Prethodno priopćenje

https://doi.org/10.31803/tg-20260502123125

Geometric Modeling of 2D Regions in AutoCAD Using the Marching Squares Algorithm with R-Functions

Nuraliev Fakhriddin Murodillayevich ; Department of Television and Media Technologies, Tashkent University of Information Technologies named after Muhammad al-Khwarizmi, Amir Temur Avenue 108, Tashkent 100084, Uzbekistan
Inoyatov Mirzayor Bakhtiyor ugli ; Department of Television and Media Technologies, Tashkent University of Information Technologies named after Muhammad al-Khwarizmi, Amir Temur Avenue 108, Tashkent 100084, Uzbekistan *
Ibodullaev Sardor Nasriddin ugli ; Department of Television and Media Technologies, Tashkent University of Information Technologies named after Muhammad al-Khwarizmi, Amir Temur Avenue 108, Tashkent 100084, Uzbekistan
Umarova Dildora Bakhtiyarovna ; Acting Associate Professor of the Department of Television and Media Technologies, Tashkent University of Information Technologies named after Muhammad al-Khwarizmi, Amir Temur Avenue 108, Tashkent 100084, Uzbekistan
Giyosov Ulugbek Eshpulatovich ; Department of Exact Sciences, Kimyo International University in Tashkent, Samarkand Branch, 63 H. Abdullae street, Samarkand, Uzbekistan

* Dopisni autor.

Sažetak

This study presents a methodology for geometric modeling of two-dimensional regions in AutoCAD based on the theory of R-functions by V. L. Rvachev combined with the Marching Squares algorithm. A specialized RFM 2D Plugin was developed in C# for the AutoCAD.NET API, enabling users to define geometric domains through implicit functions of the form f(x, y) = 0 and to construct complex composite regions via R-operations (conjunction, disjunction, and negation). Region boundaries are extracted automatically using the Marching Squares algorithm with bisection-based edge interpolation (an accuracy of Δx/1024) and are rendered as closed AutoCAD Polyline contours filled with Hatch objects and unified into a single editable Group. The method was validated on three classes of planar domains — four simple primitives (circle, ellipse, rectangle, triangle), parabolic and hyperbolic regions, and three complex composite models (a house, a six-pointed star, and a chess-king piece) composed of up to 15 primitive functions. The results show that a single analytical expression replaces the multi-command sequences required by conventional parametric modeling, that the number of contour points grows linearly and the computation time quadratically with grid resolution, and that boundary smoothness can be controlled through a single Rα parameter. The study demonstrates that embedding R-functions theory directly within the AutoCAD .NET environment yields a unified, flexible, and practically applicable framework for modeling irregular and analytically defined planar domains.

Ključne riječi

2D geometric modeling; AutoCAD; Hatch; implicit domain; Marching Squares; R-functions

Hrčak ID:

348874

URI

https://hrcak.srce.hr/348874

Datum izdavanja:

15.9.2026.

Posjeta: 0 *