Astrakhan Tatishchev State University (Assistant Professor of the Department of Electrical Engineering, Electronics and Automation)
Russian Federation
Russian Federation
Astrahan', Astrakhan, Russian Federation
Some elements of geometric objects’ parameterization theory are considered in this paper. An analysis of this theory development by leading Soviet scientists has been presented. It is known that figure’s parameters are determined by adding shape parameters with location parameters. In the drawing these parameters are expressed as dimensions. Relations between figures are determined or by their mutual affiliation, or by perpendicularity, or by their touch. These ratios allow reduce dimensions number on a drawing. The link of the parameterization theory with creation of parametric drawings has been demonstrated in the considering work. Definitions for such concepts as parameter and parametric drawing have been given. A various geometric figures’ parameters calculation principle has been considered. The order of assignment in parametric form of different geometrical objects (point, straight line), as well as any figure’s position in space has been presented. Assignments of geometrical conditions for membership, parallelism, perpendicularity, contact by parameters have been considered. A detailed description for parametric drawing in "KOMPAS-Graphic" program has been presented. Advantages and features related to carrying out of parametric fragments (with geometric and dimensional dependencies) and drawings in this program for various industries have been laid in detail. Some features and approaches in carrying out parametric drawings and fragments, which worthwhile to apply for different modifications of items when needed to creat group drawings, have been proposed for consideration. Traditional methods for creation of the group drawings using CAD systems effectively increase intellectual work’s performance. The CAD systems capabilities use will enable designers to implement various ways and possibilities comprehensively for creation and presentation of graphic information.
parameters, form parameters, position parameters, geometric objects, "KOMPAS-Graphic", parameterization, associativeness, computer technology, parametric drawing.
При разработке конструкторской документации возникает необходимость вносить изменения в конструкцию детали, размеры, особенно при выполнении нового изделия. Это становится возможным путем создания параметрического чертежа этой детали.
1. Asekritova S.V. Specifika razrabotki konstruktorskoj dokumentacii v uslovijah avtomatizirovannogo proizvodstva [The specifics of the design documentation in the context of automated production]. Geometrija i grafika [Geometry and graphics]. 2014, v. 1, i. 3-4, pp. 36-39. DOI:https://doi.org/10.12737/2131. (in Russian).
2. Volkov V.Ja. Teorija parametrizacii i modelirovanija geometricheskih ob’ektov mnogomernyh prostranstv i ee prilozhenija. Dokt. Diss. [Theory of parameterization and geometry modeling of multidimensional spaces and its applications. Doct. Diss.]. Moscow, 1983. 27 p. (in Russian).
3. Voloshinov D.V. O perspektivah razvitija geometrii i eyo instrumentarija [On the prospects of geometry and its tools]. Geometrija i grafika [Geometry and graphics]. 2014, v. 2, i. 1, pp. 15-21. DOI:https://doi.org/10.12737/3844. (in Russian).
4. Vyshnepol'skij V.I. Celi i metody obuchenija graficheskim disciplinam [Objectives and methods of teaching graphic disciplines]. Geometrija i grafika [Geometry and graphics]. 2013, v. 1, i. 2, pp. 8-9. DOI:https://doi.org/10.12737/777. (in Russian).
5. Gerasimov A.A. Novye vozmozhnosti KOMPAS-3D V13 [New features of Kompas-3D V13]. St. Peterburg, BHVPeterburg Publ., 2012. 288 p. (in Russian).
6. Gershman I.P. Konstruirovanie poverhnostej putem vydelenija ih nepreryvnyh linejnyh karkasov iz mnogoparametricheskih mnozhestv linij [Designing surfaces by providing their continuous linear frames of multiparameter sets of lines]. Trudy UDN im. P.Lumumby. T.3: Prikladnaja geometrija. Vyp. 3 [Labor PFU them. P. Lumumba, t. 3: Applied geometry. ISS. 4]. Moscow, 1967, pp. 33-47. (in Russian).
7. Gershman I.P. Mnogoparametricheskie mnozhestva geometricheskih figur i ih koordinatnye podmnozhestva [Multiparameter many geometric shapes and their axis subsets]. Trudy UDN im. P.Lumumby. T.3: Prikladnaja geometrija. Vyp. 4 [Labor PFU them. P. Lumumba, t. 3: Applied geometry. ISS. 4]. Moscow, 1971, pp. 41-59. (in Russian).
8. Ivanov G.S. Konstruktivnyj sposob issledovanija svojstv parametricheski zadannyh krivyh [Constructive way to study the properties of parametric curves]. Geometrija i grafika [Geometry and graphics]. 2014, v. 2, i. 3, pp. 3-6. DOI:https://doi.org/10.12737/6518. (in Russian).
9. Kozlova I.A. Nekotorye metodicheskie aspekty vypolnenija parametricheskih chertezhej v KOMPAS-Grafik [Some methodical aspects of performing parametric drawings in the compass-Chart]. VI Mezhdunar. nauchno-praktich. internetkonf. KGP-2016 [VI Internat. Scientific and practical. Internet Config. PCG-2016]. Available at: http://kig.pstu.ac.ru/ conf2016 /papers/54/ (Accessed 1 July 2016). (in Russian).
10. KOMPAS-GRAFIK 5.H. Prakticheskoe rukovodstvo. Chast' 2 [COMPASS-CHART 5. Practical Guide. Part 2]. AO ASKON [JC, ASCON]. 1999, 468 p. (in Russian).
11. Kotov I.I. Parametricheskoe ischislenie figur i polnota graficheskogo zadanija poverhnostej [Parametric calculation of the shape and fullness graphically set surfaces]. Trudy Moskovskogo seminara po nachertatel'noj geometrii i inzh. grafike. Vyp. 2 [Proceedings of the Moscow Seminar on descriptive geometry and ing. graph. ISS. 2]. Moscow, 1963, pp. 82-91. (in Russian).
12. Mihajlenko V.E. Inzhenernaja geometrija s jelementami teorii parametrizacii [Engineering geometry with elements of the theory of parameterization]. Kiev, UMK VO Publ., 1989. 84 p. (in Russian).
13. Polozov V.S. Avtomatizirovannoe proektirovanie [Computeraided design]. Moscow, Mashinostroenie Publ., 1983. 280 p. (in Russian).
14. Potemkin A.E. Tverdotel'noe modelirovanie v sisteme KOMPAS- 3D [Solid modelling in Kompas-3D system]. St. Peterburg, BHV-Peterburg Publ., 2004. 512 p. (in Russian).
15. Ryzhov N.N. Geometricheskie uslovija kak parametry [Geometrical conditions as parameters]. Prikl. geometrija i inzh. grafika [Applied geometry and ing. graphics]. Kiev, 1967, i. 6, pp. 7-12. (in Russian).
16. Ryzhov N.N. Karkasnaja teorija zadanija i konstruirovanija poverhnostej [Frame theory and design surfaces jobs]. Trudy UDN im. P. Lumumby. T. 3: Prikladnaja geometrija. Vyp. 3 [Proceeds PFU them P. Lumumba, t. 3: Applied geometry. Iss. 3]. Moscow, 1967, pp. 3-17. (in Russian).
17. Ryzhov N.N. Konstruirovanie i zadanie poverhnostej vydeleniem odnoparametricheskogo mnozhestva opredelitelej linij [Designing and specifying the surfaces highlighting one the many determinants of lines]. Trudy UDN im. P. Lumumby. Vyp. 8: Sb. nauchnyh trudov inzh. fakul'teta [Proceeds PFU them. P. Lumumba. 8: Sat. scientific works of ing. faculty]. Moscow, 1971, pp. 165-169. (in Russian).
18. Ryzhov N.N. Obshhie voprosy zadanija i parametrizacii poverhnostej [General questions set and parameterization of surfaces] Tez. dokladov II Vsesojuznoj geometricheskoj konferencii [Thes. reports II All-Union Conference of the geometry]. Kharkov, 1964, pp. 239-241. (in Russian).
19. Ryzhov N.N. Parametrazh geometricheskih uslovij i vyvod uravnenij ogibajushhih poverhnostej po napered zadannym uslovijam [Parametrazh geometric conditions and output equations of envelope on surfaces criteria beforehand]. Prikl. geometrija i inzh. grafika. Vyp. 14 [Applied geometry and ing. graphics. ISS. 14]. Kiev, Budivel'nik Publ., 1972, pp. 52-54. (in Russian).
20. Ryzhov N.N. Parametrizacija geometricheskih uslovij i algoritm reshenija odnoj sovokupnosti zadach prikladnoj geometrii poverhnostej [Parameterization of geometric terms and algorithm for solving one set of objectives applied geometry surfaces]. Trudy UDN im. P.Lumumby. T. 26: Matematika. Vyp. 3: Prikladnaja geometrija [Proceeds PFU them. P. Lumumba t. 26: Mathematics. Iss. 3: Applied geometry]. Moscow, 1967, pp. 139-152. (in Russian).
21. Ryzhov N.N. Parametrizacija poverhnostej [Parameterization of surfaces]. Trudy UDN im. P. Lumumby. T. 26: Matematika. Vyp. 3: Prikladnaja geometrija [Proceeds PFU them. P. Lumumba t. 26: Mathematics. Iss. 3: Applied geometry]. Moscow, 1967, pp.18-22. (in Russian).
22. Ryzhov N.N. Parametricheskaja geometrija [Parametric geometry]. Moscow, MADI Publ., 1988. 56 p. (in Russian).
23. Ryzhov N.N. Prikladnaja geometrija poverhnostej [Applied geometry surfaces]. Trudy Moskovskogo nauchno-metodicheskogo seminara po nachertatel'noj geometrii i inzhenernoj grafike. Vyp. 242 [Proceedings of the Moscow scientific-methodical seminar on descriptive geometry and engineering graphics. Iss. 242]. Moscow, Moskovskij aviacionnyj institute Publ., 1972, pp. 57-91. (in Russian).
24. Sal'kov N.A. Parametricheskaja geometrija v geometricheskom modelirovanii [Parametric geometry in geometric modeling]. Geometrija i grafika [Geometry and graphics]. 2014, v. 2, i. 3, pp. 7-13. DOI:https://doi.org/10.12737/6519. (in Russian).
25. Stolbova I.D. Ob obespechenii kachestva predmetnogo obuchenija studentov tehnicheskogo universiteta [Substantive training on quality assurance engineering students]. Geometrija i grafika [Geometry and graphics]. 2016, v. 3, i. 4, pp. 27-37. DOI:https://doi.org/10.12737/17348. (in Russian).
26. Harah M.M. Geometricheskoe modelirovanie kvadrikami i ih prilozhenie. Kand. Diss. [Geometric modeling of kvadrikami and their application. Cand. Diss]. 1968. 21 p. (in Russian).
27. Harah M.M. Konstruirovanie sborochnogo chertezha izdelija metodom 3D-modelirovanija kak zavershajushhij jetap izuchenija inzhenernoj i komp'juternoj grafiki [Design assembly drawing articles 3D modeling method as final stage of studying engineering and computer graphics]. Geometrija i grafika [Geometry and graphics]. 2014, v. 2, i. 3, pp. 36-40. DOI:https://doi.org/10.12737/5588. (in Russian).
28. Harah M.M. Otobrazhenie semejstv sfer [Collections display areas]. Respublikanskij mezhvedomstvennyj nauchnotehnicheskij sbornik «Prikladnaja geometrija i inzhenernaja grafika». [Republican interdepartmental scientific and technical collection "Applied geometry and engineering graphics”]. Kyiv: Budivel′nik, 1992, pp. 45-51. (in Russian).
29. Hejfec A.L. Inzhenernaja 3D-komp'juternaja grafika: Uchebnik i praktikum dlja akademicheskogo bakalavriata [Engineering 3D computer graphics: a tutorial and workshop for academic undergraduate ed.]. Moscow, Jurajt Publ., 2015. (in Russian).
30. Hejfec A.L., Vasil'eva V.N. Kurs komp'juternoj grafiki dlja studentov stroitel'nyh special'nostej [Computer graphics course for students of building trades]. Geometrija i grafika [Geometry and graphics]. 2015, v. 3, i. 1, pp. 31-39. DOI:https://doi.org/10.12737/10454. (in Russian).
31. Chetveruhin N.F. O parametrizacii krivyh linij i poverhnostej i ee znachenii v uchebnom processe [On the parameterization of curves and surfaces and its importance in the learning process]. Matematika v shkole [Mathematics at school]. 1964, i. 5, pp. 29-33. (in Russian).
32. Chetveruhin N.F. Parametrizacija i ee primenenie v geometrii [Parameterization and its application in geometry]. Matematika v shkole [Mathematics at school]. 1963, i. 5, pp. 15-23. (in Russian).
33. Jakubovskij A.M. Nekotorye voprosy konstruirovanija poverhnostej s pomoshh'ju trehgrannika Frene [Some design considerations surfaces using trehgrannika Fresney Some design considerations surfaces using trehgrannika Fresney]. Trudy UDN im. P. Lumumby. T. 3: Prikladnaja geometrija. Vyp. 3 [Proceedings PFU them. P. Lumumba, t. 3: Applied geometry. Iss. 3]. Moscow, 1967. (in Russian).
34. Jakunin V.I. Innovacionnaja strategija kompleksnoj informatizacii geometricheskoj i graficheskoj podgotovki v vysshem tehnicheskom professional'nom obrazovanii v GOSah 3-go pokolenija [Innovation strategy a comprehensive informatization of geometrical and graphical training in higher technical vocational education in GOSah 3rd generation]. Nauchno- metodicheskie problemy geometricheskogo modelirovanija, komp'juternoj i inzhenernoj grafiki v vysshem professional'nom obrazovanii: Sbornik statej Mezhdunarodnoj nauchno-metodicheskoj konferencii 9-11 iyunya 2009 g. Penza [Scientific and methodical problems of geometric modeling, computer graphics and engineering in higher vocational education: a collection of articles of international scientific-methodical Conference 9-11 June 2009 Penza]. 2009, 188 p. (in Russian).
35. Jakunin V.I. Teoreticheskie osnovy formirovanija modelej poverhnostej [Theoretical bases of formation of surface models]. Moscow, MAI Publ., 1985. (in Russian).