• Penio Lebamovski Bulgarian Academy of Sciences, Institute of Robotics, Sofia, Bulgaria



boundary method, curve, extrusion, stereo system, stereometry, polygon, 3D printing


The software proposed in the report can be used as a technological tool in the teaching and learning of the discipline of stereometry. The aim is to improve the learning process by supporting the development of students’ creativity and spatial imagination, qualities needed in the study of spatial geometric bodies. A new boundary method is used in the generation of geometric objects. This new method uses elements of the Cavalieri Indivisible method and Isaac Newton's boundary method, thus achieving higher accuracy with respect to generated objects compared to 3D systems that use the rules of trigonometry in the construction of geometric bodies. This article performs a comparative analysis between a traditional and a new method for generating 3D geometric objects according to certain parameters and criteria. The new method involved in the analysis was proposed by the author of the report. While the traditional one is based on trigonometry. Two parameters were studied, one for accuracy in generating objects, and the second determining speed. In order to generate cylindrical bodies, are used the quadratic Bézier curve and the 3D modeling technique known as an extrusion, which transforms two-dimensional objects into three-dimensional ones.. One way to generate a prism and pyramid is by extruding polygons. This report presents a new way of constructing edged bodies. The considered technique for 3D modeling participates in the analysis of the studied methods.


Abdul, R. (2008). Spatiel Data Modelling for 3D GIS. Berlin Heidelberg: Springer-Verlag.

Abrams, S., Allen, P. (2000). Computing swept volumes. Visualisation and Computer Animation, 69-82.

Bashmakova, I. (1975). Istoria nd metematikata[History of mathematics]. Sophia: Izdatelstvo nauka i izkustvo.

Chen, J., Chen,C. (2008). Foundations of 3D Graphics Programming Using JOGL and Java3D. London: Springer.

Christou, C., Sendova, C., Matos, J. (2007). Stereometry Activities with Dalest. Nicozia.

Chung, C, Cheng,C. (2009). Interactive Web-Based Virtual Reality with Java3D. New York.

Dogan, F., Yayli, Y. (2017). The relation between parameter curves and lines of curvature on canal surfaces. Kuwait Journal, 29-35.

Feng, Y., Owen, D. (2003). A 2D polygon/polygon contact model:algorithmic aspects. Emerald.

Fleck, S., G.S. (2013). An augmented Reality Environment for Astronomy Learning in Ele;entary Grades. 25th Conference on LInteraction Home -Machine.

Klawonn, F. (2012). Introduction to Computer Graphics Using Java 2D and 3D. Springer.

Kmetova, M. (2015). Rediscovered Anaglyph in program GeoGebra.

Luan, Xi., Xie, Yu., Ying, L. (2008). Research and Development of 3D Modelling. IJCSNS International Journal of Computer Science and Network.

Maleshkov, S. G. (2014). Komputarna graphika i photorelistichna vizualizacia[Computer graphics and photorealistic vizualization]. Sophia: Nov Bulgarski Universitet.

Nyuton, I. (1989). Matematicheskie nachala naturalna philosophia[Mathematical principles natural philosophy]. Moskva: Izdatelstvo Nauka.

Obradovich, M. (2017). Creating 3D shapes by time extrusion of moving objects. Conference 20 Generative Art Conference GA 2017.

Orourke, J. (2003). Principles of the Three-Demensional Computer Animation. W.W. North&Company.

Orourke, J. (2012). Computational Geometry in C. Cambridge University Press.

Petkov, E. (2013). Osnovi na kompyutarnata graphika [Basics of computer graphics]. Veliko Tarnovo: Faber.

Rahman, M, Puteh, M. (2013). Learning trigonometry using GeoGebra learning module: Are under achieve pupils motivated. AIP Conference Proceedings Vol. 1750.

Reimers, D. (2011). Bezier Curves An introduction.

Rososzczuk, R. (2015). Application of Cabri3D in teaching stereometry. Advances inScience and Technology Research Journal, Vol.9.

Sabati, Z. N. (2010). Standardizatation of 3D Models Creation procedures in Computer Graphics. International Design Conference. Dubrovnik.

Shirley, P. (2005). Fundamentals of Computer Graphics. Utah.

Vince, J. (2006). Mathematics for Computer Graphics. London: Springer.

Yeh, A. N. (2004). Towards a semiotic framework for using technology in mathematics education: the case of learning 3D geometry. International Conference on Computers in Education. Melbourne.

Z., Hong, Liang,Y. (2007). Computer Graphics using Java2D and Java3D. Pearson Education.

Zoneva, L. (2020). Degree of Digital technological Integration in The Bulgarian secondary technological education. CBU International Conference on innovations in Science and Education. Prague.




How to Cite

Lebamovski, P. . (2021). THE EFFECT OF 3D TECHNOLOGIES IN STEREOMETRY TRAINING. Proceedings of CBU in Natural Sciences and ICT, 2, 68-74.
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