COMPARISON OF METHODS OF DESCRIPTIVE GEOMETRY AND COMPUTER 3D GEOMETRIC SIMULATION ACCORDING TO THE ACCURACY, COMPLEXITY AND EFFECTIVENESS
Abstract
Urgent educational problem of inconsistency of content of the course of descriptive geometry
(DG) with the trends in the development of CAD and geometric simulation is considered.
While the development is aimed at expanding the scope of computer 3D geometric simulation
the teaching of descriptive geometry projection methods continues despite the fact that they are
in no demand in practical applications. To compare the estimations of versions of solutions in descriptive
geometry and 3D five specific problems of the nomination in descriptive geometry
of All-Russian Olympiad 2014 are considered. They are the construction of sphere, tangent to the
paraboloid; determining the points of intersection of the ellipse defined by the axes, with a circle
(without the ellipse); finding the reference points of the ellipse section and its projections; construction
of a tetrahedron by one projection of its face; as well as the defining the points of intersection of
the circle with an elliptical cone. The detailed versions of solutions of descriptive geometry and 3D
are given for each problem.
The comparison of versions of the solution according to the geometrical accuracy is done.
It is offered to estimate not an abstract accuracy which corresponds to constructions made
by aperfect caliper and a ruler but the real accuracy independently of methods of its achievement.
It’s shown that with the computer realization of both variants their real accuracy is either equal or
3D is much better than DG.
The estimation of the complexity of task solutions is given. The amount of information needed
for the solution is taken as a criterion. The author makes the conclusion that generally 3D versions
are easier than DG.
The examples show that 3D solutions can be easily supplemented with researches of a solvable
problem. Much higher visualization, accessibility and universality of 3D versions are highlighted.
The author makes the conclusion about much higher general effectiveness of computer
3D variants and methods of solving the structural problems and the necessity of transfer
to new training course of 3d theory.
Keywords: descriptive geometry, computer graphics, 3D modeling, structural problems, geometrical
accuracy, complexity and effectiveness of structural problems.
References
Adler A. Teoriya geometricheskikh postroeniy [The theory of geometric constructions]. St. Petersburg,
Uchpedgiz Publ., 1940. 232 p.
Vol'khin K.A., Golovnin A.A., Markova T.V., Tokarev V.A. [Standards ESKD as a basis to update the
structure and content of graphic training in technical universities ]. Problemyi kachestva graficheskoy podgotovki
studentov v tehnicheskom vuze v usloviyah FGOS VPO. Materialyi II mezhdunarodnoy nauchnoprakticheskoy internet-
konferentsii. Perm. Fevral-mart 2011 [Problems of quality of graphic training of students in technical higher
school in conditions of FSES HPE. Materials of II international scientific-practical Internet-conference]. Perm,
PGTU Publ., 2011, pp. 280–284 (in Russ.).
Vyishnepolskiy V.I. [Again to the question of the construction of points of intersection of the circle and elliptical
cone]. V Mezhdunarodnaya internet-konferentsiya «Problemy kachestva graficheskoy podgotovki studentov
v tekhnicheskom vuze: traditsii i innovatsii» KGP-2015 [V International Internet-conference "problems of quality
of graphic training of students in technical College: traditions and innovations" KGP-2015]. Available at:
http://dgng.pstu.ru/conf2015/papers/110 (in Russ.).
Kheyfets A.L., Loginovskiy A.N., Butorina I.V., Vasil'eva V.N. Inzhenernaya 3D-komp'yuternaya grafika:
uchebnik i praktikum dlya akademicheskogo bakalavriata [Engineering 3D computer graphics]. Moscow, «Yurayt
» Publ., 2015. 602 p.
Korotkiy V.A. Kheyfets A.L. [3D modeling conics in AutoCAD]. Aktualnyie voprosyi graficheskogo obrazovaniya
molodezhi. Materialyi VI Vserossiyskoy nauchno-metodicheskoy konferentsii; pod red. Yu.P. Sheveleva,
A.P. Peredbogova [Topical issues in graphic education. Proceedings of the VI all-Russian scientific-methodical
conference]. Ryibinsk: RGTA Publ., 2005, pp. 102–105 (in Russ.).
Korotkiy V.A., Khmarova L.I., Butorina I.V. Nachertatel'naya geometriya: konspekt lektsiy [Descriptive
geometry: lecture notes]. Chelyabinsk, South Ural St. Univ. Publ., 2014. 191 p.
Chetverukhin N.F., Levitskiy V.S., Pryanishnikova Z.I. Nachertatel'naya geometriya [Descriptive geometry].
Moscow, Higher school Publ., 1963. 420 p.
. Peklich V.A. Nachertatel'naya geometriya[Descriptive geometry]. Moscow, ASV Publ., 2007. 272 p.
Peklich V.A., Pavlenko S.N. Zadachi po nachertatel'noy geometrii [The tasks of descriptive geometry].
Moscow, Higher school Publ., 1999. 139 p.
Sukhina I.A., Shcheglova N.I. [Graphical method of solution of some problems with the hyperboloid without
building its contours (in order of discussions)]. Sbornik nauchno-metodicheskikh statey po nachertatel'noy geometrii i
inzhenernoy grafike [Collection of scientific and methodological articles on descriptive geometry and engineering graphics].
Moscow, Higher school Publ., 1982, iss. 9, pp. 22–31 (in Russ.).
Frolov S.A. Metody preobrazovaniya ortogonal'nykh proektsiy [Methods of transformation of orthogonal
projections]. Moscow, Mashinostroenie Publ., 1970. 152 p.
Kheyfets A.L., Barskiy Yu.K. [Comparative analysis of the effectiveness of 2D and 3D algorithms in
problems at the intersection of the surfaces]. Trudy 17-toy mezhdunarodnoy nauchno-tekhnicheskoy konferentsii
“Informatsionnye sredstva i tekhnologii. Moskva 20-22 oktyabrya 2009” [Proceedings of 17-th international scientific
and technical conference “Information means and technologies. Moscow October 20-22, 2009”]. Moscow,
Izd. dom MEI Publ., 2009, vol. 3, pp. 148–55 (in Russ.).
Kheyfets A.L., Loginovskiy A.N. [Parameterization as a means of solving 3D geometric computer modeling].
Trudy KhKh Mezhdunarodnoy nauchno-tekhnicheskoy konferentsii “Informatsionnye sredstva i tekhnologii”
Moskva, 20–2 noyabrya 2012 [Proceedings of the twentieth International scientific and technical conference “Information
means and technologies” Moscow, 20-2, 2012]. Moscow, MEI Publ., 2012, vol. 1, pp. 72–80 (in Russ.).
Kheyfets A. L. [Training course theoretical foundations of 3D computer geometric modeling and its prospects].
Trudy Mezhdunarodnoy nauchno-metodicheskoy konferentsii «Informatizatsiya inzhenernogo obrazovaniya
» INFORINO-2012 (Moskva, 10–1 aprelya 2012 g.) [Proceedings of International scientific-methodical conference
"Informatization of engineering education" INFOLINE-2012 (Moscow, 10-1 April 2012)]. Moscow, MEI
Publ., 2012, pp. 119–122 (in Russ.).
Kheyfets A.L. [Theoretical foundations of 3D computer geometric modeling and Gaspard Monge]. V sb.:
Problemy kachestva graficheskoy podgotovki studentov v tekhnicheskom vuze v usloviyakh FGOS VPO. Materialy
III nauchno-prakticheskoy konferentsii s mezhdunarodnym uchastiem (Perm', sentyabr' –noyabr' 2012 g.) [Collected
works: Problems of the quality of graphic training of students of the technical University in conditions of
FSES HPE. Proceedings of the III scientific-practical conference with international participation (Perm, September
–November 2012)]. Perm, PNIPU Publ., 2013, pp. 210–217 (in Russ.).
Kheyfets A. L. [Reorganization of the course of descriptive geometry as an urgent task in the development
of graphics departments]. Geometriya i grafika [Geometry and graphics]. Moscow, INFRA-M Publ., vol. 1., no. 2,
pp. 21–23 (in Russ.).
Kheyfets A. L. [On the prospects of the new theoretical course as an alternative to descriptive geometry]. Problemy
kachestva graficheskoy podgotovki studentov v tekhnicheskom vuze v usloviyakh FGOS VPO. Materialy II mezhdunarodnoy
nauchno-prakticheskoy internet-konferentsii. Perm'. Fevral'–mart 2011 [Problems of quality of graphic training
of students in technical higher school in conditions of FSES HPE. Materials of II international scientific-practical
Internet-conference. Perm. February – March 2011]. Perm, PNIPU Publ., 2011. pp. 38–45 (in Russ.).
Kheyfets A.L. [The calculation of the duration of insolation in the conditions of compacted land]. Privolzhskiy
nauchnyy zhurnal [The Privolzhsky scientific journal]. 2012, no. 3, pp. 99–105 (in Russ.).
Kheyfets A.L. [3D as a method of geometric modeling (the case of conic bundles combining with the quadric)].
Privolzhskiy nauchnyy zhurnal [The Privolzhsky scientific journal]. 2013, no. 1, pp. 35–40 (in Russ.).
Kheyfets A.L. [3D-model of the worm Mills]. Obrabotka metallov. Tekhnologiya. Oborudovanie. Instrumenty
[Processing of metals. Technology. Equipment. Tools]. 2013. no. 3, pp. 47–49 (in Russ.).
Kheyfets A.L. [3D model of quadric intersection with common focus points]. Bulletin of the South Ural
State University. Ser. Computer technology, control, radioelectronics, 2013, vol. 13, no. 2, pp. 88–96 (in Russ.).
Kheyfets A.L. [Descriptive geometry as a factor limiting the development of geometric modeling].
V Mezhdunarodnaya internet-konferentsiya «Problemy kachestva graficheskoy podgotovki studentov v tekhnicheskom
vuze: traditsii i innovatsii» KGP-2015 [V International Internet-conference "problems of quality of graphic
training of students in technical College: traditions and innovations" KGP-2015]. Available at:
http://dgng.pstu.ru/conf2015/papers/72 (in Russ.).
Chetverukhin N.F. Metody geometricheskikh postroeniy [Methods of geometric constructions]. Moscow,
Gos. uch. ped. izdat. Publ., 1952. 145 p.
