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Journal articles on the topic 'NURBS curves/surfaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Munira, Ali, Nur Najmiyah Jaafar, Abdul Aziz Fazilah, and Z. Nooraizedfiza. "Review on Non Uniform Rational B-Spline (NURBS): Concept and Optimization." Advanced Materials Research 903 (February 2014): 338–43. http://dx.doi.org/10.4028/www.scientific.net/amr.903.338.

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This paper is to provide literature review of the Non Uniform Rational B-Splines (NURBS) formulation in the curve and surface constructions. NURBS curves and surfaces have a wide application in Computer Aided Geometry Design (CAGD), Computer Aided Design (CAD), image processing and etc. The formulation of NURBS showing that NURBS curves and surfaces requires three important parameters in controlling the curve and also modifying the shape of the curves and surfaces. Yet, curves and surfaces fitting are still the major problems in the geometrical modeling. With this, the researches that have been conducted in optimizing the parameters in order to construct the intended curves and surfaces are highlighted in this paper.

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2

BAJAJ, CHANDRAJIT L., GUOLIANG XU, ROBERT J. HOLT, and ARUN N. NETRAVALI. "NURBS APPROXIMATION OF A-SPLINES AND A-PATCHES." International Journal of Computational Geometry & Applications 13, no. 05 (October 2003): 359–90. http://dx.doi.org/10.1142/s0218195903001232.

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Given A-spline curves and A-patch surfaces that are implicitly defined on triangles and tetrahedra, we determine their NURBS representations. We provide a trimmed NURBS form for A-spline curves and a parametric tensor-product NURBS form for A-patch surfaces. We concentrate on cubic A-patches, providing a C1-continuous surface that interpolates a given triangulation together with surface normals at the vertices. In many cases we can generate cubic trimming curves that are rationally parametrizable on the triangular faces of the tetrahedra; for the remaining faces we resort to using quadratic curves, which are always rationally parametrizable, to approximate the cubic trimming curves.

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3

Lee, Y. T., and L. Fang. "Accurate Modelling of Complex Functional Surfaces for Mechanical Design Using Freeform Surfaces." Journal of Mechanical Design 122, no. 2 (February 1, 2000): 236–39. http://dx.doi.org/10.1115/1.533572.

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Freeform curves and surfaces are commonly used in CAD, and NURBS is particularly popular because it can model freeform curves and surfaces as well as conic curves and quadric surfaces exactly. This paper describes a method that allows the creation of NURBS surfaces that approximate complex functional surfaces that can be described in closed form. The accuracy of the approximation can be controlled. [S1050-0472(00)00202-6]

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4

Perez-Arribas, Francisco L., and Erno Peter-Cosma. "Parametric Generation of Planing Hulls with NURBS Surfaces." Journal of Ship Research 57, no. 04 (December 1, 2013): 241–61. http://dx.doi.org/10.5957/jsr.2013.57.4.241.

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This article presents a mathematical method for producing hard-chine ship hulls based on a set of numerical parameters that are directly related to the geometric features of the hull and uniquely define a hull form for this type of ship. The term planing hull is used generically to describe the majority of hard-chine boats being built today. This article is focused on unstepped, single-chine hulls. B-spline curves and surfaces were combined with constraints on the significant ship curves to produce the final hull design. The hard-chine hull geometry was modeled by decomposing the surface geometry into boundary curves, which were defined by design constraints or parameters. In planing hull design, these control curves are the center, chine, and sheer lines as well as their geometric features including position, slope, and, in the case of the chine, enclosed area and centroid. These geometric parameters have physical, hydrodynamic, and stability implications from the design point of view. The proposed method uses two-dimensional orthogonal projections of the control curves and then produces three-dimensional (3-D) definitions using B-spline fitting of the 3-D data points. The fitting considers maximum deviation from the curve to the data points and is based on an original selection of the parameterization. A net of B-spline curves (stations) is then created to match the previously defined 3-D boundaries. A final set of lofting surfaces of the previous B-spline curves produces the hull surface.

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5

Piegl, Les A., and Wayne Tiller. "Computing offsets of NURBS curves and surfaces." Computer-Aided Design 31, no. 2 (February 1999): 147–56. http://dx.doi.org/10.1016/s0010-4485(98)00066-9.

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6

Yang, Yi-Jun, Wei Zeng, Cheng-Lei Yang, Xiang-Xu Meng, Jun-Hai Yong, and Bailin Deng. "G1 continuous approximate curves on NURBS surfaces." Computer-Aided Design 44, no. 9 (September 2012): 824–34. http://dx.doi.org/10.1016/j.cad.2012.04.004.

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7

Pan, Jianjiang, Jianmin Zheng, and Gang Zhao. "Blind watermarking of NURBS curves and surfaces." Computer-Aided Design 45, no. 2 (February 2013): 144–53. http://dx.doi.org/10.1016/j.cad.2012.09.001.

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8

Li, Aimin, and Zongde Fang. "Multiresolution Geometric Modeling for NURBS Curves and Surfaces." Journal of Computer-Aided Design & Computer Graphics 22, no. 8 (September 6, 2010): 1339–43. http://dx.doi.org/10.3724/sp.j.1089.2010.10952.

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9

Liu, Ligang, and Guojin Wang. "Explicit matrix representation for NURBS curves and surfaces." Computer Aided Geometric Design 19, no. 6 (June 2002): 409–19. http://dx.doi.org/10.1016/s0167-8396(02)00124-3.

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10

Tiller, W. "Knot-removal algorithms for NURBS curves and surfaces." Computer-Aided Design 24, no. 8 (August 1992): 445–53. http://dx.doi.org/10.1016/0010-4485(92)90012-y.

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11

Perles, Brian P., and Judy M. Vance. "Interactive Virtual Tools for Manipulating NURBS Surfaces in a Virtual Environment." Journal of Mechanical Design 124, no. 2 (May 16, 2002): 158–63. http://dx.doi.org/10.1115/1.1464132.

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DN-Edit is a virtual environment developed to allow the manipulation of non-uniform rational b-spline (NURBS) surfaces using virtual shaping tools. NURBS have become the industry standard for representation of free-form curves and surfaces. The contribution of the work presented here is in the development of shaping tools which are used to operate directly on the NURBS data and change the shape of the surfaces in a virtual environment. These shaping tools allow surface manipulations to be made using methods that match the shaping of real malleable objects. The virtual shaping tools are three-dimensional shapes that are controlled through a six degree-of-freedom tracking system that converts user hand motions into computer input. The NURBS surface updates itself in real time due to the effect of the tools on the surface. The new shape of the surface is dependent on the position and orientation of the shaping tool relative to the surface. Constraint-based surface manipulation is used to obtain multiple point direct manipulation of NURBS surfaces. In addition, computational methods to allow the user to have direct control of the first derivative of the surface over an area are implemented. This application has been developed using the C2 software libraries and Iowa State University’s C2 surround screen virtual environment.

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12

Jang, Jeongki, and Kyungmok Kim. "Modeling of a Microscale Surface Using NURBS Technique." Coatings 9, no. 12 (November 20, 2019): 775. http://dx.doi.org/10.3390/coatings9120775.

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This article describes microscale surface modeling using the Non-Uniform Rational B-Spline (NURBS) surface interpolation technique. A three-dimensional surface model was generated on the basis of measured surface profile data. To validate this model, three brass specimens having different roughness values were used. Direct comparison between measured profiles and the curves modeled with NURBS was employed. It was identified that the proposed method allows the generation of microscale models similar to actual surfaces. Finally, a method to extract the Bearing Area Curve (BAC) from a 3D model was detailed. The proposed modeling will be useful for the characterization of bearing capacity of the surface and for contact analysis.

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Miura, Kenjiro T., and R. U. Gobithaasan. "Aesthetic Curves and Surfaces in Computer Aided Geometric Design." International Journal of Automation Technology 8, no. 3 (May 5, 2014): 304–16. http://dx.doi.org/10.20965/ijat.2014.p0304.

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Aesthetic shapes are usually actualized as 3D objects represented by free-form surfaces. The main components used to achieve aesthetic surfaces are 2D and 3D curves, which are the elements most basic for determining the shapes and silhouettes of industrial products. Bézier, B-Spline and NURBS are types of flexible curves developed for various design intents. These curves, however produce complex curvature functions that may undermine the formulation of shape aesthetics. A viable solution to this problem is to formulate aesthetic curves and surfaces from well-defined curvatures to improve aesthetic design quality. This paper advocates formalizing aesthetic curve and surface theories to fill the gapmentioned above, which has existed since the 1970s. This paper begins by reviewing on fair curves and surfaces. It then extensively discusses on the technicalities of Log-Aesthetic (LA) curves and surfaces and touches on industrial design applications. These emerging LA curves have a high potential for being used as standards to generate, evaluate and reshape aesthetic curves and surfaces, thus revolutionizing efficiency in developing curve and shape aesthetics.

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14

Yang, Lin, Shuai Nan Ren, Zhen Yu Wang, and Peng Zhang. "Research on Spiral Bevel Gear Tooth Surface Reconstruction Based on NURBS." Applied Mechanics and Materials 130-134 (October 2011): 701–5. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.701.

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The tooth surface shape of spiral bevel gear is complex. In the detection process of errors tooth surface model is constructed based on coordinate data of limited the actual tooth surface sampling points. The model is used to analysis and manufacture of gear to meet the processing requirements. NURBS (non-uniform rational B-Spline) method is the most effective reconstruction method for geometry there are both freedom and analytic curves and surfaces. NURBS method is used to calculate non-uniform knot vector, NURBS control points and B-Spline inverse and reconstruct tooth surface. Reconstructionof spiral bevel gears in using NURBS is achieved and the tooth surface reconstruction is drawn out in Open GL in VC environment. And then reconstruction error on the tooth surface is analyzed. It proves that using the method of NURBS to reconstruct spiral bevel gear tooth surface is correct and feasible.

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15

Xu, Jia Chuan, Shang Peng Gao, and Yong Fu Yin. "Representation Method and Degree Selection of Class A Surfaces for Auto-Body." Advanced Materials Research 156-157 (October 2010): 451–55. http://dx.doi.org/10.4028/www.scientific.net/amr.156-157.451.

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To represent curves and surfaces unified, many commercial soft-wares adopt non-uniform rational B-spline (NURBS) as the method. The NURBS method includes Bézier, B-spline and so forth. In surfaces smoothing Class A surfaces of auto-body are a kind of surfaces that have high desire. While different representing methods can fit curves and surfaces with prodigiously different qualities and efficiency. So the representing methods and degree selection of curves and surfaces for auto-body are fundamental issues that auto-body engineers must be solved. Based on analyzing the character of Bézier and B-spline representing methods, Bézier method is adopted to represent Class A surfaces of auto-body according to the desire of auto-body surfaces. At the same time, the degree of curves and surfaces for auto-body is limited between 2nd-7th according to the oscillation of high degree curves and surfaces and continuity desire. The example verified that the Bézier method can improve the quality and efficiency.

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16

Jacquemyn, Carl, Matthew D. Jackson, and Gary J. Hampson. "Surface-Based Geological Reservoir Modelling Using Grid-Free NURBS Curves and Surfaces." Mathematical Geosciences 51, no. 1 (September 11, 2018): 1–28. http://dx.doi.org/10.1007/s11004-018-9764-8.

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17

KWON, Junghoon, Jeongin LEE, Harksu KIM, Gilsoo JANG, and Youngho CHAI. "Deforming NURBS Surfaces to Target Curves for Immersive VR Sketching." IEICE Transactions on Information and Systems E93-D, no. 1 (2010): 167–75. http://dx.doi.org/10.1587/transinf.e93.d.167.

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18

Wulamu, Aziguli, Marc Goetting, and Dirk Zeckzer. "Approximation of NURBS curves and surfaces using adaptive equidistant parameterizations." Tsinghua Science and Technology 10, no. 3 (June 2005): 316–22. http://dx.doi.org/10.1016/s1007-0214(05)70075-4.

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19

Krishnamurthy, Adarsh, Rahul Khardekar, and Sara McMains. "Optimized GPU evaluation of arbitrary degree NURBS curves and surfaces." Computer-Aided Design 41, no. 12 (December 2009): 971–80. http://dx.doi.org/10.1016/j.cad.2009.06.015.

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20

Ülker, Erkan, and İsmail Babaoğlu. "Gravitational Search Algorithm for NURBS Curve Fitting." KnE Social Sciences 3, no. 1 (January 15, 2018): 33. http://dx.doi.org/10.18502/kss.v3i1.1395.

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By providing great flexibility non-uniform rational B-spline (NURBS) curves and surfaces are reason of preferability on areas like computer aided design, medical imaging and computer graphics. Knots, control points and weights provide this flexibility. Computation of these parameters makes the problem as a non-linear combinational optimization problem on a process of reverse engineering. The ability of solving these problems using meta-heuristics instead of conventional methods attracts researchers. In this paper, NURBS curve estimation is carried out by a novel optimization method namely gravitational search algorithm. Both knots and knots together weights simultaneous optimization process is implemented by using research agents. The high performance of the proposed method on NURBS curve fitting is showed by obtained results.Keywords: Non-uniform rational B-spline, gravitational search algorithm, meta-heuristic

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21

Liu, Xun, Yin Zhang, Nan Liu, and Zhi Yang Chen. "Blind Watermarking for CAD Models Based on Identification." Advanced Materials Research 479-481 (February 2012): 245–49. http://dx.doi.org/10.4028/www.scientific.net/amr.479-481.245.

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Currently there has been much interested in developing the watermarking for 3D graphic data of NURBS or mesh model, for its function of copyright protecting, private detection under the network environment. Since the majority of computer aided design (CAD) applications employ parametric curves and surfaces, this paper proposes a watermarking mechanism for CAD models, those employ non-uniform rational B-spine (NURBS) curves and surfaces as their main shape-defining primitives. This algorithm using relative knot insertion method embeds the watermarks generated by features sequence identification into the NURBS primitives. The shapes are exactly preserved. We don’t need ether original model or original message to extract the watermarks from the watermarked models, since it is blind. By experimental result, we confirmed the watermarking mechanism is robust against most common attacks.

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22

Elber, Gershon, Xianming Chen, and Elaine Cohen. "Mold Accessibility via Gauss Map Analysis." Journal of Computing and Information Science in Engineering 5, no. 2 (December 24, 2004): 79–85. http://dx.doi.org/10.1115/1.1875572.

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In manufacturing processes like injection molding or die casting, a two-piece mold is required to be separable, that is, be able to have both pieces of the mold removed in opposite directions while interfering neither with the mold nor with each other. The fundamental problem is to find a viewing (i.e., separating) direction, from which a valid partition line (i.e., the contact curves of the two mold pieces) exists. While previous research work on this problem exists for polyhedral models, verifying and finding such a partition line for general freeform shapes, represented by NURBS surfaces, is still an open question. This paper shows that such a valid partition exists for a compact surface of genus g, if and only if there is a viewing direction from which the silhouette consists of exactly g+1 nonsingular disjoint loops. Hence, the two-piece mold separability problem is essentially reduced to the topological analysis of silhouettes. In addition, we deal with removing almost vertical surface regions from the mold so that the form can more easily be extracted from the mold. It follows that the aspect graph, which gives all topologically distinct silhouettes, allows one to determine the existence of a valid partition as well as to find such a partition when it exists. In this paper, we present an aspect graph computation technique for compact free-form objects represented as NURBS surfaces. All the vision event curves (parabolic curves, flecnodal curves, and bitangency curves) relevant to mold separability are computed by symbolic techniques based on the NURBS representation, combined with numerical processing. An image dilation technique is then used for robust aspect graph cell decomposition on the sphere of viewing directions. Thus, an exact solution to the two-piece mold separability problem is given for such models.

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Kurbak, Arif. "Models for basic warp knitted fabrics Part III: the two guide bar fabrics (Double Tricot, Locknit, Reverse Locknit, Satin, Sharkskin)." Textile Research Journal 89, no. 10 (June 18, 2018): 1917–37. http://dx.doi.org/10.1177/0040517518779998.

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Two guide bar warp knitted fabrics are used as technical textile applications nowadays. In this, Part III of these series of papers, models for basic two guide bar warp knitted fabrics are created and given based on Parts I and II. Modeling of warp knitted fabrics started in the 1960s with some basic geometrical models and it was continued with using Non Uniform Basis Spline (NURBS) curves and surfaces. There were discontinuities in the loop parts in early created geometrical models and the NURBS models needed some control points from some sources. In this work instead of using NURBS curves, modeling of warp knitted fabric is attempted by using known curves. During creation of the models, curvature equalities are attained as much as possible, loop connection parts are modeled by having two continuously connected parabolas for the Double Tricot fabric and the loop connection parts of the other two bar fabrics are obtained by applying a sinus square curve to the connection part of the Double Tricot fabric. The models created are versatile and they can be changed and used for special cases. Models created are drawn to scale by using the 3DS-Max Computer Graphical Program. At first glance, it is seen that the model shapes are similar to the real fabric structures, which can be observed on photographs of them.

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WANG, Qing. "Shape modification of nurbs curves and surfaces based on force density method." Chinese Journal of Mechanical Engineering 43, no. 03 (2007): 135. http://dx.doi.org/10.3901/jme.2007.03.135.

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Selimovic, Ilijas. "Improved algorithms for the projection of points on NURBS curves and surfaces." Computer Aided Geometric Design 23, no. 5 (July 2006): 439–45. http://dx.doi.org/10.1016/j.cagd.2006.01.007.

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26

Бычков, И. В., А. К. Мялица, Н. И. Бычков, and А. М. Григорович. "КІНЕМАТИЧНІ ВЛАСТИВОСТІ ТРАЄКТОРІЙ, ОПИСАНИХ NURBS СПЛАЙНАМИ." Open Information and Computer Integrated Technologies, no. 85 (July 29, 2019): 83–95. http://dx.doi.org/10.32620/oikit.2019.85.04.

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The purpose of the article is to solve a number of problems of using NURBS curves in the implementation of high-speed processing of complex products on machining equipment. NURBS-splines are becoming increasingly popular among CNC specialists, which is motivated by their wide application in the modeling of the production facility in CAD/CAM systems. Advanced manufacturers of CNC devices in the number of shaping algorithms necessarily include NURBS - interpolation. But despite the extensive capabilities of CAD/CAM systems for describing the shape of products and toolpaths of processing equipment using spline curves, many manufacturers of CNC systems use more primitive methods for describing the trajectory of the tool - piecewise linear and linear-circular. This negates the benefits of using spline curves, including smooth curvature change, which is very important when moving the tool at high speed processing. Such simplification of trajectories is associated with a number of difficulties in the implementation of spline curves in modern CNC systems. In addition, the requirements for industrial cleanliness of the surfaces of the parts is information about the processing parameters, the directions of relative movements of the tool and the workpiece on the finishing operations in order to provide technological conditions to the size of the burrs formed. It is possible that the choice of strategy of processing for obtaining the minimum size of a Burr or reduction of their number. The sizes of the turned-out agnails define methods of their elimination in technological process of production of a detail. Therefore, the provision of technological information using the analytical standard of the part is a necessary condition for ensuring the quality of products and their high reliability. NURBS - interpolation allows to obtain a compact description of the tool movement in the process of forming, which allows to correctly formulate the problem of working of complex-shaped parts.

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Kurbak, Arif. "Models for basic warp knitted fabrics Part I: Chain stitches and their applications on marquisette and weft-inserted warp-knitted fabrics." Textile Research Journal 89, no. 10 (June 18, 2018): 1863–85. http://dx.doi.org/10.1177/0040517518779992.

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Chain stitches are basics structures to obtain a group of net grounds in warp knitting such as marquisette, curtain-net ground and full-width weft-inserted fabrics. These net grounds are, in turn, used as technical fabrics as well as household goods. Modeling of warp-knitted fabrics started with some basic geometrical models and it was continued using non-uniform basis-spline (NURBS) curves and surfaces. There were discontinuities in the loop parts in the early models and the NURBS models needed some control points from some sources. In this work instead of using NURBS curves, an attempt is made to model warp-knitted fabrics using known curves and continuities in loop parts are attained as much as possible. First of all, open chain stitch is modeled. Closed chain stitch is obtained by changing some parts of open chain stitch model. Models then applied to marquisette, curtain-net ground and full-width weft-inserted warp-knitted fabrics are presented. Models created are drawn to scale by using 3DS-Max computer graphical program. It is seen that the shapes obtained by the models are similar to those which can be observed on real samples.

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Hongyao, Shen, Fu Jianzhong, and Chen Zichen. "AXIS-BASED LOOK-AHEAD INTERPOLATOR FOR MACHINING OF SURFACES REPRESENTED BY NURBS CURVES." Machining Science and Technology 12, no. 4 (December 11, 2008): 546–62. http://dx.doi.org/10.1080/10910340802519262.

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Sun, Y. F., A. Y. C. Nee, and K. S. Lee. "Modifying free-formed NURBS curves and surfaces for offsetting without local self-intersection." Computer-Aided Design 36, no. 12 (October 2004): 1161–69. http://dx.doi.org/10.1016/j.cad.2003.11.002.

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30

Liao, Huanyu, Pavan Kumar Vaitheeswaran, Tao Song, and Ganesh Subbarayan. "Algebraic Point Projection for Immersed Boundary Analysis on Low Degree NURBS Curves and Surfaces." Algorithms 13, no. 4 (March 31, 2020): 82. http://dx.doi.org/10.3390/a13040082.

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Point projection is an important geometric need when boundaries described by parametric curves and surfaces are immersed in domains. In problems where an immersed parametric boundary evolves with time as in solidification or fracture analysis, the projection from a point in the domain to the boundary is necessary to determine the interaction of the moving boundary with the underlying domain approximation. Furthermore, during analysis, since the driving force behind interface evolution depends on locally computed curvatures and normals, it is ideal if the parametric entity is not approximated as piecewise-linear. To address this challenge, we present in this paper an algebraic procedure to project a point on to Non-uniform rational B-spline (NURBS) curves and surfaces. The developed technique utilizes the resultant theory to construct implicit forms of parametric Bézier patches, level sets of which are termed algebraic level sets (ALS). Boolean compositions of the algebraic level sets are carried out using the theory of R-functions. The algebraic level sets and their gradients at a given point on the domain are then used to project the point onto the immersed boundary. Beginning with a first-order algorithm, sequentially refined procedures culminating in a second-order projection algorithm are described for NURBS curves and surfaces. Examples are presented to illustrate the efficiency and robustness of the developed method. More importantly, the method is shown to be robust and able to generate valid solutions even for curves and surfaces with high local curvature or G 0 continuity—problems where the Newton–Raphson method fails due to discontinuity in the projected points or because the numerical iterations fail to converge to a solution, respectively.

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Wu, Xiao Gang, and Wei Qing Guo. "Surface Fitting of Parametric Improvement Based on Original Points." Applied Mechanics and Materials 58-60 (June 2011): 1797–801. http://dx.doi.org/10.4028/www.scientific.net/amm.58-60.1797.

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During the fitting of parametric curves and surfaces, selecting the parameters based on original points is very important, because it will affect the result of the fitting. In this paper an improved method of fitting surfaces by improving the parameters is proposed, this method is based on original points to interpolate NURBS curves and surfaces, it uses uniform knot vector, which is not affected by the distribution of original points, and it can reduce the amount of computation and improve some phenomena, such as break points and encircle. The results show that using this method can get satisfying figures.

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Mirhosseini, R. Tabatabaei. "Simulation of Seismic Response of Reinforced Concrete Beam-Column Joints with Nurbs Surface Fitting." Archives of Civil Engineering 63, no. 3 (September 26, 2017): 71–84. http://dx.doi.org/10.1515/ace-2017-0029.

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Abstract This paper presents an approach based on NURBS (non-uniform rational B-splines) to achieve a seismic response surface (SRS) from a group of points obtained by using an analytical model of RC joints. NURBS based on the genetic algorithm is an important mathematical tool and consists of generalizations of Bezier curves and surfaces and B-splines. Generally, the accuracy of the design process of joints depends on the number of control points that are captured in the results of experimental research on real specimens. The values obtained from the specimens are the best tools to use in seismic analysis, though more expensive when compared to values simulated by SRSs. The SRS proposed in this paper can be applied to obtain surfaces that show site effect results on destructions of beam-column joint, taking into account different site conditions for a specific earthquake. The efficiency of this approach is demonstrated by the retrieval of simulated-versus-analytical results.

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Hamann, Bernd, and Po-Yu Tsai. "A tessellation algorithm for the representation of trimmed nurbs surfaces with arbitrary trimming curves." Computer-Aided Design 28, no. 6-7 (June 1996): 461–72. http://dx.doi.org/10.1016/0010-4485(95)00043-7.

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Ma, Xiao Yong, Jun Qiang Ai, Ji Xiang Shan, and Yong Hong Li. "Aerodynamic Shape Deformation of Underwing Nacelle-Pylon Configuration Based on B-Spline Surface." Applied Mechanics and Materials 444-445 (October 2013): 191–95. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.191.

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A free deformation method based on the B-Spline (NURBS) and surface superposition technique was presented for complex aerodynamic shape deformation. The influences of control parameters including control points, order, knots and weights are analyzed with B-spline curves case. Using the developed method, the application of surface grids deformation on the wing and pylon of DLR-F6 plane shows that the control parameters only influence its local surface, and this method could describe complex surfaces effectively, which means that this method is feasible and applicable to model representation, surface grids deformation and aerodynamic shape optimization.

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Lyu, Xuegeng, Hongying Yu, and Jialu Wu. "Surface reconstruction for thin aero engine blade from disorganized contact measured points." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 5 (February 6, 2017): 746–58. http://dx.doi.org/10.1177/0954406217692007.

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Blade surface reconstruction is one of the necessary steps in blade adaptive machining system. The majority of the current reconstruction methods are based on point-cloud, which is obtained using noncontact measurements. Correspondingly, these methods are invalid when the points are obtained using contact measurements. In this paper, we studied the method of surface reconstruction for thin features based on measured contact points. Owing to the random order of the measured points, and the fact that when the distance between two measured points is larger than the wall thickness of the blade will lead to interpolation errors, a quad tree-based region division method, and a points sorting algorithm, are proposed for correctly ordering the points. On this basis, inverse interpolation of cross-sectional curves using a cubic NURBS curve is used to fit them and reconstruct surfaces. Surface reconstruction examples are presented herein, and a comparison between the reconstructed and designed surfaces is used to verify the validity of our method.

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Hashemian, Ali, and Seyed Farhad Hosseini. "An integrated fitting and fairing approach for object reconstruction using smooth NURBS curves and surfaces." Computers & Mathematics with Applications 76, no. 7 (October 2018): 1555–75. http://dx.doi.org/10.1016/j.camwa.2018.07.007.

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Thilmany, Jean. "No Mesh, No Fuss." Mechanical Engineering 128, no. 05 (May 1, 2006): 46–48. http://dx.doi.org/10.1115/1.2006-may-5.

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This paper highlights the design of finite element analysis (FEA) without the finite element. The analysis can use the same information, the CAD system used to create the geometry in the first place. The geometry as well as the analysis fields-like displacement or temperature all uses the non-uniform rational B-spline mathematical representation. Software makers generally use the NURBS mathematical model to generate curves and surfaces in a digitized image. The framework lets mechanical engineers run quick, what-if scenarios to determine how changing a piece of a subassembly would affect the entire assembly. The full assembly need not be remeshed.

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Abrams, S. L., L. Bardis, C. Chryssostomidis, N. M. Patrikalakis, S. T. Tuohy, F. E. Wolter, and J. Zhou. "The Geometric Modeling and Interrogation System Praxiteles." Journal of Ship Production 11, no. 02 (May 1, 1995): 117–32. http://dx.doi.org/10.5957/jsp.1995.11.2.117.

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After establishment of design requirements and creation of an initial shape, the design process of free form shapes should include interrogation and fairing until a desired shape, with appropriate geometric and performance characteristics, is achieved. Afterwards, the quality of the manufactured product can be determined by comparing measured data with the design model. To permit automated design and manufacturing, mathematical methods and algorithms for the creation, interrogation, fairing, and inspection of curves and surfaces have been developed and integrated into a computer system called Praxiteles. The general layout of Praxiteles, along with a description of design capabilities, is presented. This description covers the areas of input, output, approximation and conversion for data exchange, a summary of some shape creation methods, and a description of some advanced interactive interrogation, fairing, and inspection methods for NURBS curves and surfaces. Examples illustrate some of the features of the system, as applied in the design and inspection of marine propellers. Recommendations for future development of the system are also presented.

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Tsai, Mi-Ching, and Chung-Wei Cheng. "A Real-Time Predictor-Corrector Interpolator for CNC Machining." Journal of Manufacturing Science and Engineering 125, no. 3 (July 23, 2003): 449–60. http://dx.doi.org/10.1115/1.1578670.

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This paper presents a predictor-corrector interpolator (PCI) for the CNC machining of parts with parametric curves or surfaces. In contrast to existing parametric interpolators, the proposed method uses a simple algorithm as a predictor and the current feedrate command feedback compensation scheme as the corrector. The predictor adjusts itself according to the current feedrate command feedback, it also has the capability of predicting the next reference point of the parametric curves from the current reference point. As a result, the deviations between the current and desired feedrate commands will always fall within the specified feedrate command tolerances. This study aims at developing the mathematical analysis of the PCI, where the convergence condition is derived for the corrector. In this present approach, the user can specify either constant or variable federate and also its feedrate command accuracy. Both the simulation and experiment results are presented to demonstrate the feasibility of the proposed PCI for machining the parametric curves represented in the Non-Uniform Rational B-Spline (NURBS) form.

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Tong, Yi Fei, Yi Chun Yang, Hao Tian, and Dong Bo Li. "Integrated Environment for PDM, RE and CAD/ CAM System." Applied Mechanics and Materials 130-134 (October 2011): 491–94. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.491.

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Functional model for realizing the data integration of product data management, reverse engineering software and CAD/CAM system is proposed to support digitized prototyping and shorten the time market of new product. Measured data from CMM (Coordinate Measuring Machine), describing the geometric information of product would be sent directly to RE software. After refining and smoothing the “data cloud”, meshes of curves would be generated and sent to CAD/CAM system. The original data will be overlaid onto NURBS model obtained from CAD system to verify the reconstructed surfaces. The CAD model may be further faired, analyzed or NC machined within the context of current CAD/CAM system. Feasibility of such an approach has been testified on a sample part.

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Ai, Ping, and Bo Zhao. "Research and Implementation on the Quality Controlling Method of NURBS Curve." Applied Mechanics and Materials 121-126 (October 2011): 4269–73. http://dx.doi.org/10.4028/www.scientific.net/amm.121-126.4269.

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In CAID software based on NURBS technology, the quality of curve directly affects the quality of surface, and the post-editing and modification of the surface, so good curve is the core and key to build high-quality surface. In this paper, combining the basic theory of NURBS curves with practical experience, we conduct an in-depth study in the method of controlling the quality of the NURBS curves, and propose an implementation to improve the quality of the NURBS curves.

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Li, J.-G., M.-M. Qiu, T.-H. Zhang, and Z.-X. Li. "A practical real-time non-uniform rational B-spline curve interpolator for computer numerical control machining." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 226, no. 4 (September 7, 2011): 1068–83. http://dx.doi.org/10.1177/0954406211418026.

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Non-uniform rational B-spline (NURBS) interpolator, a key technique in computer numerical control (CNC) machining, has many advantages over linear and circular interpolator. A practical real-time NURBS interpolator based on an off-line algorithm, which is developed to handle the limitation of velocity and acceleration, is presented in this article. Two processing modules are employed to realize the real-time interpolator. In one module, a NURBS curve is split into shorter NURBS curves or approximated as continuous line segments according to the minimum splitting length first, and then the velocity planning of a short curve is applied. Inthe other module, the interpolation according to the velocity planning results is implemented. The proposed algorithm realizes the real-time velocity planning and interpolation of a NURBS curve regardless of the curve length or the continuity. It is also applicable to three-dimensional surface designed by computer-aided design system, which is composed of multiple NURBS curves or both NURBS curves and continuous line segments. Both the simulation and experiment results have proved the effectiveness of the proposed practical real-time NURBS interpolator.

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Bajaj, Chandrajit L., and Guoliang Xu. "NURBS approximation of surface/surface intersection curves." Advances in Computational Mathematics 2, no. 1 (January 1994): 1–21. http://dx.doi.org/10.1007/bf02519033.

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Choi, In hugh, Tae sung Jung, Min Yang Yang, and Dong yoon Lee. "NURBS Curve Interpolator for Controlling the Surface Roughness." Transactions of the Korean Society of Mechanical Engineers A 29, no. 5 (May 1, 2005): 698–706. http://dx.doi.org/10.3795/ksme-a.2005.29.5.698.

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Yue, Ying, and Jun Jia. "Computing Offsets of NURBS Curve and Surface." Advanced Materials Research 542-543 (June 2012): 537–40. http://dx.doi.org/10.4028/www.scientific.net/amr.542-543.537.

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This paper presents an algorithm for the offsetting of NURBS curve/surface. First the unit normal vectors of the progenitor NURBS curve/surface is computed precisely, then the offset curve/surface can be obtained by offsetting the progenitor curve/surface in the normal vector direction with the required distance. Considerable extra computational time can be saved, especially when they are to be offset by several times. As the method successfully computes the unit normal vector of the progenitors, the offset error of this method is zero. The method can also be generalized to other degree NURBS curve/surface.

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Yu, Cun Guang. "NURBS Curve Fitting Based on Arc Centripetal Parameterization for Tool Path Generation." Applied Mechanics and Materials 274 (January 2013): 121–23. http://dx.doi.org/10.4028/www.scientific.net/amm.274.121.

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NURBS curve fitting is used for tool path planning for sculptured surface NC machining. The cutter location data is parameterized by equal chord arc length parameterization, and Centripetal Parameterization is improved. It is not only more approach to curves nature equation in theory, but also closer to the interpolated curves in actual fitting. It is directly to reflect the curvature of curves of cutter location in NC machining.

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Pérez-Arribas, Leonardo Fernández-Jambrina &. Francisco. "Developable Surface Patches Bounded by NURBS Curves." Journal of Computational Mathematics 38, no. 5 (June 2020): 693–709. http://dx.doi.org/10.4208/jcm.1904-m2018-0209.

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Ma, Yuewen, Jianmin Zheng, and Kai Wang. "Physically-Based NURBS Surface Editing With Curves." Computer-Aided Design and Applications 9, no. 3 (January 2012): 361–74. http://dx.doi.org/10.3722/cadaps.2012.361-374.

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Pu, Xionig Ying, Wei Jun Liu, and Ji Bin Zhao. "Model of End Milling Force Based on Undeformed Chip Surface with NURBS in Peripheral Milling." Applied Mechanics and Materials 33 (October 2010): 356–62. http://dx.doi.org/10.4028/www.scientific.net/amm.33.356.

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A new cutting force model for peripheral milling is presented based-on a developed algorithm for instantaneous undeformed chip surface with NURBS. To decrease the number of the differential element, the contact cutting edges of end-milling cutter with the part and the chip thickness curve are represented by NURBS helix, and the instantaneous undeformed chip is constructed as a ruled surface with the two curves. The cutting force generated by the edge contact length and the uncut chip area. Using the cutting coefficients from Budak[1] , the cutting-force model verified by simulation. The simulation results indicate that new cutting-force model predict the cutting forces in peripheral milling accurately.

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Schumaker, Larry L., and Gerald Farin. "NURBS for Curve and Surface Design." Mathematics of Computation 60, no. 201 (January 1993): 439. http://dx.doi.org/10.2307/2153186.

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