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Journal articles on the topic 'B-Spline surfaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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1

Le-Thi-Thu, Nga, Khoi Nguyen-Tan, and Thuy Nguyen-Thanh. "Reconstruction of Low Degree B-spline Surfaces with Arbitrary Topology Using Inverse Subdivision Scheme." Journal of Science and Technology: Issue on Information and Communications Technology 3, no. 1 (2017): 82. http://dx.doi.org/10.31130/jst.2017.41.

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Multivariate B-spline surfaces over triangular parametric domain have many interesting properties in the construction of smooth free-form surfaces. This paper introduces a novel approach to reconstruct triangular B-splines from a set of data points using inverse subdivision scheme. Our proposed method consists of two major steps. First, a control polyhedron of the triangular B-spline surface is created by applying the inverse subdivision scheme on an initial triangular mesh. Second, all control points of this B-spline surface, as well as knotclouds of its parametric domain are iteratively adju

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2

Wang, Zhihua, Falai Chen, and Jiansong Deng. "Evaluation Algorithm of PHT-Spline Surfaces." Numerical Mathematics: Theory, Methods and Applications 10, no. 4 (2017): 760–74. http://dx.doi.org/10.4208/nmtma.2017.0003.

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AbstractPHT-splines are a type of polynomial splines over hierarchical T-meshes which posses perfect local refinement property. This property makes PHT-splines useful in geometric modeling and iso-geometric analysis. Current implementation of PHT-splines stores the basis functions in Bézier forms, which saves some computational costs but consumes a lot of memories. In this paper, we propose a de Boor like algorithm to evaluate PHT-splines provided that only the information about the control coefficients and the hierarchical mesh structure is given. The basic idea is to represent a PHT-spline l

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3

Lin, Hongwei, Yunyang Xiong, and Hongwei Liao. "Semi-structured B-spline for blending two B-spline surfaces." Computers & Mathematics with Applications 68, no. 7 (2014): 706–18. http://dx.doi.org/10.1016/j.camwa.2014.07.013.

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4

Dube, Mridula, and Reenu Sharma. "Cubic TP B-Spline Curves with a Shape Parameter." International Journal of Engineering Research in Africa 11 (October 2013): 59–72. http://dx.doi.org/10.4028/www.scientific.net/jera.11.59.

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In this paper a new kind of splines, called cubic trigonometric polynomial B-spline (cubic TP B-spline) curves with a shape parameter, are constructed over the space spanned by As each piece of the curve is generated by three consecutive control points, they posses many properties of the quadratic B-spline curves. These trigonometric curves with a non-uniform knot vector are C1 and G2 continuous. They are C2 continuous when choosing special shape parameter for non-uniform knot vector. These curves are closer to the control polygon than the quadratic B-spline curves when choosing special shape

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5

Rogers, David F., and Linda A. Adlum. "Dynamic rational B-spline surfaces." Computer-Aided Design 22, no. 9 (1990): 609–16. http://dx.doi.org/10.1016/0010-4485(90)90046-f.

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6

Garcia-Capulin, C. H., F. J. Cuevas, G. Trejo-Caballero, and H. Rostro-Gonzalez. "Hierarchical Genetic Algorithm for B-Spline Surface Approximation of Smooth Explicit Data." Mathematical Problems in Engineering 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/706247.

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B-spline surface approximation has been widely used in many applications such as CAD, medical imaging, reverse engineering, and geometric modeling. Given a data set of measures, the surface approximation aims to find a surface that optimally fits the data set. One of the main problems associated with surface approximation by B-splines is the adequate selection of the number and location of the knots, as well as the solution of the system of equations generated by tensor product spline surfaces. In this work, we use a hierarchical genetic algorithm (HGA) to tackle the B-spline surface approxima

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7

Wang, Aizeng, Gang Zhao, and Chuan He. "Unified Representation of Curves and Surfaces." Mathematics 9, no. 9 (2021): 1019. http://dx.doi.org/10.3390/math9091019.

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In conventional modeling, shared control points can be employed to realize a unified representation for an object consisting of only curves or only surfaces touching one another. However, this method fails in treating the following two cases: (a) a system consisting of detached curves or surfaces; (b) a system having both curves and surfaces. The purpose of the present paper is to develop a new theoretical tool to solve such problems. By introducing the definitions of naked knot and I-mesh, the concept of I-spline is put forth, which is, in essence, an expanded B-spline or T-spline. It is veri

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8

Cheng, Xian Guo, and Wei Jun Liu. "A New Method for Deformation of B-Spline Surfaces." Advanced Materials Research 139-141 (October 2010): 1260–63. http://dx.doi.org/10.4028/www.scientific.net/amr.139-141.1260.

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This paper presents an efficient method for deforming B-spline surfaces, based on the surface energy minimization. Firstly, using an analogy between the B-spline surface patch and the thin-plate element of the finite element method, and applying external forces on the surface with some given geometric constraints, the forces can locate on part of the surface or the surface. Then, the energy of the B-spline surface can change with the change of the forces. Finally, a new B-spline surface is generated by solving an optimization problem of change of the energy. The forces can be a single force, a

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9

Lord, Marilyn. "Curve and Surface Representation by Iterative B-Spline Fit to a Data Point Set." Engineering in Medicine 16, no. 1 (1987): 29–35. http://dx.doi.org/10.1243/emed_jour_1987_016_008_02.

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The method of B-splines provides a very powerful way of representing curves and curved surfaces. The definition is ideally suited to applications in Computer Aided Design (CAD) where the designer is required to remodel the surface by reference to interactive graphics. This particular facility can be advantageous in CAD of body support surfaces, such as design of sockets of limb prostheses, shoe insoles, and custom seating. The B-spline surface is defined by a polygon of control points which in general do not lie on the surface, but which form a convex hull enclosing the surface. Each control p

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10

Wang, Zhiguo. "Direct manipulation of B-spline surfaces." Chinese Journal of Mechanical Engineering (English Edition) 18, no. 01 (2005): 103. http://dx.doi.org/10.3901/cjme.2005.01.103.

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11

Walker, Marshall. "Interpolation with hybrid B-spline surfaces." Computers & Graphics 18, no. 4 (1994): 525–30. http://dx.doi.org/10.1016/0097-8493(94)90065-5.

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12

Patrikalakis, N. M., and L. Bardis. "Localization of rational B-spline surfaces." Engineering with Computers 7, no. 4 (1991): 237–52. http://dx.doi.org/10.1007/bf01206365.

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13

Ajjanagadde, Venkatramana G., and L. M. Patnaik. "Systolic architecture for B-spline surfaces." International Journal of Parallel Programming 15, no. 6 (1986): 551–65. http://dx.doi.org/10.1007/bf01407413.

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14

Lott, N. J., and D. I. Pullin. "Method for fairing B-spline surfaces." Computer-Aided Design 20, no. 10 (1988): 597–600. http://dx.doi.org/10.1016/0010-4485(88)90206-0.

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15

Hoschek, Josef, and Franz-Josef Schneider. "Spline conversion for trimmed rational Bézier- and B-spline surfaces." Computer-Aided Design 22, no. 9 (1990): 580–90. http://dx.doi.org/10.1016/0010-4485(90)90043-c.

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16

Fujioka, Hiroyuki, Hiroyuki Kano, and Clyde F. Martin. "Constrained smoothing and interpolating spline surfaces using normalized uniform B-splines." Communications in Information and Systems 14, no. 1 (2014): 23–56. http://dx.doi.org/10.4310/cis.2014.v14.n1.a2.

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17

Chalfant, Julie S., and Takashi Maekawa. "Design for Manufacturing Using B-Spline Developable Surfaces." Journal of Ship Research 42, no. 03 (1998): 207–15. http://dx.doi.org/10.5957/jsr.1998.42.3.207.

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A developable surface can be formed by bending or rolling a planar surface without stretching or tearing; in other words, it can be developed or unrolled isometrically onto a plane. Developable surfaces are widely used in the manufacture of items that use materials that are not amenable to stretching such as the formation of ducts, shoes, clothing and automobile parts including upholstery and body panels (Frey & Bindschadler 1993). Designing a ship hull entirely of developable surfaces would allow production of the hull using only rolling or bending. Heat treatment would only be required f

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18

Rabut, Christophe. "Even degree B-spline curves and surfaces." CVGIP: Graphical Models and Image Processing 54, no. 4 (1992): 351–56. http://dx.doi.org/10.1016/1049-9652(92)90082-9.

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19

Franssen, Michael, Remco C. Veltkamp, and Wieger Wesselink. "Efficient evaluation of triangular B-spline surfaces." Computer Aided Geometric Design 17, no. 9 (2000): 863–77. http://dx.doi.org/10.1016/s0167-8396(00)00030-3.

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20

Sweeney, Michael A. J., and Richard H. Bartels. "Ray Tracing Free-Form B-Spline Surfaces." IEEE Computer Graphics and Applications 6, no. 2 (1986): 41–49. http://dx.doi.org/10.1109/mcg.1986.276691.

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21

Loop, Charles, and T. D. DeRose. "Generalized B-spline surfaces of arbitrary topology." ACM SIGGRAPH Computer Graphics 24, no. 4 (1990): 347–56. http://dx.doi.org/10.1145/97880.97917.

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22

Shi, Xiquan, Tianjun Wang, Peiru Wu, and Fengshan Liu. "Reconstruction of convergent smooth B-spline surfaces." Computer Aided Geometric Design 21, no. 9 (2004): 893–913. http://dx.doi.org/10.1016/j.cagd.2004.08.001.

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23

Fernández-Jambrina, L. "B-spline control nets for developable surfaces." Computer Aided Geometric Design 24, no. 4 (2007): 189–99. http://dx.doi.org/10.1016/j.cagd.2007.03.001.

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24

Mizrahi, Jonathan, Sijoon Kim, Iddo Hanniel, Myung Soo Kim, and Gershon Elber. "Minkowski sum computation of B-spline surfaces." Graphical Models 91 (May 2017): 30–38. http://dx.doi.org/10.1016/j.gmod.2017.02.003.

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25

Mikkola, Aki, Ahmed A. Shabana, Cristina Sanchez-Rebollo, and Jesus R. Jimenez-Octavio. "Comparison between ANCF and B-spline surfaces." Multibody System Dynamics 30, no. 2 (2013): 119–38. http://dx.doi.org/10.1007/s11044-013-9353-z.

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26

Woodward, Charles D. "Cross-sectional design of B-spline surfaces." Computers & Graphics 11, no. 2 (1987): 193–201. http://dx.doi.org/10.1016/0097-8493(87)90032-x.

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27

Pottmann, Helmut, and Gerald Farin. "Developable rational Bézier and B-spline surfaces." Computer Aided Geometric Design 12, no. 5 (1995): 513–31. http://dx.doi.org/10.1016/0167-8396(94)00031-m.

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28

Wang, Yan-Wei, Zheng-Dong Huang, Ying Zheng, and Sheng-Gang Zhang. "Isogeometric analysis for compound B-spline surfaces." Computer Methods in Applied Mechanics and Engineering 261-262 (July 2013): 1–15. http://dx.doi.org/10.1016/j.cma.2013.04.001.

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29

Bhatt, Amba D., Archak Goel, Ujjaval Gupta, and Stuti Awasthi. "Reconstruction of Branched Surfaces: Experiments with Disjoint B-spline Surface." Computer-Aided Design and Applications 12, no. 1 (2014): 76–85. http://dx.doi.org/10.1080/16864360.2014.949577.

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30

DUBE, MRIDULA, and REENU SHARMA. "PIECEWISE QUARTIC TRIGONOMETRIC POLYNOMIAL B-SPLINE CURVES WITH TWO SHAPE PARAMETERS." International Journal of Image and Graphics 12, no. 04 (2012): 1250028. http://dx.doi.org/10.1142/s0219467812500283.

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Analogous to the quartic B-splines curve, a piecewise quartic trigonometric polynomial B-spline curve with two shape parameters is presented in this paper. Each curve segment is generated by three consecutive control points. The given curve posses many properties of the B-spline curve. These curves are closer to the control polygon than the different other curves considered in this paper, for different values of shape parameters for each curve. With the increase of the value of shape parameters, the curve approach to the control polygon. For nonuniform and uniform knot vector the given curves

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31

Wang, Hui Ping, Denton E. Hewgill, and Geoffrey W. Vickers. "An efficient algorithm for generating B-spline interpolation curves and surfaces from B-spline approximations." Communications in Applied Numerical Methods 6, no. 5 (1990): 395–400. http://dx.doi.org/10.1002/cnm.1630060510.

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32

Yan, Rui-Jun, Jing Wu, Ji Yeong Lee, and Chang-Soo Han. "Representation of 3D Environment Map Using B-Spline Surface with Two Mutually Perpendicular LRFs." Mathematical Problems in Engineering 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/690310.

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This paper proposes a map representation method of three-dimensional (3D) environment by using B-spline surfaces, which are first used to describe large environment in 3D map construction research. Initially, a 3D point cloud map is constructed based on extracted line segments with two mutually perpendicular 2D laser range finders (LRFs). Then two types of accumulated data sets are separated from the point cloud map according to different types of robot movements, continuous translation and continuous rotation. To express the environment more accurately, B-spline surface with covariance matrix

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33

Koch, K., and M. Schmidt. "N-dimensional B-spline surface estimated by lofting for locally improving IRI." Journal of Geodetic Science 1, no. 1 (2011): 41–51. http://dx.doi.org/10.2478/v10156-010-0006-3.

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N-dimensional B-spline surface estimated by lofting for locally improving IRIN-dimensional surfaces are defined by the tensor product of B-spline basis functions. To estimate the unknown control points of these B-spline surfaces, the lofting method also called skinning method by cross-sectional curve fits is applied. It is shown by an analytical proof and numerically confirmed by the example of a four-dimensional surface that the results of the lofting method agree with the ones of the simultaneous estimation of the unknown control points. The numerical complexity for estimating vn control poi

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34

Mu, Kaiyuan, Tadahiro SHIBUTANI, Kazumi MATSUI, and Takashi MAEKAWA. "2110 Isogeometric analysis of shell models with accurate curvatures represented by B-spline surfaces B-spline." Proceedings of Design & Systems Conference 2011.21 (2011): 171–75. http://dx.doi.org/10.1299/jsmedsd.2011.21.171.

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35

Jie Liew, Khang, Ahmad Ramli, Nur Nadiah Abd Hamid, and Ahmad Abd Majid. "Sharp edge preservation using bicubic B-spline surfaces." ScienceAsia 43S, no. 1 (2017): 20. http://dx.doi.org/10.2306/scienceasia1513-1874.2017.43s.020.

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36

Szilvasi-Nagy, M. "Shaping and fairing of tubular B-spline surfaces." Computer Aided Geometric Design 14, no. 8 (1997): 699–706. http://dx.doi.org/10.1016/s0167-8396(96)00056-8.

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37

Hoschek, Josef, and Rainer Müller. "Turbine blade design by lofted B-spline surfaces." Journal of Computational and Applied Mathematics 119, no. 1-2 (2000): 235–48. http://dx.doi.org/10.1016/s0377-0427(00)00381-2.

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38

Shi, Xiquan, Piqiang Yu, and Tianjun Wang. "G1 continuous conditions of biquartic B-spline surfaces." Journal of Computational and Applied Mathematics 144, no. 1-2 (2002): 251–62. http://dx.doi.org/10.1016/s0377-0427(01)00565-9.

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39

Dyn, N., D. Levin, and I. Yad-Shalom. "Conditions for regular $B$-spline curves and surfaces." ESAIM: Mathematical Modelling and Numerical Analysis 26, no. 1 (1992): 177–90. http://dx.doi.org/10.1051/m2an/1992260101771.

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40

Watanabe, Toshiaki. "Picture coding making use of B-spline surfaces." Electronics and Communications in Japan (Part I: Communications) 78, no. 7 (1995): 17–29. http://dx.doi.org/10.1002/ecja.4410780702.

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41

Huitric, Herve, and Monique Nahas. "B-Spline Surfaces: A Tool for Computer Painting." IEEE Computer Graphics and Applications 5, no. 3 (1985): 39–47. http://dx.doi.org/10.1109/mcg.1985.276341.

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42

SUN, SHUSEN, ZHIGENG PAN, and TAE-WAN KIM. "BLIND WATERMARKING OF NON-UNIFORM B-SPLINE SURFACES." International Journal of Image and Graphics 08, no. 03 (2008): 439–54. http://dx.doi.org/10.1142/s0219467808003179.

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In this paper, we propose a watermarking scheme for non-uniform B-spline (NUBS) surface. Firstly, we first do sampling on a NUBS surface and get the sample points, then the watermark is embedded into the DCT coefficients of the sample points and the watermarked sample points are transformed back, finally the watermarked surface is reconstructed from watermarked sample points using global interpolation. A sign correlation detector is used to test for the presence of the watermark, and the original surface is not required at this stage. Experimental results show that our algorithm can preserve t

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43

Watanabe, T. "Image coding making use of B-spline surfaces." IEEE Transactions on Circuits and Systems for Video Technology 7, no. 2 (1997): 409–13. http://dx.doi.org/10.1109/76.564118.

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44

Maekawa, T., and J. Chalfant. "Design and Tessellation of B-Spline Developable Surfaces." Journal of Mechanical Design 120, no. 3 (1998): 453–61. http://dx.doi.org/10.1115/1.2829173.

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Developable surfaces are widely used in various engineering applications. However, little attention has been paid to implementing developable surfaces from the onset of a design. The first half of the paper describes a user friendly method of designing developable surfaces in terms of a B-Spline representation whose two directrices lie on parallel planes. The second half of the paper investigates a new method for development and tessellation of such B-Spline developable surfaces, which is necessary for plate cutting and finite element analysis.

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45

Chen, Jun, and Guo-jin Wang. "Approximate merging of B-spline curves and surfaces." Applied Mathematics-A Journal of Chinese Universities 25, no. 4 (2010): 429–36. http://dx.doi.org/10.1007/s11766-010-2169-1.

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46

Patrikalakis, N. M., and L. Bardis. "Offsets of curves on rational B-spline surfaces." Engineering with Computers 5, no. 1 (1989): 39–46. http://dx.doi.org/10.1007/bf01201996.

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47

Rodrigues, Romulo T., Nikolaos Tsiogkas, Antonio Pascoal, and A. Pedro Aguiar. "Online Range-Based SLAM Using B-Spline Surfaces." IEEE Robotics and Automation Letters 6, no. 2 (2021): 1958–65. http://dx.doi.org/10.1109/lra.2021.3060672.

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48

Feng, Jiawei, Jianzhong Fu, Zhiwei Lin, Ce Shang, and Bin Li. "Direct slicing of T-spline surfaces for additive manufacturing." Rapid Prototyping Journal 24, no. 4 (2018): 709–21. http://dx.doi.org/10.1108/rpj-12-2016-0210.

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Purpose T-spline is the latest powerful modeling tool in the field of computer-aided design. It has all the merits of non-uniform rational B-spline (NURBS) whilst resolving some flaws in it. This work applies T-spline surfaces to additive manufacturing (AM). Most current AM products are based on Stereolithograph models. It is a kind of discrete polyhedron model with huge amounts of data and some inherent defects. T-spline offers a better choice for the design and manufacture of complex models. Design/methodology/approach In this paper, a direct slicing algorithm of T-spline surfaces for AM is

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49

Ateshian, G. A. "A B-Spline Least-Squares Surface-Fitting Method for Articular Surfaces of Diarthrodial Joints." Journal of Biomechanical Engineering 115, no. 4A (1993): 366–73. http://dx.doi.org/10.1115/1.2895499.

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The B-spline least-squares surface-fitting method is employed to create geometric models of diarthrodial joint articular surfaces. This method provides a smooth higher-order surface approximation from experimental three-dimensional surface data that have been obtained with any suitable measurement technique. Akima’s method for surface interpolation is used to provide complete support to the B-spline surface. The surface-fitting method is successfully tested on a known analytical surface, and is applied to the human distal femur. Applications to other articular surfaces are also shown. Results

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50

Sun, Lanyin, and Chungang Zhu. "B-Spline Solutions of General Euler-Lagrange Equations." Mathematics 7, no. 4 (2019): 365. http://dx.doi.org/10.3390/math7040365.

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The Euler-Lagrange equations are useful for solving optimization problems in mechanics. In this paper, we study the B-spline solutions of the Euler-Lagrange equations associated with the general functionals. The existing conditions of B-spline solutions to general Euler-Lagrange equations are given. As part of this work, we present a general method for generating B-spline solutions of the second- and fourth-order Euler-Lagrange equations. Furthermore, we show that some existing techniques for surface design, such as Coons patches, are exactly the special cases of the generalized Partial differ

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