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A Certified cubic b-spline Interpolation Method with Tangential Direction Constraints

Journal of Systems Science & Complexity 2024年第3期37卷 1271-1294页

作者： HE Shitao SHEN Liyong WU Qin YUAN Chunming School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China KLMM Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

Curve interpolation with b-spline is widely used in various areas. This problem is classic and recently raised in application scenario with new requirements such as path planning following the tangential vector field under certified error in CNC machining. This paper proposes an algorithm framework to solve Hausdorff distance certified cubic b-spline interpolation problem with or without tangential direction constraints. The algorithm has two stages: The first stage is to find the initial cubic b-spine fitting curve which satisfies the Hausdorff distance constraint;the second stage is to set up and solve the optimization models with certain constraints. Especially, the sufficient conditions of the global Hausdorff distance control for any error bound are discussed, which can be expressed as a series of linear and quadratic constraints. A simple numerical algorithm to compute the Hausdorff distance between a polyline and its b-spline interpolation curve is proposed to reduce our *** results are presented to show the advantages of the proposed algorithms.

关键词： cubic b-spline Hausdorff distance interpolation tangential direction

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UAV safe route planning based on PSO-bAS algorithm

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Journal of Systems Engineering and Electronics 2022年第5期33卷 1151-1160页

作者： ZHANG Honghong GAN Xusheng LI Shuangfeng CHEN Zhiyuan Air Traffic Control and Navigation College Air Force Engineering UniversityXi’an 710051China National Key Laboratory of Air Traffic Collision Prevention Xi’an 710051China

In order to solve the current situation that unmanned aerial vehicles(UAVs)ignore safety indicators and cannot guarantee safe operation when operating in low-altitude airspace,a UAV route planning method that considers regional risk assessment is ***,the low-altitude airspace is discretized based on rasterization,and then the UAV operating characteristics and environmental characteristics are combined to quantify the risk value in the low-altitude airspace to obtain a 3D risk *** path risk value is taken as the cost,the particle swarm optimization-beetle antennae search(PSO-bAS)algorithm is used to plan the spatial 3D route,and it effectively reduces the generated path redun􀅫***,cubic b-spline curve is used to smooth the plan􀅫ned discrete path.A flyable path with continuous curvature and pitch angle is *** simulation results show that the generated path can exchange for a path with a lower risk value at a lower path *** the same time,the path redundancy is low,and the curvature and pitch angle continuously *** is a flyable path that meets the UAV performance constraints.

关键词： unmanned aerial vehicle(UAV) low-attitude airspace mission planning risk assessment particle swarm optimization beetle antennae search(bAS) cubic b-spline

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Performance Analysis of Image Smoothing Techniques on a New Fractional Convolution Mask for Image Edge Detection

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Open Journal of Applied Sciences 2016年第7期6卷 478-488页

作者： Peter Amoako-Yirenkyi Justice Kwame Appati Isaac Kwame Dontwi Department of Mathematics Kwame Nkrumah University of Science and Technology Kumasi Ghana National Institute of Mathematical Sciences Kumasi Ghana

We present the analysis of three independent and most widely used image smoothing techniques on a new fractional based convolution edge detector originally constructed by same authors for image edge analysis. The implementation was done using only Gaussian function as its smoothing function based on predefined assumptions and therefore did not scale well for some types of edges and noise. The experiments conducted on this mask using known images with realistic geometry suggested the need for image smoothing adaptation to obtain a more optimal performance. In this paper, we use the structural similarity index measure and show that the adaptation technique for choosing smoothing function has significant advantages over a single function implementation. The new adaptive fractional based convolution mask can smoothly find edges of various types in detail quite significantly. The method can now trap both local discontinuities in intensity and its derivatives as well as locating Dirac edges.

关键词： cubic b-spline Edge Detection Fractional Edge Gaussian Filter Image Smoothing Median Filter Structural Similarity Index Measure

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Comparing Solutions to the Nonlinear Dissipative Wave Equation

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Journal of Applied Mathematics and Physics 2022年第4期10卷 1281-1296页

作者： Zaki Mrzog Alaofi Talaat Sayed El-Danaf Silvestru Sever Dragomir Department of Mathematics College of Science and Arts King Khalid University Muhayil Asir KSA Mathematics College of Engineering & Science Victoria University Melbourne Australia Department of Mathematics Faculty of Sciences and Arts Taibah University Medina KSA

In previous decades, many of the practical problems arising in scientific fields such as physics, engineering, and mathematics have been related to nonlinear fractional partial differential equations. One of these nonlinear partial differential equations, the dissipative wave equation, has been found to have a plethora of useful applications in different fields. A special class of solutions has been studied for the dissipative wave equation including exact solutions and approximate solutions. The aim of this article is to compare the non-polynomial spline method and the cubic b-spline method with the solution of a nonlinear dissipative wave equation. We will conduct a comparison of the stability of the two methods using the Von Neumann stability analysis. In addition, a numerical example will be presented to illustrate the accuracy of these methods.

关键词： Dissipative Wave Equation cubic b-spline Non-Polynomial spline Truncation Error Von Neumann Stability

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