TY - GEN

T1 - Finding a Minimum Distance Between Two Smooth Curves in 3D Space

AU - Аббасов, Меджид Эльхан оглы

AU - Полякова, Людмила Николаевна

PY - 2024/10/17

Y1 - 2024/10/17

N2 - This study investigates the problem of determining the minimum distance between two smooth 3D curves. We propose its solution on the basis of the newly formulated idea of Charged Balls Method. The main idea behind this method is the physical model which tends to the solution of the original problem. We can derive equations of motion for the system and apply the difference scheme for the solution of the obtained ordinary differential equations. This is the way we get an iterative algorithm for the initial problem. We employ Lyapunov theory of stability to prove the convergence of the proposed method. More specifically, the Barbashin-Krasovskii theorem on asymptotic stability is employed. The convergence rate of the algorithm is analyzed and the corresponding results are presented. We provide a number of numerical examples to demonstrate its work. These examples acknowledge the effectiveness of the method and stresses that the choice of the parameters one may significantly affect the convergence rate.

AB - This study investigates the problem of determining the minimum distance between two smooth 3D curves. We propose its solution on the basis of the newly formulated idea of Charged Balls Method. The main idea behind this method is the physical model which tends to the solution of the original problem. We can derive equations of motion for the system and apply the difference scheme for the solution of the obtained ordinary differential equations. This is the way we get an iterative algorithm for the initial problem. We employ Lyapunov theory of stability to prove the convergence of the proposed method. More specifically, the Barbashin-Krasovskii theorem on asymptotic stability is employed. The convergence rate of the algorithm is analyzed and the corresponding results are presented. We provide a number of numerical examples to demonstrate its work. These examples acknowledge the effectiveness of the method and stresses that the choice of the parameters one may significantly affect the convergence rate.

KW - Charged Balls Method

KW - Computational Geometry

KW - LaSalle’s Invariance Principle

KW - Lyapunov’s Second Method

KW - Mathematical Programming

KW - Minimal Distance

UR - https://www.mendeley.com/catalogue/65e7f3fe-ea7c-3994-b049-c679f5d68321/

U2 - 10.1007/978-3-031-73420-5_26

DO - 10.1007/978-3-031-73420-5_26

M3 - Conference contribution

SN - 9783031734199

T3 - Communications in Computer and Information Science

SP - 313

EP - 324

BT - Information Technologies and Their Applications (ITTA 2024)

Y2 - 23 April 2024 through 25 April 2024

ER -