rac sasualebas izleva operatiulad iqnas Setanili Sesabamisi cvlilebebi. eskizebis damzadebis paralelurad, mxatvar-konstruqtori awarmoebs Ziebas da naketobis formis daxvewas maketirebis gamoyenebit. maketireba sruldeba pirobiti masalit (plastilinit, muyaoti, TixiT da a.s.). yvela damusavebuli winadadeba analizs unda eqvemdebarebodes. Sedegad ki SeirCeva sauketeso varianti, romelzedac gagrzeldeba musaoba. proeqtirebis mesame stadiaa mxatvrul-sakonsruqtoro proeqtis Sedgena, romelic naketobis teqnikuri proeqtis damusavebas Seesabameba. am stadiaze samusaos moculoba da monawile specialistebis ricxvi sagrznoblad izrdeba. adre 77

78 Sesrulebuli eskizebi sabolood ixveweba, damusavdeba konsruqciis kvanzebi da Semadgeneli elementebi. mxatvarkonstruqtorma formis Camoyalibebisas yvela is cvlileba unda gaitvaliswinos, romelic proeqtirebis processi SeiZleba moxdes. amave dros, es gadawyvetilebebi aucileblad unda SeuTanxmos injiner-konstruqtors. teqnikuri proeqtis Sesrulebis stadiaze, roca naketobis formastan dakavsirebuli sakitxebi sabolood gadawyvetilia, mxatvar-konstruqtori ufro guldasmit amusavebs calkeuli detalebis formebs, gansakutrebit ki im nawilebisas, romlebic gansazrvravs momxmareblis mier naketobis mosaxerxebel moxmarebas. sabolood, teqnologtan, fiziologtan da sxva specialistebtan ertad mxatvar-konstruqtori ircevs dasamzadeblad aucilebel da zedapiris mosapirketebel masalebs, radgan garda estetikuri motxovnebisa, zedapiris feri da faqtura unda akmayofilebdes fiziologis motxovnebsac. eskizuri proeqtis sirrmiseuli damusavebis garda, proeqtirebis am stadiaze wydeba rigi sxva sakitxebic: racionaluri konstruqciuli masalebis SerCeva da naketobis damzadebis optimaluri teqnologiebi, kvanzebisa da Semadgeneli nawilebis unifikacia da normalizacia. mxatvrul-sakonstruqtoro proeqtirebis stadiaze, naxazebis garda, sruldeba maketebi pirobit masalebsi an gamoiyeneba wina stadiaze Sesrulebuli da SeniSvnebis gatvaliswinebit damusavebuli maketebi. aucileblobis SemTxvevaSi naketobis naturaluri sididis modelic mzaddeba. es exmareba mxatvarkonstruqtors moaxdinos formisa da feris koreqtireba, romelic unda SeTanxmdes saproeqto jgufis danarcen wevrebtan, radgan am cvlilebebma naketobis damzadebis teqnologiasa da masalis SerCevaze SeiZleba moaxdinos gavlena. meotxe stadiaa mxatvrul-sakonstruqtoro damusavebis stadia. am stadiaze naketobis samusao naxazebi musavdeba. formata warmoqmnisa da feris SerCevis sakitxebi wina stadiaze ukve 78

79 damusavebulia da mxatvar-konstruqtoris samusaota moculoba mkvetrad mcirdeba. samusao naxazebis damusavebisas konsultantis rangsi igi mxolod masin CaerTveba, roca es aucilebeli gaxdeba. mxatvar-konstruqtori usualo monawileobas Rebulobs Sablonebisa da rtuli zedapirebis damusavebasi, sxvadasxva warwerebis damzadebasi. samusao naxazebis Sesrulebis Semdeg mzaddeba erti an ramdenime sacdeli nimusi, romelic gankutvnilia axali naketobis mxatvrul-konstruqciuli SefasebisTvis, funqcionaluri motxovnebis Sesabamisobaze, simtkiceze da xangamzleobaze gamocdistvis. nimusebi unda damzaddes imave masalisagan, romelic proeqtis mixedvit masiuri warmoebistvis aris gankutvnili. ar SeiZleba masalebisa da zedapirebis mopirketebis Secvla, radgan aman proeqtis ideis damaxinjeba da nawarmis garegnuli saxis Secvla SeiZleba gamoiwvios. mexute stadia-sacdeli nimusebis gamocda. momaval saeqsploatacio pirobebtan maqsimalurad miaxloebul pirobebsi mowmdeba proeqtirebis processi mirebuli yvela gadawyvetilebis siswore da aucileblobis SemTxvevaSi SeiZleba Setanil iqnas Sesabamisi cvlilebebi. mxatvar-konstruqtori specialistebis im jgufis sruluflebiani wevria, romelic sacdeli nimusis damzadebis procesze axorcielebs saavtoro zedamxedvelobas da am procesis Sedegebze gamoaqvs daskvna. proeqtirebis zemot moyvanili stadiebi damaxasiatebelia SedarebiT rtuli naketobebistvis, rogoricaa Carxebi, manqanebi, xelsawyoebi, fotoaparatebi, mtversasrutebi, televizorebi, aveji da sxva. rigi naketobebis proeqtireba ar moitxovs specialistebis did raodenobas, orond zogadi saorganizacio principi igive iqneba. mxatvar-konstruqtoris musaobis metodika arsebitad dasaproeqtebeli naketobis danisnulebaze, gamoyenebis areze da estetikur motxovnebzea damokidebuli. 79

80 2.3.6 saproeqto amocanebis ZiriTadi tipebi rogorc zemot iyo arnisnuli, nebismieri samrewvelo naketobis daproeqtebis procesi pirobitad xut stadiad SeiZleba davyot. Cvens mier moziebul literaturasi[36] saproeqto amocanebis otxi ZiriTadi tipia gamoyofili: 1)umartivesi sagnebisa da meqanikuri mowyobilobebis daproeqteba 2)rTuli praqtikuli da sivrcobriv-moculobiti struqturis meqanizmebis daproeqteba 3)samrewvelo naketobata kompleqsis daproeqteba da 4)sagnobrivi garemos daproeqteba. specialistta jgufis mier Sesrulebuli analizis Semdeg, romelic damokidebulia naketobis sirtulesa da mis urtiertkavsirze adamiantan da garemostan, unda ganisazrvros, saproeqto amocanis zemot CamoTvlili tipebidan romels miekutvneba konkretuli amocana. yoveli tipis Sesruleba ki Tavis TavSi gulisxmobs im ZiriTadi stadiebis nabij-nabij gavlas, romelis aucilebelia saproeqto amocanis warmatebit dasrulebistvis saproeqto grafika saproeqto grafikis ramdenime saxe arsebobs: wrfovani gamosaxuleba, monoqromuli (ertferiani) gamosaxuleba, Sesrulebuli e.w. amorecxvit an dafervit da poliqromuli, romelic ramdenime fersi sruldeba. saproeqto grafikis ama Tu im saxis SerCeva damokidebulia dasaproeqtebeli obieqtis xasiatze, Sesasrulebeli gamosaxulebis (gegmilis) saxeze (perspeqtiva, Wrili, ortogonaluri gegmili) da zogad kompoziciur Canafiqrze. wrfovani gamosaxuleba-naxazis Sesruleba, saproeqto grafikis sxva danarcen saxeebtan SedarebiT, drois nakleb danaxarjs moitxovs da im SemTxvevebSi gamoiyeneba, roca gamosaxulebas mnisvnelovani moculobit-sivrcobrivi STabeWdilebis moxdena ar moetxoveba. wrfovani grafika met- 80

81 naklebad bevr pirobitobas Seicavs, meti yuradreba eqceva teqnikur da geometriul informacias, interieris, eqsterierisa da sxvadasxva sqemebis dagegmarebas. simartive, lakoniuroba, mkafiod Sesrulebuli naxazi, Tavisufali sxvadasxva garegnuli efeqtebisagan, xsirad xdis ortogonalur gegmilebs ertadert misareb sasualebad. monoqromuli (Suq-Crdilovani) gamosaxuleba, Sesrulebuli Sav-TeTri, e.w. amorecxvis an dafervis mesveobit TvalsaCinod gadmogvcems sagnis moculobit formasa da mis ZiriTad sivrcobriv gansakutrebulobas. mxatvrul proeqtirebasi, Cveulebriv, monoqromuli gamosaxulebebi poliqromul gamosaxulebebtan ertad kompleqssi gamoiyeneba[38]. poliqromuli naxazi akvarelit an guasit sruldeba. SemuSavebulia poliqromiuli naxazebis Sesrulebis sxvadasxva metodi. TiToeul metods Tavisi teqnologia, Tavisebureba da gamoyenebis are aqvs modelireba samrewvelo naketobis maketis damzadeba mxatvruli daproeqtebis yvela ZiriTad stadiaze SeiZleba gaxdes sawiro. imisda mixedvit, Tu Ziebis romel stadiaze xdeba ama Tu im cvlilebis Setana, sakonstruqtoro Tu teqnologiuri winadadebebis gatvaliswiba an daxvewa, maketi SeiZleba iyos saziebo an saboloo. mxatvrul-sakonstruqtoro winadadebebis damusavebis stadiaze(meore stadia) saziebo maketireba pirobiti masalit(plastilini, muyao, xe,, TabaSiri da a.s.) sruldeba. saganta formebi, ise rogorc mati fuqcionaluri danisnuleba, mravalferovania. formata sirtulis mixedvit SeirCeva maketirebistvis sawiro masala da optimaluri teqnologiuri procesi[38]. 81

82 P praqtikasi xsirad gvxvdeba furclovani masalisgan maketis dazadebis SemTxvevebi. mxazvelobiti geometriidan cnobilia, rom amisatvis sawiroa winaswar, monjis epiurze Sesruldes figuris naxazi da am naxazis mixedvit ganisazrvros figuris maxasiatebeli elementebis ZiriTadi zomebi, kutxeebi da fartobebi. mirebuli sidideebis gatvaliswinebit gamoixazos figuris zedapiris Slili anu ganfena sibrtyeze. mirebuli Slili gadatanil unda iqnas furclovan masalaze da gamoiwras Targi. am Targis mesveobit xdeba saziebo maketis damzadeba. rac Seexeba daproeqtebis im stadias, roca xdeba mxatvrulsakonstruqtoro proeqtis Sedgena, gamoiyeneba ukve Sesrulebuli maketi an mzaddeba axali da ufro daxvewili. formisa da feris koreqtirebis miznit ki SeiZleba naturaluri sididis modelic damzaddes. modeli warmoadgens saboloo saxis makets, romelic zustad imeorebs masiur warmoebasi CasaSveb naketobas Tavisi zomebis, feris, faqturisa da sxva maxasiateblebis gatvaliswinebit da imave masalisgan unda damzaddes, romelic proeqtis mixedvit aris gadawyvetili. mxatvruli proeqtirebis teqnikisa da metodebis Tavisufali floba ert-erti mnisvnelovani pirobaa SemoqmedebiTi miznebis warmatebit ganxorcielebisa da Tanamedrove motxovnebis Sesabamisi samrewvelo produqciis Sesaqmnelad. dizaineris ostatoba aadvilebs (da acqarebs) am Ziebis process. formebis daxvewa ki samrewvelo nawarmis funqcionalur da estetikur srulyofas ganapirobebs sainjinro geometriis gamoyeneba samrewvelo dizainis amocanebsi kompiuteruli mxardawerit mnisvnelovania zedapirebis roli mecnierebasa da gamoyenebit xelovnebasi, teqnikasa da arqiteqturasi. 82

83 matematikasi zedapirebs ganixilaven, rogorc wertilta uwyvet simravles, romlebic ertmanettan garkveuli kanonzomierebit aris dakavsirebuli. mxazvelobit geometriasi zedapirebi mocemulia grafikuli saxit. amitom mizansewonilia, zedapiri ganvixilot, rogorc sivrcesi garkveuli kanonzomierebit mozravi wiris mdebareobata ertoblioba. zedapiris gansazrvris arnisnul metods kinematikuri metodi ewodeba. kinematikuri metodit SesaZlebelia martivad warmoiqmnas da aisaxos sainjinro praqtikasi fartod gavrcelebuli sxvadasxva zedapiri. arsebobs zedapiris asaxvis e.w. karkasuli metodi, romlis mixedvitac zedapiri ganisazrvreba misi kutvnili wertilebis an wirebis ertobliobit. teqnikasi da kerzod manqanatmseneblobasi fartod gamoiyeneba brunvis zedapirebi. es aixsneba imit, rom sainjinro mowyobilobebisa da meqanizmebis musaoba ZiriTadad brunviti mozraobebit aris ganpirobebuli. aseve gasatvaliswinebelia sxvadasxva tipis Carxebze mati damzadebis teqnologiac. zemot ganxiluli iyo meore rigis zedapiris, kerzod elifsuri paraboloidis kveta zogadi mdebareobis sibrtyit (nax. 28). amocanis gamartivebis miznit elifsuri paraboloidi natesauri SesabamisobiT brunvis paraboloidad gardavqmenit. natesaobis sibrtye SevirCieT horizontaluri gegmilta sibrtyis paralelurad. mocemuli elifsi epiurze wrewirad rom gardaiqmnas, vipovot C 2 wertilis natesaurad Sesabamisi C 1 2 wertili. sivrcesi mocemuli zedapiri brunvis zedapirad gardaiqmneba[24]. nax.62-ze igive amocana Sesrulebulia grafikuli programa Auto CAD- is daxmarebit. frontalur gegmilta sibrtyeze srulad aris damyarebuli natesauri Sesabamisoba. miviret wrewiri, romelic mocemuli elifsis natesaurad Sesabamisi wiria. amis Semdeg ukve SegviZlia damxmare mkveti sibrtyeebis gamoyeneba. 83

84 mivirebt saziebel wirs, romelic Tavis mxriv elifss warmoadgens (nax.62). qvemot moyvanilia arnisnuli amocanis amoxsnisatvis gamoyenebuli bazuri primitivebis CamonaTvali Auto CAD 2011-is versiasi: Command: _mtedit Command: Specify opposite corner: Command: _mtedit Command: _copy 1 found Current settings: Copy mode = Multiple Specify base point or [Displacement/mOde] <Displacement>: Specify second point or <use first point as displacement>: Specify second point or [Exit/Undo] <Exit>: *Cancel* Command: _mtedit Command: _copy 1 found Current settings: Copy mode = Multiple Specify base point or [Displacement/mOde] <Displacement>: Specify second point or <use first point as displacement>: Specify second point or [Exit/Undo] <Exit>: *Cancel* Command: _mtedit Command: _copy 1 found Current settings: Copy mode = Multiple Specify base point or [Displacement/mOde] <Displacement>: Specify second point or <use first point as displacement>: Specify second point or [Exit/Undo] <Exit>: Specify second point or [Exit/Undo] <Exit>: Specify second point or [Exit/Undo] <Exit>: Specify second point or [Exit/Undo] <Exit>: *Cancel* Command: Specify opposite corner: Command: _mtedit Command: _mtedit Command: _mtedit Command: Command: _mtedit Command: _mtext Current text style: "Standard" Text height: 2.5 Annotative: No Specify first corner: Specify opposite corner or [Height/Justify/Line spacing/rotation/style/width/columns]: Command: _move 1 found 84

85 Specify base point or [Displacement] <Displacement>: Specify second point or <use first point as displacement>: Command: Command: _copy 1 found Current settings: Copy mode = Multiple Specify base point or [Displacement/mOde] <Displacement>: Specify second point or <use first point as displacement>: Specify second point or [Exit/Undo] <Exit>: Specify second point or [Exit/Undo] <Exit>: *Cancel* Command: _mtedit Command: Command: _mtedit ** STRETCH ** Specify stretch point or [Base point/copy/undo/exit]: Command: Command: *Cancel* Command: _.erase 1 found Command: _mtext Current text style: "Standard" Text height: 2.5 Annotative: No Specify first corner: Specify opposite corner or [Height/Justify/Line spacing/rotation/style/width/columns]: Automatic save to C:\Documents and Settings\Administrator\local settings\temp\drawing1_1_1_6500.sv$... Command: *Cancel* Command: _copy 1 found Current settings: Copy mode = Multiple Specify base point or [Displacement/mOde] <Displacement>: Specify second point or <use first point as displacement>: <Ortho on> Specify second point or [Exit/Undo] <Exit>: Specify second point or [Exit/Undo] <Exit>: *Cancel* Command: _copy 1 found Current settings: Copy mode = Multiple Specify base point or [Displacement/mOde] <Displacement>: Specify second point or <use first point as displacement>: Specify second point or [Exit/Undo] <Exit>: <Ortho off> Specify second point or [Exit/Undo] <Exit>: Specify second point or [Exit/Undo] <Exit>: *Cancel* Command: _mtedit Command: _mtedit 85

86 Command: _mtedit Command: _mtedit Command: Command: _mtedit Command: _mtedit Command: _line Specify first point: Specify next point or [Undo]: <Ortho on> 8 Specify next point or [Undo]: *Cancel* Command: _copy 1 found Current settings: Copy mode = Multiple Specify base point or [Displacement/mOde] <Displacement>: Specify second point or <use first point as displacement>: Specify second point or [Exit/Undo] <Exit>: Specify second point or [Exit/Undo] <Exit>: Specify second point or [Exit/Undo] <Exit>: Specify second point or [Exit/Undo] <Exit>: *Cancel* Command: *Cancel* Command: Specify opposite corner: Command: _.erase 2 found Command: _move 1 found Specify base point or [Displacement] <Displacement>: Specify second point or <use first point as displacement>: Command: _line Specify first point: *Cancel* Command: _copy 1 found Current settings: Copy mode = Multiple Specify base point or [Displacement/mOde] <Displacement>: Specify second point or <use first point as displacement>: Specify second point or [Exit/Undo] <Exit>: *Cancel* Command: _move 1 found Specify base point or [Displacement] <Displacement>: Specify second point or <use first point as displacement>: Command: _move 1 found Specify base point or [Displacement] <Displacement>: Specify second point or <use first point as displacement>: : Command: _move 1 found Specify base point or [Displacement] <Displacement>: Specify second point or 86

87 <use first point as displacement>: Command: _move 1 found Specify base point or [Displacement] <Displacement>: Specify second point or <use first point as displacement>: Command: _move 1 found Specify base point or [Displacement] <Displacement>: Specify second point or <use first point as displacement>: Command: *Cancel* Command: _line Specify first point: Specify next point or [Undo]: <Ortho off> Specify next point or [Undo]: *Cancel* Command: *Cancel* ** STRETCH ** Specify stretch point or [Base point/copy/undo/exit]: Command: *Cancel* Command: _line Specify first point: Specify next point or [Undo]: Specify next point or [Undo]: *Cancel* Command: *Cancel* Command: _trim Current settings: Projection=UCS, Edge=None Select cutting edges... Select objects or <select all>: Select object to trim or shift-select to extend or [Fence/Crossing/Project/Edge/eRase/Undo]: Select object to trim or shift-select to extend or [Fence/Crossing/Project/Edge/eRase/Undo]: Select object to trim or shift-select to extend or [Fence/Crossing/Project/Edge/eRase/Undo]: Select object to trim or shift-select to extend or [Fence/Crossing/Project/Edge/eRase/Undo]: Select object to trim or shift-select to extend or [Fence/Crossing/Project/Edge/eRase/Undo]: Specify opposite corner: Select object to trim or shift-select to extend or [Fence/Crossing/Project/Edge/eRase/Undo]: *Cancel* Command: _.undo Current settings: Auto = On, Control = All, Combine = Yes, 87

88 Layer = Yes Enter the number of operations to undo or [Auto/Control/BEgin/End/Mark/Back] <1>: 1 Trim GROUP Command: _.undo Current settings: Auto = On, Control = All, Combine = Yes, Layer = Yes Enter the number of operations to undo or [Auto/Control/BEgin/End/Mark/Back] <1>: 1 INTELLIZOOM INTELLIPAN INTELLIPAN INTELLIZOOM Command: *Cancel* Command: *Cancel*Command: _trim Current settings: Projection=UCS, Edge=None Select cutting edges... Select objects or <select all>: Select object to trim or shift-select to extend or [Fence/Crossing/Project/Edge/eRase/Undo]: Select object to trim or shift-select to extend or [Fence/Crossing/Project/Edge/eRase/Undo]: Command: '_Layer Command: Command: _mtext Current text style: "Standard" Text height: 2.5 Annotative: No Specify first corner: Specify opposite corner or [Height/Justify/Line spacing/rotation/style/width/columns]: Command: _spline Specify first point or [Object]: Specify next point: Specify next point or [Close/Fit tolerance] <start tangent>: Specify next point or [Close/Fit tolerance] <start tangent>: Specify start tangent: Specify end tangent: Command: _spline Specify first point or [Object]: Specify next point: Specify next point or [Close/Fit tolerance] <start tangent>: Command: _ucs Current ucs name: *NO NAME* Specify origin of UCS or [Face/NAmed/OBject/Previous/View/World/X/Y/Z/ZAxis] <World>: _w Command: _saveas Command: _qsave 88

89 nax. 62 nax.63-ze mocemulia zemsubuqi rva adgiliani biznes klasis TviTmfrinavi Elite, romelic warmoadgens ass-sa da Tbilisis aviamsenebeli qarxnis ertobliv proeqts. Aam TviTmfrinavis pirveli prototipi 2008 wlis 1 ivliss dafrinda Tbilisis saertasoriso aeroportsi. 89

90 sahaero xomaldi srulad kompoziciuri masalebisgan aris awyobili(nax.64). winaswar xdeba urtulesi zedapirebis geometriuli analizi. Aam analizis safuzvelze musavdeba zedapiris warmoqmnisa da asaxvis karkasuli metodi da mirebul formaze gadaiwimeba kompoziciuri masalebi. Gganxiluli metodis upiratesoba imasi mdgomareobs, rom TviTmfrinavi praqtikulad ar Seicavs litonis detalebs da amit aris ganpirobebuli misi simsubuqe. axali biznes get iseelite-s masa m=1814 kg. sawvavis avzis moculoba-850l. safreni manzili s=2590km. frenis simarle h=12000m. frenis maqsimaluri sicqare v=760km\st. ekipaji 1-2 adamianisgan Sedgeba. TviTmfrinavis sigrze 12,60 m-ia, xolo sigane-13,41 m. afrenistvis s=450m. dasafreni manzili s=490m wlis zafxulsi SevZeliT, Tvali migvedevnebina Tbilisis aviamsenebel qarxanasi zemotarnisnuli TviTmfrinavis Semadgeneli garkveuli kvanzebis daxvewisa da damusavebis procesistvis(nax.65). Cvens mier Seswavlil iqna grafikuli programa CATIA, romlitac TbilaviamSenis saproeqto ganyofilebasi EElitget is daproeqteba mimdinareobs umartivesi detalebidan dawyebuli, TviTmfrinavis eqsploataciis pirobebis dadgenita da ergonomikit damtavrebuli. nax.66-ze mocemulia Cvens mier Sesrulebuli, am TviTmfrinavis Zravis garsacmis, e.w.,,motogandolas naxazi.ees zedapiri ramdenime zedapiris kombinaciitaa mirebuli. Nnax.67-ze ki misi TvalsaCino gamosaxulebaa mocemuli. nax.68-ze agebulia EElitget is cxviri. Nnaxazebi Sesrulebulia grafikul programa CATIA- Si. 90

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97 2007 wlidan Tbilisis elmavalmsenebelma qarxanam daiwyo B BL11M/5 elmavlis gamosveba, romelic BL11 elmavlis modifikacias warmoadgens. elmavalze arsebitad Semcirda metalis Semcveloba, gazrdilia memanqanis jixuris moculoba, dayenebulia memanqanisa da misi TanaSemwis gaumjobesebuli martvis pultebi, dayenebulia MORS SMITT (germania) warmoebis avtomaturi amomrtvelebi da releebi. radgan kvanzebisa da lokomotivebis aparatebis mnisvnelovani nawili fizikurad da moralurad ufro male Zveldeba, vidre mtlianad manqana, amitom am nawilebis kapitalur remontsa da modernizaciaze gacilebit naklebi dro da Tanxebi ixarjeba. amastan wlit izrdeba manqanis eqspluataciisatvis gansazrvruli dro. ss elmavalmsenebeli warmatebit axorcielebs magistraluri da samrewvelo elmavlebis kapitalur remontsa da modernizacias. Sedegad gaumjobesebul teqnikur maxasiateblebsa da saimedoobis maral xarisxs ireben. lokomotivis teqnikuri arwurvis paralelurad proeqtirdeba memanqanis samusao adgilic wels Seviswavle memanqanis jixuris modernizaciis procesi. nax.70-ze memanqanis jixuris wina nawilis sami xedia gamosaxuli (saamwyobo naxazi). nax.69-ze ki TvalsaCino gamosaxulebaa A AutoCad-ში -Si Sesrulebuli. naxazis mixedvit Seikvreba jixuris karkasi da Semdeg am karkasze Semoifineba furclovani masala. xdeba mrebuli formis gadarunva da zumfaris sasualebit, xelit misi zedapiris damusavebagaprialeba ufro gluvi zedapiris misarebad. rogorc nax.71-dan Cans t msaxvelita da m mimmartvelit gansazrvruli φ zedapiri wrfovani da arxiseburi zedapirebis ertobliobas warmoadgens. 97

98 mxazvelobit geometriasi zedapiri grafikulad ganisazrvreba. amitom mizansewonilia φ zedapiri ganvixilot, rogorc sivrcesi mozravi t wiris (msaxvelis) Tanmimdevrul mdebareobata ertoblioba. am mdebareobebs m mimmartvelis kutvnili wertilebi gansazrvravs. am msjelobis gatvaliswinebit nax.72-ze AutoCad -Si Sesrulebulia arnisnuli zedapiris TvalsaCino gamosaxuleba LOFT brzanebis gamoyenebit. aseti TvalsazrisiT Tu miudgebit, memanqanis jixuris damzadebis procesi sagrznoblad gamartivdeba. kerzod, furclovani masalis Semofenamde mivirebt sasurveli formis (nax.73) karkass. rasakvirvelia, Semcirdeba teqnologiuri procesistvis gansazrvruli dro da saxsrebi (nax.74). nax

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