arXiv subjects

Igor Orynyak

Publications and source records attributed to Igor Orynyak.

3 recordsLinked to original sources

arXiv2025

The reversed "von Karman/Brazier effect" and a compendiary analytical solution

The goal of the present study is to offer some accurate analytical formulae for the evaluation of the here defined reversed "von Karman/Brazier's effect", which may appear at first sight anomalous and has previously been noticed and successively explained using both Finite Element analyses and approximate analytical formulations. The proposed analytical formulae, based on the previous contribution of one of the present authors and on the Donnell's equations for cylindrical shells can be helpful in emphasizing the possible impact that some arrangements may have in various fields and especially in offshore engineering and can assist design calculations.

math-ph↗

arXiv2025

Thin Plate Spline Surface Reconstruction via the Method of Matched Sections

This paper further develops the Method of Matched Sections (MMS), a robust numerical framework for the solution of boundary value problems governed by partial differential equations. It demonstrates its unique applicability to the challenges of surface modeling, which lie at the intersection of computational mechanics and computer graphics. This work shows how the MMS successfully bridges this gap. By decomposing the domain into an assembly of 1D directional components matched along their entire boundaries, the method inherently enforces the continuity of all variational parameters, including second-order (curvature) and third-order (shear) derivatives. We demonstrate the method's advanced capabilities in high-fidelity surface reconstruction and blending, showing that it consistently generates energetically optimal, fair surfaces even from complex boundary conditions or sparse internal data points. By advancing the application of the MMS, this research establishes it as a powerful, physics-informed geometric tool that satisfies the dual demands of rigorous numerical analysis and aesthetic computer-aided design.

cs.GR↗

arXiv2025

Apictorial Jigsaw Puzzle Reconstruction Based on Curve Matching via a Corotational Beam Spline

Automatic assembly of apictorial jigsaw puzzles presents a classic curve matching problem, fundamentally challenged by discrete and noisy contour data obtained from digitization. Conventional smoothing methods, which are required to process these data, often distort the curvature-based criteria used for matching and cause a loss of critical information. This paper proposes a method to overcome these issues, demonstrated on the automatic reconstruction of a 54-piece puzzle. We reconstruct each piece's contour using a novel corotational beam spline, which models the boundary as a flexible beam with compliant spring supports at the measured data points. A distinctive feature is the dynamic re-indexing of these points; as their calculated positions are refined, they are re-numbered based on their projection onto the computed contour. Another contribution is a method for determining spring compliance in proportion to the distance between the point projections. This approach uniquely ensures a uniform degree of smoothing for corresponding curves, making the matching process robust to variations in point density and dependent only on measurement accuracy. Practical computations and the successful automatic reconstruction of the puzzle demonstrate the proposed method's effectiveness.

cs.CG↗