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Unified strategy of supermesh generation for planar, cylindrical, and spherical non-conformal interfaces by using 2-D intersection algorithm

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APPLIED MATHEMATICAL MODELLING 2021年 94卷 791-813页

作者： Xiao, Y. Ming, P. J. Huang, J. Harbin Engn Univ Coll Power & Energy Engn Harbin 150001 Peoples R China Sun Yat Sen Univ Sino French Inst Nucl Engn & Technol Zhuhai 519082 Peoples R China

Aimed at decreasing the complexity of calculating the intersection of a pair of overlapped interfaces, this paper presents an efficient unified strategy to generate a supermesh for planar, cylindrical, and spherical non-conformal interfaces uniquely, which retains the computational efficiency of a 2-D intersection algorithm. The coordinate transformations for both the cylindrical and spherical interfaces are considered because the nodes of both types of interfaces can be described by two variable coordinates and a constant coordinate. The coordinate transformation of the spherical interfaces is performed by combining the Gnomonic projection and notion of rigid rotation. This task is incorporated in the local-supermeshing approach to generate the supermesh, which is employed as an auxiliary mesh to realize one-to-one addressing between the cells on both sides of the interfaces. Tests are performed to determine the pure geometric error of the supermeshing approach, and the results show the method does not induce additional geometric error. Besides, the accuracy and conservation of the fluxes when applying the supermeshing approach in a particular solver are studied. The results of the full-cycle unsteady simulation of internal combustion engine indicate the feasibility to applying the proposed method to realistic numerical problems. (c) 2021 Elsevier Inc. All rights reserved. Aimed at decreasing the complexity of calculating the intersection of a pair of overlapped interfaces, this paper presents an efficient unified strategy to generate a supermesh for planar, cylindrical, and spherical non-conformal interfaces uniquely, which retains the computational efficiency of a 2-D intersection algorithm. The coordinate transformations for both the cylindrical and spherical interfaces are considered because the nodes of both types of interfaces can be described by two variable coordinates and a constant coordinate. The coordinate transformation of the spherical interfaces is p

关键词： Finite volume method Non-conformal interfaces Unstructured meshes Spherical interfaces Supermesh intersection algorithm

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An intersection algorithm for disk B-spline curves

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COMPUTERS & GRAPHICS-UK 2018年 70卷 99-107页

作者： Ao, Xuefeng Fu, Qian Wu, Zhongke Wang, Xingce Zhou, Mingquan Chen, Quan Seah, Hock Soon Beijing Normal Univ 19 XinJieKouWai St Beijing 100875 Peoples R China Nanyang Technol Univ Sch Comp Sci & Engn Nanyang Ave Singapore 639798 Singapore

In this paper, we propose a method for finding all 2D intersection regions between disk B-spline curves (DBSCs), which is very crucial for DBSC's wide applications such as computer calligraphy, computer 2D animations, and non-photorealistic rendering. As a DBSC represents a region on a plane, the intersection of two DBSCs is a 2D region. To determine the region, the key is to compute the intersection points of the boundaries of two DBSCs. In our algorithm, the boundary of a DBSC is decomposed into four components: the upper boundary, the lower boundary, the start arc, and the end arc. The intersection of two DBSCs can be converted into the intersections between these four components. The main difficulty is to find the intersection involving the upper and lower boundaries of the two DBSCs, as they are variable offsets from the skeletons of the DBSC that are B-spline curves. In our approach, first the DBSCs are subdivided into several disk Bezier curves (DBCs). Therefore the problem of computing intersections of the DBSCs is converted into computing intersection of two DBCs. Then, the disk Bezier clipping method is proposed to exclude regions that have no intersection for the intersection of the two DBCs. In the case of where there is an intersection, we calculate the comparatively rough intersection to be used as initial values for later refinement through the disk Bezier clipping method. Besides, high precision (up to 10e-15) intersections are achieved by using the Newton's iteration, which is quadratic convergent. The experimental results demonstrate that our algorithm can very efficiently compute all intersections between DBSCs with high precision. Our main contributions in this paper are as follows. First, for the first time, we give the direct parametric expression of DBSC's boundary, which can be simply and conveniently used to compute the properties of DBSC's boundary. Second, our proposed approach of calculating high-accuracy intersections of DBSCs makes DBSC

关键词： intersection algorithm Disk B-spline curve Clipping method Newton's method

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Subspace algorithms for identifying separable-in-denominator two-dimensional systems with deterministic inputs

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IET CONTROL THEORY AND APPLICATIONS 2011年第15期5卷 1748-1765页

作者： Ramos, J. A. Alenany, A. Shang, H. dos Santos, P. J. L. Nova SE Univ Farquhar Coll Arts Sci Div Math Sci & Technol Ft Lauderdale FL 33314 USA Zagazig Univ Dept Syst & Comp Engn Fac Engn Zagazig 44519 Egypt Laurentian Univ Sch Engn Sudbury ON P3E 2C6 Canada Univ Porto Dept Engn Electrotecn & Comp Fac Engn P-4200465 Oporto Portugal

The class of subspace system identification algorithms is used here to derive new identification algorithms for 2-D causal, recursive, and separable-in-denominator (CRSD) state space systems in the Roesser form. The algorithms take a known deterministic input-output pair of 2-D signals and compute the system order (n) and system parameter matrices {A, B, C, D}. Since the CRSD model can be treated as two 1-D systems, the proposed algorithms first separate the vertical component from the state and output equations and then formulate a set of 1-D horizontal subspace equations. The solution to the horizontal subproblem contains all the information necessary to compute (n) and {A, B, C, D}. Four algorithms are presented for the identification of CRSD models directly from input-output data: an intersection algorithm, (N4SID), (MOESP), and (CCA). The intersection algorithm is distinguished from the rest in that it computes the state sequences, as well as the system parameters, whereas N4SID, MOESP, and CCA differ primarily in the way they compute the system parameter matrices {A1, C1}. The advantage of the intersection algorithm is that the identified model is in balanced coordinates, thus ideally suited for 2-D model reduction. However, it is computationally more expensive than the other algorithms. A comparison of all algorithms is presented.

关键词： state-space system 2D model reduction deterministic input Algebra separable-in-denominator two-dimensional system intersection algorithm Control system analysis and synthesis methods identification subspace system identification algorithm state-space methods Roesser form matrix algebra

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An intersection algorithm suitable for geometric trimming of B-spline surfaces of aircraft fuselages and wings

An intersection algorithm suitable for geometric trimming of...

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International Conference on Imaging Science, Systems, and Technology - Computer Graphics

作者： Zhang, XY Myklebust, A Gelhausen, P Virginia Polytech Inst & State Univ Dept Mech Engn Blacksburg VA 24061 USA

ISBN: (纸本)1932415645

B-spline surfaces have been widely used in aircraft design to represent different types of components in a uniform format. Unlike the visual trimming, which hides unwanted portions in rendering, geometric trimming gives a mathematically clean representation. To trim two intersecting surfaces requires finding their intersections effectively. Most of the existing algorithms focus on providing intersections suitable for rendering. In this paper, an intersection algorithm suitable for geometric trimming of B-spline surfaces is presented. This algorithm selects isoparametric curves based on the characteristics of one surface and intersects these curves with the other surface. The intersection points are then connected to create intersection curves by a marching scheme. A subdivision method is used to obtain such curve-surface intersection. The curve is subdivided until it can be approximated by a straight line and the surface is subdivided until the patch can be approximated by a quadrilateral within a given tolerance. Finally, the intersection points are computed by a line-quadrilateral intersection algorithm. The number Of intersection Points depends on the number of isoparametric curves selected, and thus is controllable and independent of the error bound of intersection points. Examples are given for obtaining intersections of aircraft fuselages and wings.

关键词： B-spline surface intersection algorithm aircraft design

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A new technique for ray tracing point-based geometry

A new technique for ray tracing point-based geometry

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6th International Conference on Machine Learning and Cybernetics

作者： Quan, Yong Zhang, Zhen-Hua Li, Wen-Hui Liu, Wei Jilin Univ Coll Comp Sci & Technol Comp Graph Lab Changchun 130012 Peoples R China

ISBN: (纸本)9781424409723

In this paper a new technique for ray tracing point-based models is presented. Our approach offers a higher ray tracing speed in comparison with previous methods. During pre-process, we add an important attribute to each point for the purpose of ray tracing. During rendering, an algorithm of intersecting a ray with point geometry is demonstrated to get satisfied results. Our approach makes it possible to render high quality ray traced images with global illumination. It performs well especially in the way of boundary representation. We have tested our idea for shadows, reflection and refraction.

关键词： points neighbor radius ray tracing intersection algorithm boundary representation

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A NEW TECHNIQUE FOR RAY TRACING POINT-BASED GEOMETRY

A NEW TECHNIQUE FOR RAY TRACING POINT-BASED GEOMETRY

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2007 International Conference on Machine Learning and Cybernetics(IEEE第六届机器学习与控制论国际会议)

作者： YONG QUAN ZHEN-HUA ZHANG WEN-HUI LI WEI LIU Computer Graphics Laboratory College of Computer Science and Technology Jilin University Qianwei Road Changchun 130012 P.R.China Key Laboratory for Symbolic Computation and Knowledge Engineering of Ministry of Education

In this paper a new technique for ray tracing point-based models is *** approach offers a higher ray tracing speed in comparison with previous *** pre-process, we add an important attribute to each point for the purpose of ray *** rendering, an algorithm of intersecting a ray with point geometry is demonstrated to get satisfied *** approach makes it possible to render high quality ray traced images with global *** performs well especially in the way of boundary *** have tested our idea for shadows, reflection and refraction.

关键词： Points Neighbor radius Ray tracing intersection algorithm Boundary representation

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PREDICTOR CORRECTOR TYPE OF intersection algorithm FOR C2 PARAMETRIC SURFACES

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COMPUTER-AIDED DESIGN 1988年第6期20卷 347-352页

作者： CHEN, JJ OZSOY, TM Department of Mechanical Engineering and Mechanics Lehigh University PA 18015 USA

A predictor-corrector type of intersection algorithm is developed for free-form parametric surfaces with C 2 continuity. A surface-surface intersection is solved as a number of curve-surface intersections in which each of the curves is defined in the parameter space of the ‘primary surface’ as a straight line, passing through an initial point and pointing at an ‘engaging direction’. Concepts from differential geometry are employed to predict the initial points and the engaging directions before the Newton-Raphson iterations are performed to compute the actual intersection points. The algorithm proceeds in a predictor-corrector type of way with the propagation steps controlled by the user-specified tolerance. The computer implementation of the algorithm has presented quite satisfying results.

关键词： computer-aided design surfaces intersection algorithm

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ANALYTIC APPROACH TO intersection OF ALL PIECEWISE PARAMETRIC RATIONAL CUBIC CURVES

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COMPUTER-AIDED DESIGN 1987年第6期19卷 282-292页

作者： GOLDMAN, RN SEDERBERG, TW CONTROL DATA CORP ARDEN HILLSMN 55126 BRIGHAM YOUNG UNIV DEPT CIVIL ENGNPROVOUT 84602

Elimination theory is applied to develop an analytic approach to the intersection of any two piecewise parametric rational cubic curves. By splitting the general intersection problem into several simple cases, this algorithm reduces the intersection problem to the problem of finding the roots of a single polynomial in one variable of minimal degree. This technique is fast, automatic, efficient and robust.

关键词： computer-aided geometric design intersection algorithm cubic curves elimination resultants resolvants

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OFFSET CURVES IN THE PLANE

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COMPUTER-AIDED DESIGN 1985年第2期17卷 77-82页

作者： HOSCHEK, J Fachbereich Mathematik Technische Hochschule D-6100 Darmstadt FRG

For applications such as the generation of ornamental patterns for the numerical control of sewing machines in the textile industry or in the shoe industry or the numerical control of milling machines in the car body industry, offset curves must be generated from curves D i given by a designer. During the generation process further problems arise, for example finding the intersection points of neighbouring branches of the offset curves or deleting undesirable portions of the offset curves with cusps or with self-intersection points. In this paper methods are developed for attacking this problems.

关键词： offset curves cusps self-intersection points intersection algorithm

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