POINTS ON THE SPHERE SURFACE

O. S. Danilova, A. S. Shcherbak, А. V. Krasniuk

Abstract


Purpose. The extensive use of the computer-aided design system (CAD) in education and industry puts forward new demands on the scope, content and quality of up-to-date descriptive geometry course. The purpose of the work is topicality analysis of traditional descriptive geometry methods for 3D modelling and development of methodological recommendations for its teaching as a subject together with a selected CAD. Methodology. Conclusions about effectiveness and expedience of application of descriptive geometry methods are drawn on the basis of tools analysis and comparison of modern CADs and descriptive geometry for solving problems arising during 3D modelling. Generalization of teaching experience made it possible to give recommendations about optimization of the descriptive geometry course taking into account present-day requirements to professional skills of an engineer.
Findings. CADs tools and descriptive geometry methods are compared by way of specific example to give the answer what is more suitable for solving problems arising during 3D modelling. Originality. We presented the methodological recommendations about optimization of descriptive geometry teaching together with a selected CAD. We proposed the conception of a modern textbook on descriptive geometry. First of all, the textbook must describe algorithms for solving problems by means of standard CAD tools exactly in 3D, not on the plane. It is desirable to accompany these algorithms by pictorial images in order to have an opportunity to grasp an idea quickly and implement it through methods of direct modeling in CAD application. We also touched practical problems of students’ motivation to ensure high effectiveness of graphical education. Practical value. This paper may be useful mainly for educators in the field of engineering graphics because it raises a vital question ‘Descriptive Geometry versus CAD’ which now has no definite answer. Topicality and teaching approaches of different solution methods of spatial problems by means of projections is subject of a dispute, taking into account that CAD tools are continuously updated. This paper by way of specific example shows some advantages and limitations of descriptive geometry and CAD, as well as touches the issues of their efficient joint application for teaching.


Keywords


descriptive geometry; CAD; sphere; teaching methods; motivation

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References


Ivanov, G. (2013). Descriptive geometry prospects as educational subject. Geometry & Graphics, 1(1), 26-28. doi: 10.12737/467. (in Russian)

Losev, N. V. (1992). 200 olimpiadnykh zadach po nachertatelnoy geometrii: prakticheskoye posobiye. Moscow: Vysshaya shkola. (in Russian)

Dmitrieva, I., Ivanov, G., Seregin, V., & Muravev, K. (2013). Interdisciplinary connections of descriptive geometry and related sections of higher mathematics. Geometry & Graphics, 1(3), 8-12. doi: 10.12737/2124. (in Russian)

Sal’kov, N. (2016). Geometric Simulation and Descriptive Geometry. Geometry & Graphics, 4(4), 31-40. doi: 10.12737/22841. (in Russian)

Salkov, N. (2016). Place of Descriptive Geometry in the System of Geometric Education of Technical Universities. Geometry & Graphics, 4(3), 53-61. doi: 10.12737/21534. (in Russian)

Sal’kov, N. (2016). Descriptive Geometry – the Base of Computer Graphics. Geometry & Graphics, 4(2), 37-47. doi: 10.12737/19832. (in Russian)

Kheyfets, A. L. (2015). Nachertatelnaya geometriya kak «beg v meshkakh». Problemy kachestva graficheskoy podgotovki studentov v tekhnicheskom VUZe: traditsii i innovatsii. Proceedings of the Vth International Scientific and Practical Internet Conference. Perm, 1, 298-325. (in Russian)

Kheyfets, A. (2013). Descriptive geometry course reorganization as the actual task of graphics chairs development. Geometry & Graphics, 1(2), 21-23. doi: 10.12737/781. (in Russian)

Autodesk AutoCAD Help (2016). Retrieved from: http://help.autodesk.com/view/ACD/2016/ENU/. (in English)

Bokan, N., Ljucovic, M., & Vukmirovic, S. (2009). Computer-Aided Teaching of Descriptive Geometry. Journal for Geometry and Graphics, 13(2), 221-229. (in English)

Danilov, E. (2014). Descriptive Geometry for CAD Users: Ribs Construction. Journal for Geometry and Graphics, 18(1), 115-124. (in English)

SolidWorks Web Help. Retrived from: http://help.solidworks.com/. (in English)

Suzuki, K., & Schroecker, H-P (2008). Application of descriptive geometry procedures in solving spatial problems with feature and parametric modelling 3D-CAD. Proceedings of the 13th International Conference on Geometry and Graphics (ICGG). Dresden, August 4-10, 2008, Germany, II, 1-8. (in English)

Suzuki, K., Yokoyama, Y., & Kanai T. (2012). Introduction to 3D-CAD/CG – Learning geometry and graphics through Inventor and 3ds Max-2nd edition. [M]. Saiensu, Tokyo, Japan. (in Japanese)

Suzuki, K. Significance of traditional geometry in teaching and learning graphic science (2013). CADDM: Computer Aided Drafting, Design and Manufacturing, 23/3, 49-55. (in English)

Suzuki, K. (2014). Traditional Descriptive Geometry Education in the 3D-CAD/CG Era. Journal for Geometry and Graphics, 18(2), 249-258. (in English)

Zsombor-Murray, P., & S. El Fashny (2006). A Cylinder of Revolution on Five Points. Journal for Geometry and Graphics, 10(2), 207-213. (in English)


GOST Style Citations


  1. Иванов, Г. С. Перспективы начертательной геометрии как учебной дисциплины / Г. С. Иванов // Геометрия и графика – 2013. – Т. 1, вып. 1 – С. 26–28. doi: 10.12737/467.
  2. Лосев, Н. В. 200 олимпиадных задач по начертательной геометрии : практ. пособие / Н. В. Лосев. – Москва : Высш. шк., 1992. – 144 с.
  3. Междисциплинарные связи начертательной геометрии и смежных разделов высшей математики / И. М. Дмитриева, Г. С. Иванов, В. И. Серегин, К. А. Муравьев // Геометрия и графика. – 2013. – Т. 1, вып. 3. – С. 8–12. doi: 10.12737/2124.
  4. Сальков, Н. А. Геометрическое моделирование и начертательная геометрия / Н. А. Сальков // Геометрия и графика. – 2016. – Т. 4, вып. 4. – С. 31–40. doi: 10.12737/22841.
  5. Сальков, Н. А. Место начертательной геометрии в системе геометрического образования технических вузов / Н. А. Сальков // Геометрия и графика. – 2016. – Т. 4, вып. 3. – С. 53–61. doi: 10.12737/21534.
  6. Сальков, Н. А. Начертательная геометрия — база для компьютерной графики / Н. А. Сальков // Геометрия и графика. – 2016. – Т. 4, вып. 2. – С. 37–47. doi: 10.12737/19832.
  7. Хейфец, А. Л. Начертательная геометрия как «бег в мешках» / А. Л. Хейфец // Проблемы качества графической подготовки студентов в техническом ВУЗе: традиции и инновации : материалы V Междунар. науч.-практ. интернет-конф. – Пермь, 2015. – Т. 1. – С. 298–325.
  8. Хейфец, А. Л. Реорганизация курса начертательной геометрии как актуальная задача развития кафедр графики / А. Л. Хейфец // Геометрия и графика. – 2013. – Т. 1, вып. 2. – С. 21–23. doi: 10.12737/781.
  9. Autodesk AutoCAD Help [Electronic resource]. – Available at: http://help.autodesk.com/view/ACD/2016/ENU/. – Title from screen. – Accessed : 02.10.2017.
  10. Bokan, N. Computer-Aided Teaching of Descriptive Geometry / N. Bokan, M. Ljucovic, S. Vukmirovic // Journal for Geometry and Graphics. – 2009. – Vol. 13, No. 2. – P. 221–229.
  11. Danilov, E. Descriptive Geometry for CAD Users: Ribs Construction / E. Danilov // Journal for Geometry and Graphics. – 2014. – Vol. 18, No. 1. – P. 115–124.
  12. SolidWorks Web Help [Electronic resource]. – Available at: http://help.solidworks.com/. – Title from screen. –Accessed : 02.10.2017.
  13. Suzuki, K. Application of descriptive geometry procedures in solving spatial problems with feature and parametric modelling 3D-CAD / K. Suzuki, H-P. Schroecker // Proc. of the 13th ICGG. – Dresden, Germany, 2008. – Vol. II. – P. 1–8.
  14. Suzuki, K. Introduction to 3D-CAD/CG – Learning geometry and graphics through Inventor and 3ds Max. – 2nded. [in Japanese] / K. Suzuki, Y. Yokoyama, T. Kanai. – Tokyo, Japan, 2012.
  15. Suzuki, K. Significance of traditional geometry in teaching and learning graphic science / K. Suzuki // CADDM: computer aided drafting, design and manufacturing. – 2013. – Vol. 23/3. – P. 49–55.
  16. Suzuki, K. Traditional Descriptive Geometry Education in the 3D-CAD/CG Era / K. Suzuki // Journal for Geometry and Graphics. – 2014. – Vol. 18, No. 2. – P. 249–258.
  17. Zsombor-Murray, P. A Cylinder of Revolution on Five Points / P. Zsombor-Murray, S. El Fashny // Journal for Geometry and Graphics. – 2006. – Vol. 10, No. 2. – P. 207–213.


DOI: https://doi.org/10.15802/stp2017/117973

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