THE ROLE AND ESSENCE OF 'POSITIONAL AND METRIC PROBLEMS' IN PERSPECTIVE

Mamarajabova Shamsiqamar Nishon kizi

Termez State Pedagogical Institute, 2nd-year Master’s Student in Engineering Graphics and Design Theory

Keywords: Keywords: Perspective, Positional Problems, Metric Problems, Descriptive Geometry, Vanishing Point, Horizon Line, Spatial Reasoning, Architectural Projection, Geometric Transformations, Visual Representation.

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Abstract

Abstract: This article examines the theoretical and practical significance of "Positional and Metric Problems" within the science of perspective. Positional problems focus on the mutual intersection, belonging, and placement of geometric elements (points, lines, and planes) on a perspective plane, while metric problems deal with determining the actual dimensions, distances, angles, and natural shapes of objects depicted in a distorted perspective view. The study analyzes the algorithmic approach to solving these problems, which forms the core of descriptive geometry and architectural drawing. The integration of these classical problems with modern computer-aided design (CAD) systems is also discussed, highlighting their necessity in developing spatial reasoning for future engineers and architects.

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References

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training pedagogical personnel."

2. Resolution of the President of the Republic of Uzbekistan No. PQ-4688 (April 21, 2020). "On measures to further increase the efficiency of the fine and applied arts sphere."

3. Murodov, Sh., & others. (2008). Course of Descriptive Geometry. Tashkent: "O‘zbekiston".

4. Gordon, V. O., & Sementsov-Ogievsky, M. A. (2010). A Course in Descriptive Geometry. Moscow: Higher School Publishing House.

5. Alberti, L. B. (2004). On Painting (De Pictura). (C. Grayson, Trans.). London: Penguin Classics. (Original: 1435).

6. Panofsky, E. (1991). Perspective as Symbolic Form. New York: Zone Books.

7. Zelenskiy, A. L. (2019). Fundamentals of 3D Modeling in Engineering Graphics. Moscow: "Visshaya shkola".

8. ZiyoNet Information and Education Network: www.ziyonet.uz (Accessed February 2026).

9. National Library of Uzbekistan named after Alisher Navoi: www.natlib.uz

10. Journal of Engineering Graphics and Design: Digital archive for geometric modeling.