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Topologically Correct Intersection Curves of Two Trimmed Quadrics with Tolerance Control

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Journal of Systems Science & Complexity 2024年第5期37卷 2207-2239页

作者： SHAO Wenbing chen falai Department of Mathematics University of Science and Technology of China

Surface/surface intersection is a fundamental problem in Compute Aided Design and Geometric Modeling since it is essential to solid modeling, numerically controlled machining, feature recognition, computer animation, etc. In practical applications, quadric surfaces, which are the most basic type of surfaces, are typically bounded surfaces trimmed by a sequence of planes. In this paper,a robust algorithm is proposed for computing the intersection curve segments of two trimmed quadrics based on the parametric representation of the intersection curves of two quadrics. The proposed algorithm guarantees correct topology and ensures that the approximation errors of the end points of the intersection curve segments are less than a given tolerance. The error control is based on an effective solution to a set of polynomial inequality system using the root isolation technique. Some examples are presented to validate the robustness and effectiveness of the proposed algorithm.

关键词： Polynomial inequality system root isolation surface/surface intersection tolerance control trimmed quadrics

A Spectral Segmentation Method for Large Meshes

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Communications in Mathematics and Statistics 2023年第3期11卷 583-607页

作者： Xiaohan Bao Weihua Tong falai chen School of Mathematical Sciences University of Science and Technology of ChinaHefei230026AnhuiPeople’s Republic of China

Mesh segmentation is a fundamental and critical task in mesh processing,and it has been studied extensively in computer graphics and geometric modeling ***,current methods are not well suited for segmenting large meshes which are now common in many *** paper proposes a new spectral segmentation method specifically designed for large meshes inspired by multi-resolution *** on edge collapse operators and progressive mesh representations,we first devise a feature-aware simplification algorithm that can generate a coarse mesh which keeps the same topology as the input mesh and preserves as many features of the input mesh as ***,using the spectral segmentation method proposed in Tong et al.(IEEE Trans Vis Comput Graph 26(4):1807–1820,2020),we perform partition on the coarse mesh to obtain a coarse segmentation which mimics closely the desired segmentation of the input *** reversing the simplification process through vertex split operators,we present a fast algorithm which maps the coarse segmentation to the input mesh and therefore obtain an initial segmentation of the input ***,to smooth some jaggy boundaries between adjacent parts of the initial segmentation or align with the desired boundaries,we propose an efficient method to evolve those boundaries driven by geodesic curvature *** demonstrated by experimental results on a variety of large meshes,our method outperforms the state-of-the-art segmentation method in terms of not only speed but also usability.

关键词： Mesh segmentation Spectral method Progressive mesh Feature-aware simplification Geodesic curvature flow

Boundary Correspondence for Iso-Geometric Analysis Based on Deep Learning

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Communications in Mathematics and Statistics 2023年第1期11卷 131-150页

作者： Zheng Zhan Ye Zheng Wenping Wang falai chen School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026AnhuiPeople’s Republic of China College of Architecture Texas A&M UniversityCollege StationTX 77843-3112USA

One of the key problems in isogeometric analysis(IGA)is domain parameterization,i.e.,constructing a map between a parametric domain and a computational *** a preliminary step of domain parameterization,the mapping between the boundaries of the parametric domain and the computational domain should be *** boundary correspondence strongly affects the quality of domain parameterization and thus subsequent numerical ***,boundary correspondence is generally determined manually and only one approach based on optimal mass transport discusses automatic generation of boundary *** this article,we propose a deep neural network based approach to generate boundary correspondence for 2D simply connected computational *** the boundary polygon of a planar computational domain,the main problem is to pick four corner vertices on the input boundary in order to subdivide the boundary into four segments which correspond to the four sides of the parametric *** synthesize a dataset with corner correspondence and train a fully convolutional network to predict the likelihood of each boundary vertex to be one of the corner vertices,and thus to locate four corner vertices with locally maximum *** evaluate our method on two types of datasets:MPEG-7 dataset and CAD model *** experiment results demonstrate that our algorithm is faster by several orders of magnitude,and at the same time achieves smaller average angular distortion,more uniform area distortion and higher success rate,compared to the traditional optimization-based ***,our neural network exhibits good generalization ability on new datasets.

关键词： Isogeometric analysis Domain parameterization Boundary correspondence Deep neural network

Computing μ-Bases of Univariate Polynomial Matrices Using Polynomial Matrix Factorization

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Journal of Systems Science & Complexity 2021年第3期34卷 1189-1206页

作者： HUANG Bingru chen falai Department of Mathematics University of Science and Technology of ChinaHefei 230000China

This paper extends the notion of μ-bases to arbitrary univariate polynomial matrices and present an efficient algorithm to compute a μ-basis for a univariate polynomial matrix based on polynomial matrix factorization. Particularly, when applied to polynomial vectors, the algorithm computes a μ-basis of a rational space curve in arbitrary dimension. The authors perform theoretical complexity analysis in this situation and show that the computational complexity of the algorithm is O(dn4+d2 n3),where n is the dimension of the polynomial vector and d is the maximum degree of the polynomials in the vector. In general, the algorithm is n times faster than Song and Goldman’s method, and is more efficient than Hoon Hong’s method when d is relatively large with respect to n. Especially, for computing μ-bases of planar rational curves, the algorithm is among the two fastest algorithms.

关键词： Computational complexity matrix factorization μ-bases

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An Improved Algorithm for Constructing Moving Quadrics from Moving Planes

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Journal of Systems Science & Complexity 2017年第6期30卷 1483-1506页

作者： LAI Yisheng chen falai Department of Mathematics Zhejiang Gongshang University Department of Mathematics University of Science and Technology of China

This paper proposes an improved algorithm to construct moving quadrics from moving planes that follow a tensor product surface with no base points, assuming that there are no moving planes of low degree following the surface. These moving quadrics provide an efficient method to implicitize the tensor product surface which outperforms a previous approach by the present authors.

关键词： Implicitization moving plane moving quadric rational surface

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A REMARK ON IMPLICITIZING RATIONAL CURVES WITH BASE POINTS

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高校应用数学学报A辑 1998年第S1期 123-128页

作者： chen falai

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Modified Bases of PHT-Splines

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Communications in Mathematics and Statistics 2017年第4期5卷 381-397页

作者： Yuanpeng Zhu falai chen School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026People’s Republic of China

Recently,it was found that during the process of certain refinement of hier-archical T-meshes,some basis functions of PHT-splines decay severely,which is not expected in solving numerical PDEs and in least square data fitting since the matrices assembled by these basis functions are likely to be *** this paper,we present a method to modify the basis functions of PHT-splines in the case that the sup-ports of the original truncated basis functions are rectangular domains to overcome the decay *** modified basis functions preserve the same nice properties of the original PHT-spline basis functions such as partition of unity,local support,linear *** examples show that the modified basis functions can greatly decrease the condition numbers of the stiffness matrices assembled in solving Poisson’s equation with Dirichlet boundary conditions.

关键词： PHT-spline B-spline Hierarchical T-mesh Poisson’s equation

A Review of Process Optimization for Additive Manufacturing Based on Machine Learning

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Annals of Applied Mathematics 2023年第4期39卷 493-543页

作者： Xiaoya Zhai falai chen School of Mathematical Sciences University of Science and Technology of ChinaHefeiAnhui 230026China

Additive manufacturing(AM),also known as 3D printing,has emerged as a groundbreaking technology that has transformed the manufacturing *** ability to produce intricate and customized parts with remarkable speed and reduced material waste has revolutionized traditional manufacturing ***,the AM process itself is a complex and multifaceted undertaking,with various parameters that can significantly influence the quality and efficiency of the printed *** address this challenge,researchers have explored the integration of machine learning(ML)techniques to optimize the AM *** paper presents a comprehensive review of process optimization for additive manufacturing based on machine learning,highlighting the recent advancements,methodologies,and challenges in this field.

关键词： Additive manufacturing 3D printing machine learning process optimization

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A REMARK ON IMPLICITIZING RATIONAL CURVES WITH BASE POINTS

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高校应用数学学报（A辑） 1998年第B6期13卷 121-126页

作者： chen falai

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关键词：基点有理曲线隐式化矩阵