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The article is exclusively applied and methodical in nature and is intended for the study of constructions in the section "Perspective". The paper considers the construction of the perspective of a straight line of the general position with the help of a picture trace and a vanishing point. In perspective, the traces of a straight line are the points of intersection with the picture and subject planes. Vanishing point – the perspective of an improper point of a straight line. The article discusses the picture trail, the vanishing point and the construction of a straight line segment by means of these perspective points. In textbooks for builders, such a task is not set at all and is not considered. Three authors have solutions in textbooks for architects: A.G. Klimukhin, Yu.I. Koroev and T.S. Timrot. However, they also have some disadvantages, which are discussed in this article. In the work proposed to the reader, such an arrangement of geometric components is performed that there is neither parallelism nor perpendicularity between them, that is, they are all located at acute angles to each other, which means that a general case of construction is proposed for consideration. So, we have a right angle only between the horizontal and frontal planes of projections, as well as between the picture and object (horizontal plane of projections) planes. The angles between the other geometric components are exceptionally sharp: a straight line of general position in the P1/P2 system is taken, it is also a straight line of general position in the P1/K system. Thus, the article considers, unlike other textbooks, the general case of a direct task.
descriptive geometry; perspective; straight line; traces of a straight line, a picture trace; vanishing point
1. Bubennikov A.V., Gromov M.Ja. Nachertatel'naja geometrija [Descriptive geometry]. Moscow, Vysshaja shkola Publ., 1973. 416 p. (in Russian)
2. Budarin O.S. Nachertatel`naya geometriya Kratkij kurs [Descriptive geometry A short course]. St. Petersburg: Lan`Publ., 2019. 360 p. (in Russian)
3. Vinnickij I.G. Nachertatel'naja geometrija [Descriptive geometry]. Moscow, Vysshaja shkola Publ., 1975. 280 p. (in Russian)
4. Vinogradov V.N. Nachertatel`naya geometriya [Descriptive geometry]. Minsk, Vy`sh. Shkola Publ., 1977. 268 p. (in Russian)
5. Voloshin-Chelpan Je.K. Nachertatel'naja geometrija. Inzhenernaja grafika [Descriptive geometry. Engineering graphics]. Moscow, Akademicheskij proekt Publ., 2009. 183 p. (in Russian)
6. Glagolev N.A. Nachertatel'naja geometrija [Descriptive geometry]. M.-L., ONTI NKTP SSSR, Glavnaja redakcija obshhetehnicheskoj literatury i nomografii Publ., 1936. 160 p. (in Russian)
7. Gordon V.O., Semencov-Ogievskij M.A. Kurs nachertatel'noj geometrii [A course in descriptive geometry]. Moscow, Nauka Publ., 1977. 268 p. (in Russian)
8. Dobrjakov A.I. Kurs nachertatel'noj geometrii [A course in descriptive geometry]. M.-L., Gos. izdatel'stvo literatury po stroitel'stvu i arhitekture Publ., 1952. 496 p. (in Russian)
9. Ivanov G.S. Nachertatel`naya geometriya [Descriptive geometry]. Moskow, FGBOU VPO MGUL Publ., 2012. 340 p. (in Russian)
10. Ishhenko A.A. K voprosu o neobhodimosti prepodavanija nachertatel'noj geometrii i grafiki dlja himikov i himikovtehnologov [To the question about the necessity of descriptive geometry and graphics teaching for chemists and chemical technologists]. Geometrija i grafika [Geometry and graphics]. 2013, V. 1, I. 2, pp. 6-7. DOI:https://doi.org/10.12737/776. (in Russian).
11. Klimuhin A.G. Nachertatel'naja geometrija [Descriptive geometry]. Moscow, Strojizdat Publ., 1978. 334 p. (in Russian)
12. Kolotov S.M., Dol'skij E.E., Mihajlenko V.E. Kurs nachertatel'noj geometrii [Course in descriptive geometry]. Kiev, Gos. izd-vo literatury po stroitel'stvu i arhitekture USSR Publ., 1961. 316 p. (in Russian)
13. Koroev Ju.I. Nachertatel'naja geometrija [Descriptive geometry]. Moscow, KNORUS Publ., 2011. 432 p. (in Russian)
14. Korotkij V.A., Xmarova L.I., Butorina I.V. Nachertatel`naya geometriya: konspekt lekcij [Descriptive geometry]. Chelyabinsk, YuUrGU Publ., 2014. 191 p. (in Russian)
15. Krylov N.N., Lobandievskij P.I., Mjen S.A., Nikolaev V.L., Ikonnikova G.S. Nachertatel'naja geometrija [Descriptive geometry]. Moskow, Vysshaja shkola Publ., 1977. 231 p. (in Russian)
16. Krylov N.N., Ikonnikova G.S., Nikolaev V.L., Lavruhina N.M. Nachertatel'naja geometrija [Descriptive geometry]. Moskow, Vysshaja shkola Publ., 1990. 240 p. (in Russian)
17. Kuznecov N.S. Nachertatel'naja geometrija [Descriptive geometry]. Moskow, Vysshaja shkola Publ., 1981. 262 p. (in Russian)
18. Loktev O.V. Kratkij kurs nachertatel'noj geometrii [A short course in descriptive geometry]. Moscow, Vysshaja shkola Publ., 1985. 136 p. (in Russian)
19. Peklich V.A. Nachertatel'naja geometrija [Descriptive geometry]. Moskow, Izdatel'stvo associacii stroitel'nyh vuzov Publ., 2007. 272 p. (in Russian)
20. Russkevich N.L. Nachertatel'naja geometrija [Descriptive geometry]. Kiev, Vishha shkola Publ., 1978. 312 p. (in Russian)
21. Ry`zhov N.N. Nachertatel`naya geometriya. Ch. 1 [Descriptive geometry. P. 1]. Moskow, MADI Publ., 1995. 72 p. (in Russian)
22. Ry`zhov N.N. Nachertatel`naya geometriya. Ch. 2 [Descriptive geometry. P. 2]. Moskow, MADI Publ., 1996, 68 p. (in Russian)
23. Rynin N.N. Nachertatel'naja geometrija [Descriptive geometry]. L.: Gosstrojizdat Publ., 1939. 448 p. (in Russian)
24. Sal`kov N.A. Nachertatel'naja geometrija. Bazovyj kurs [Descriptive geometry. Basic course]. Moskow, INFRA-M Publ., 2013. 184 p. (in Russian)
25. Sal'kov N.A. Nachertatel'naja geometiya do 1917 goda [Descriptive Geometry until 1917]. Geometrija i grafika [Geometry and graphics]. 2013, V. 1, I. 2, pp. 18-20. DOI:https://doi.org/10.12737/780. (in Russian)
26. Sal`kov N.A. Nachertatel'naja geometrija: Osnovnoj kurs [Descriptive geometry. The main course]. Moscow, INFRA-M Publ., 2014. 235 p. (in Russian)
27. Sal`kov N.A. Nachertatel`naya geometriya - teoriya izobrazhenij [Descriptive geometry-image theory]. Geometriya i grafika [Geometry and graphics]. 2016, V. 4, I. 4, pp. 41-47. DOI:https://doi.org/10.12737/22842. (in Russian)
28. Tevlin A.M., Ivanov G.S., Nartova L.G. Kurs nachertatel`noj geometrii (na baze E`VM) [The course of descriptive geometry (based on a computer)]. Moskow, Vy`ssh. Shkola Publ., 1983. 175 p. (in Russian)
29. Timrot E.S. Nachertatel'naya geometriya [Descriptive geometry]. Moskow, Gos. izdatel'stvo literatury po stroitel'stvu, arhitekture i stroitel'nym materialam Publ., 1962. 280 p. (in Russian)
30. Frolov S.A. Nachertatel'naya geometriya [Descriptive geometry]. Moscow, Mashinostroenie Publ., 1978. 240 p. (in Russian)
31. Chetverukhin N.F. Kurs nachertatel'noy geometrii [Course descriptive geometry]. Moscow, Gos. izd-vo tekhniko-teo¬reticheskoy literatury Publ., 1956. 436 p. (in Russian)
32. Chetveruxin N.F., Leviczkij V.S. Nachertatel`naya geometriya [Descriptive Geometry]. Moskow, Vy`sshaya shkola Publ., 1963. (in Russian)
