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Global continuity Adjustment and Local Shape Optimization Technique for Complex Trimmed Surface Model

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Chinese Journal of Mechanical Engineering 2010年第2期23卷 225-232页

作者： BIAN Keke KE Yinglin The State Key Lab of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

Smoothly stitching multiple surfaces mainly represented by B-spline or NURBS together is an extremely important issue in complex surfaces modeling and reverse engineering. In recent years, a lot of progress has been made in smooth join of non-trimmed surface patches, while there has been seldom research on smoothly stitching trimmed surface patches together. This paper studies the problem of global continuity adjustment, damaged hole repair and local shape optimization for complex trimmed surface model, and presents a uniform scheme to deal with continuity adjustment of trimmed surfaces and geometric repair of local broken region. Constrained B-spline surface refitting technique and trim calculation are first utilized to achieve global G^1 continuity, and then local shape optimization functional is adopted to reduce fitting error and improve local quality of refitted surface patch. The proposed approach is applied to a discontinuity ship hull surface model with an irregular hole, and the result demonstrates the validation of our method. Furthermore, on the premise of global continuity, the proposed locally repairing damaged surface model provides a better foundation for following research work, such as topology recovery technique for complex surface model after geometric repair.

关键词： computer aided geometric design(CAGD) geometric continuity trimmed surface surface fitting shape optimization reverse engineering

PRACTICAL G^2 continuity ALGORITHMS BETWEEN ADJACENT NURBS PATCHES

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Chinese Journal of Aeronautics 1997年第2期10卷 110-118页

作者： Zhou Xijun Yang Haicbeng(Research Center for Computer Aided Design and Mannufacturing, NorthwesternPolytehnical University, Xi’an, 710072, China) Res. Ctr. Comp. Aided Des. and Mfg. NW Polytechnical University Xi'an 710072 China

Non-uniform rationa1 B-spline (NURBS) curves and sdrices are becomingincreasingly widespread. 'The authors have explored G1 continuity condition between adja-cent NURBS surface patches along common boundary curve. This paper presents a G2continuity condition between adjacent NURBS patches along common quadratic boundarycurve and deduces a specific algorithm for control Points and weights of NURBS *** making another NURBS patch and one given NURBS patch to attain G2, according toalgorithms condition, one can adjust another patch control ponts and weights. It is muchmore convenient for engineers to apply.

关键词： contours surfaces models nonuniform rational B-spline geometric continuity

CLOSED SMOOTH SURFACE DEFINED FROM CUBIC TRIANGULAR SPLINES

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Journal of Computational Mathematics 2005年第1期23卷 67-74页

作者： Ren-zhongFeng Ren-hongWang DepartmentofMathematics BeijingUniversityofAeronauticsandAstronauticsKeylaboratoryofMathematicsInformaticsandBehavioralSemanticsMinistryofEducationBeijing100083China MathematicalScienceInstitute DalianUniversityofTechnologyDalian116023China

In order to construct closed surfaces with continuous unit normal, we introduce a news pline space on an arbitrary closed mesh of three-sided faces. Our approach generalizes an idea of Goodman and is based on the concept of 'geometric continuity' for piecewise polynomial parametrizations. The functions in the spline space restricted to the faces are cubic triangular polynomials. A basis of the spline space is constructed of positive functions which sum to 1. It is also shown that the space is suitable for interpolating data at the midpoints of the faces。

关键词： Closed triangular mesh geometric continuity Smooth spline Triangular Bernstein polynomial

Storage-efficient reconstruction framework for planar contours

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Geo-Spatial Information Science 2017年第1期20卷 14-28页

作者： Hiroyuki Goto Yoichi Shimakawa Department of industrial and system engineering Hosei UniversitytokyoJapan Department of computer science and technology salesian polytechniquetokyoJapan

A storage-efficient reconstruction framework for cartographic planar contours is *** a smaller number of control points,we aim to calculate the area and perimeter as well as to reconstruct a smooth *** input data forms an oriented contour,each control point of which consists of three values:the Cartesian coordinates(x,y)and tangent angleθ.Two types of interpolation methods are developed,one of which is based on an arc spline while the other one is on a cubic Hermite *** arc spline-based method reconstructs a G1 continuous curve,with which the exact area and perimeter can be *** benefit of using the Hermite spline-based method is that it can achieve G2 continuity on most control points and can obtain the exact area,whereas the resulting perimeter is *** a numerical experiment for analytically defined curves,more accurate computation of the area and perimeter was achieved with a smaller number of control *** another experiment using a digital elevation model data,the reconstructed contours were smoother than those by a conventional method.

关键词： Oriented contour arc spline cubic Hermite spline geometric continuity storage efficient

CAN A CUBIC SPLINE CURVE BE G^(3)

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Journal of Computational Mathematics 2021年第2期39卷 178-191页

作者： Wujie Liu Xin Li School of Mathematical Science University of Science and Technology of ChinaHefei 230026China

This paper proposes a method to construct an G^(3)cubic spline curve from any given open control *** any two inner Bezier points on each edge of a control polygon,we can de ne each Bezier junction point such that the spline curve is *** by suitably choosing the inner Bezier points,we can construct a global G^(3)spline *** curvature combs and curvature plots show the advantage of the G^(3)cubic spline curve in contrast with the traditional C2 cubic spline curve.

关键词： Cubic Spline geometric continuity G^(3)continuity

G^2 continuity Algorithms between Adjacent NURBS Patches along Common Cubic Boundary Curve

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Chinese Journal of Aeronautics 2003年第4期16卷 241-246,242-246页

作者：周西军 Mechanical and Electrical Engineering College Northwestern Polytechnical University Xi'an 710072 China

Non-uniform rational B-spline (NURBS) curves and surfaces are becoming increasingly widespread. The author have explored G^1 continuity condition between adjacent NURBS surface patches along common cubic boundary curve. On the basis of the research performed, this paper presents a G^2 continuity condition between adjacent NURBS patches along common cubic boundary curve and deduces a specific algorithm for contro1 points and weights of NURBS patch. For making another NURBS patch and one given NURBS patch to attain G^2, according to algorithm condition, one can adjust another patch control points and weights. It is much more convenient for engineers to apply.

关键词： computer aided design geometric continuity non-uniform rational B-spline

Interpolation by G^(2) Quintic Pythagorean-Hodograph Curves

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Numerical Mathematics(Theory,Methods and Applications) 2014年第3期7卷 374-398页

作者： Gasper Jaklic Jernej Kozak Marjeta Krajnc Vito Vitrih Emil Zagar FMF University of Ljubljanaand IAMUniversity of PrimorskaJadranska 191000 LjubljanaSlovenia FMF and IMFM University of LjubljanaJadranska 191000 LjubljanaSlovenia FAMNIT and IAM University of PrimorskaMuzejski trg 26000 KoperSlovenia

In this paper,the G^(2) interpolation by Pythagorean-hodograph(PH)quintic curves in R^(d),d≥2,is *** obtained results turn out as a useful tool in practical *** of the dimension d,they supply a G^(2) quintic PH spline that locally interpolates two points,two tangent directions and two curvature vectors at these *** interpolation problem considered is reduced to a system of two polynomial equations involving only tangent lengths of the interpolating curve as *** several solutions might exist,the way to obtain the most promising one is suggested based on a thorough asymptotic analysis of the smooth data *** numerical algorithm traces this solution from a particular set of data to the general case by a homotopy continuation *** examples confirm the efficiency of the proposed method.

关键词： Pythagorean-hodograph curve Hermite interpolation geometric continuity nonlinear analysis homotopy

Modeling of Smooth Closed Surfaces With Bezier Patches

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Progress in Natural Science:Materials International 1993年第3期3卷 253-269页

作者：马利庄彭群生 Hangzhou 310027 PRC State Key Laboratory of CAD & CG Department of Computer Science State Key Laboratory of CAD & CG at Zhejiang University Zhejiang University

A unified method for modeling smooth closed surfaces with bicubic Bezier patches is *** method is capable of dealing with an arbitrary mesh of control points:an arbitrary number ofpatches are allowed to meet at any *** smooth closed surface is represented as a union ofgeometrically continuous bicubic Bezier *** vector can be interpolated at any *** theproposed procedure,it is simple and convenient to control and modify the shape of smooth closed surfaces lo-cally and *** results show the potential of our method.

关键词： surface modeling closed surface Bezier patches geometric continuity

geometrically Continuous Interpolation in Spheres

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Journal of Mathematical Research with Applications 2012年第4期32卷 379-391页

作者： Zhongxuan LUO1,2, , Qian WANG11. School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 2. School of Software, Dalian University of Technology, Liaoning 116620, P. R. China School of Mathematical Sciences Dalian University of Technology School of Software Dalian University of Technology

In this paper, a new method for geometrically continuous interpolation in spheres is proposed. The method is entirely based on the spherical B′ezier curves defined by the generalized de Casteljau algorithm. Firstly we compute the tangent directions and curvature vectors at the endpoints of a spherical B′ezier curve. Then, based on the above results, we design a piecewise spherical B′ezier curve with G 1 and G 2 continuity. In order to get the optimal piecewise curve according to two different criteria, we also give a constructive method to determine the shape parameters of the curve. According to the method, any given spherical points can be directly interpolated in the sphere. Experimental results also demonstrate that the method performs well both in uniform speed and magnitude of covariant acceleration.

关键词： interpolation sphere geometric continuity B′ezier.