Relevant bibliographies by topics / NURBS curves/surfaces

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'NURBS curves/surfaces'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "NURBS curves/surfaces"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "NURBS curves/surfaces"

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O'Neill, Edward Finbar. "Geometry based constructions for curves and surfaces." Thesis, University of Birmingham, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.251132.

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Lockyer, Peter Stephen. "Controlling the interpolation of NURBS curves and surfaces." Thesis, University of Birmingham, 2007. http://etheses.bham.ac.uk//id/eprint/6502/.

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The primary focus of this thesis is to determine the best methods for controlling the interpolation of NURBS curves and surfaces. The various factors that affect the quality of the interpolant are described, and existing methods for controlling them are reviewed. Improved methods are presented for calculating the parameter values, derivative magnitudes, data point spacing and twist vectors, with the aim of producing high quality interpolants with minimal data requirements. A new technique for obtaining the parameter values and derivative magnitudes is evaluated, which constructs a C\(^1\) cubic spline with orthogonal first and second derivatives at specified parametric locations. When this data is used to create a C\(^2\) spline, the resulting interpolant is superior to those constructed using existing parameterisation and derivative magnitude estimation methods. Consideration is given to the spacing of data points, which has a significant impact on the quality of the interpolant. Existing methods are shown to produce poor results with curves that are not circles. Three new methods are proposed that significantly reduce the positional error between the interpolant and original geometry. For constrained surface interpolation, twist vectors must be estimated. A method is proposed that builds on the Adini method, and is shown to have improved error characteristics. In numerical tests, the new method consistently outperforms Adini. Interpolated surfaces are often required to join together smoothly along their boundaries. The constraints for joining surfaces with parametric and geometric continuity are discussed, and the problem of joining \(N\) patches to form an \(N\)-sided region is considered. It is shown that regions with odd \(N\) can be joined with G\(^1\) continuity, but those with even \(N\) or requiring G\(^2\) continuity can only be obtained for specific geometries.
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Ondroušková, Jana. "Modelování NURBS křivek a ploch v projektivním prostoru." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2009. http://www.nusl.cz/ntk/nusl-228872.

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In the first part I discuss ancestors of NURBS curves and surfaces, rather Ferguson, Beziere, Coons and B-spline curves and surfaces and furthermore B-spline functions. In the second part I devote to NURBS curves and surfaces, their description as a linear combination of B-spline functions in the projective space. I specify conical arcs more detailed, their submit in the projective space and NURBS surfasec given as tensor product of NURBS curves. Last part is devote to describtion programs for modeling conicals and NURBS surface.
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Arrouk, Khaled. "Techniques de conception assistée par ordinateur (CAO) pour la caractérisation de l'espace de travail de robots manipulateurs parallèles." Phd thesis, Université Blaise Pascal - Clermont-Ferrand II, 2012. http://tel.archives-ouvertes.fr/tel-00766814.

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Les environnements CAO fournissent des outils puissants pour la programmation graphique et la manipulation d'entités géométriques complexes. Dans cette thèse, nous proposons d'exploiter ce potentiel dans le domaine de la conception de robots parallèles. Ces robots sont considérés comme une alternative intéressante vis-à-vis de leurs homologues sériels dans différentes applications comme le " pick and place " et l'usinage. Cependant, leur utilisation industrielle est encore restreinte en raison d'un espace de travail limité, de modèles géométriques difficiles à résoudre et l'existence de configurations singulières délimitant leur domaine d'exploitation. L'analyse et la caractérisation de l'espace de travail jouent alors un rôle fondamental dans la phase de conception de robots manipulateurs parallèles. Dans ce travail de thèse, nous proposons des approches géométriques originales donnant lieu à un ensemble de méthodes et techniques basées CAO pour l'analyse et la caractérisation de l'espace de travail de robots parallèles plans et spatiaux. L'espace de travail est généré comme un solide dans l'environnement CAO à partir d'un paramétrage géométrique, d'esquisses et d'opérations élémentaires telles que le balayage hélicoïdal et l'intersection. Nous avons montré que ces méthodes constituent des outils pertinents et efficaces d'aide à la conception des mécanismes parallèles. Ils permettent également la résolution du problème géométrique direct et la génération de trajectoires libres de singularités. Plusieurs types de manipulateurs ont été considérés dans ce travail pour mettre en avant et illustrer les techniques CAO / Géométriques proposées : robots parallèles plans à 3 degrés de mobilité de type 3-RPR, 3-RRR, 3-PPR et 3-PRR, robots parallèles spatiaux à 6 degrés de mobilité de type ou 3-CRS ou 3-PRRS.
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Liu, Haiying. "Interfacing comprehensive rotorcraft analysis with advanced aeromechanics and vortex wake models." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/22534.

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Thesis (Ph. D.)--Aerospace Engineering, Georgia Institute of Technology, 2008.
Committee Chair: Bauchau, Olivier; Committee Member: Armanios, Erian; Committee Member: Hodges, Dewey; Committee Member: Ruzzene, Massimo; Committee Member: Stallybrass, Michael.
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Yeh, Tsung-Chi, and 葉宗祺. "6-DOF Manipulator Motion Trajectory and Attitude Planning Based on NURBS Curves and Surfaces." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/46xnyy.

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碩士
國立臺北科技大學
自動化科技研究所
104
Traditionally, 6-DOF manipulator trajectory planning is only based on the trajectory of tool contact locations and takes the inverse kinematics transformation to get the angular position of each axis. However, the motion states for each axis will beyond the mechanical specification (velocity, acceleration or jerk) when we consider the tool pose in the high curvature motion trajectory. That will affect the machining performance and even destroy the manipulator. This thesis proposes the 6-DOF manipulator motion trajectory and attitude planning based on NURBS curves and surfaces. The key techniques include: (1) NURBS curve pre-processing, (2) NURBS curve planning, (3) NURBS curve and surface interpolation, and (4) planning of motion trajectory attitude. Firstly, the curve segmentation is applied to filter the line segments and separate the different NURBS curve segments. Then, the estimated feedrate, which satisfies the chord accuracy and maximum feedrate limitation, can be evaluated by adaptive feedrate. Furthermore, the above estimated feedrate will be fed into two kinds of S-Curve and S-L-Curve ACC/DEC profiles based on mechanical specification, to generate accurate servo command by compensated NURBS curve and surface interpolator. The tool pose is designed according to user’s requirements in the final step. The proposed method simultaneously satisfies the specifications of chord accuracy, the limitation of maximum velocity, acceleration, jerk and feedrate error in each segment. Finally, the proposed methods are implemented to control the 6-DOF manipulator to verify the motion performance.
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Bonneau, Georges-Pierre. "Variational Design of Rational Bezier Curves and Surfaces." Phd thesis, 1993. http://tel.archives-ouvertes.fr/tel-01064604.

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The design of curves and surfaces in C.A.D. systems has many applications in car, plane or ship industry. Because they offer more flexibility, rational functions are often preferred to polynomial functions to modelize curves and surfaces. In this work, several methods to generate rational Bezier curves and surfaces which minimize some functionals are proposed. The functionals measure a technical smoothness of the curves and surfaces, and are related to the energy of beams and plates in the sense of the elasticity theory.
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Jan, Yung Ning, and 鄭元寧. "NURBS curve and surface application in reversing engineering." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/46543549645953998131.

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Cheng, Chung-Wei, and 鄭中緯. "Design and Implementation of Real-time NURBS Curve and Surface Interpolators for Motion Controllers." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/48763572027740817342.

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博士
國立成功大學
機械工程學系碩博士班
91
NURBS (Non-Uniform Rational B-Spline) has been widely used in commercial CAD systems for geometric representation of part shapes, especially for free-form curves and surfaces. However, traditional CNC controllers only provide line and circular interpolators, that is, only motion along straight line and circular paths are supported. In order to perform mold machining, the tool paths are approximated to many short linear or circular segments by CAM systems before being downloaded to the CNC controllers. Such approximation may result in several problems such as large contouring error, increase of NC program sizes and data transfer load, velocity discontinuity, shocks or variations in mechanical systems and low machining efficiency. To overcome these drawbacks, novel real-time NURBS curve and surface interpolators are developed in this dissertation. The proposed methods include: (1) a simple method to efficiently compute the NURBS curve (surface) with its derivatives in real-time; (2) a predictor-corrector interpolator (PCI) for the machining of parts with NURBS curves, whereby it can be ensured that the feedrate command errors will fall within the specified feedrate command tolerances. In addition, the mathematical analysis and convergence condition of the corrector are also presented; (3) algorithms for the “ACC/DEC before feedrate interpolation” based on the real-time variable feedrate NURBS curve interpolator. The ACC/DEC (acceleration/deceleration) planning on the feedrate command executes before the interpolation takes place, so that the path command errors caused by conventional ACC/DEC planning using the after federate interpolation can be eliminated; and (4) a novel real-time NURBS surface interpolator that is capable of real-time generation of cutter location (CL) motion command for ball-end milling of NURBS surfaces and maintaining a constant cutter contact (CC) velocity along the CC path and its intervals. The efficiency and quality of machining can be improved significantly since the CC velocity along the surface is kept constant. These methods are evaluated on a multi-axis servomechanism with a DSP-based motion control system. Experimental results have indicated that these techniques are effective to significantly reduce the contouring error, decrease the data transfer load, and improve the machining efficiency and quality.
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Books on the topic "NURBS curves/surfaces"

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NURB curves and surfaces: From projective geometry to practical use. Wellesley, Mass: A.K. Peters, 1995.

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E, Farin Gerald, and SIAM Activity Group on Geometric Design., eds. NURBS for curve and surface design. Philadelphia: Society for Industrial and Applied Mathematics, 1991.

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Farin, Gerald. NURBS for Curve & Surface Design. A K Peters/CRC Press, 1999. http://dx.doi.org/10.1201/9781439863909.

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Farin, Gerald. NURBS for Curve and Surface Design: From Projective Geometry to Practical Use. CRC Press LLC, 1999.

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Farin, Gerald. NURBS for Curve and Surface Design: From Projective Geometry to Practical Use. CRC Press LLC, 1999.

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Book chapters on the topic "NURBS curves/surfaces"

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Piegl, Les, and Wayne Tiller. "B-spline Curves and Surfaces." In The NURBS Book, 81–116. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-59223-2_3.

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Piegl, Les, and Wayne Tiller. "Rational B-spline Curves and Surfaces." In The NURBS Book, 117–39. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-59223-2_4.

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Grabowski, Hans, and Xiaohe Li. "General matrix representation for NURBS curves and surfaces for interfaces." In Freeform Tools in CAD Systems, 219–31. Wiesbaden: Vieweg+Teubner Verlag, 1991. http://dx.doi.org/10.1007/978-3-322-86773-5_13.

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Duran, Guilherme C., and Marcos S. G. Tsuzuki. "A Kinematics Framing Methodology for Computing Sweep Surfaces Using N-Dimensional NURBS Curves." In Advances in Intelligent Systems and Computing, 592–603. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-63403-2_53.

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Piegl, Les, and Wayne Tiller. "Curve and Surface Basics." In The NURBS Book, 1–46. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-59223-2_1.

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Piegl, Les, and Wayne Tiller. "Curve and Surface Fitting." In The NURBS Book, 361–453. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-59223-2_9.

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Potier, Christine, Mustapha Bel Guermah, and Christine Vercken. "Curve Fitting Using NURBS." In Curves and Surfaces, 367–70. Elsevier, 1991. http://dx.doi.org/10.1016/b978-0-12-438660-0.50058-3.

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Ventura, M., and C. Guedes Soares. "Hull form modelling using NURBS curves and surfaces." In Developments in Marine Technology, 289–96. Elsevier, 1998. http://dx.doi.org/10.1016/s0928-2009(98)80165-0.

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"NURBS." In NURBS for Curve & Surface Design, 169–84. A K Peters/CRC Press, 1999. http://dx.doi.org/10.1201/9781439863909-15.

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"Pythagorean Curves." In NURBS for Curve & Surface Design, 185–96. A K Peters/CRC Press, 1999. http://dx.doi.org/10.1201/9781439863909-16.

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Conference papers on the topic "NURBS curves/surfaces"

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Zhang, Pifu, Caiming Zhang, and Fuhua (Frank) Cheng. "Constrained Shape Scaling of Trimmed NURBS Surfaces." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/dtm-8755.

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Abstract A method to scale and deform a trimmed NURBS surface while holding the shape and size of specific features (trimming curves) unchanged is presented. The new surface is formed by scaling the given surface according to the scaling requirement first; and then attaching the (original) features to the scaled NURBS surface at appropriate locations. The attaching process requires several geometric operations and constrained free-form surface deformation. The resulting surface has the same features as the original surface and same boundary curves as the scaled surface while reflecting the shape and curvature distribution of the scaled surface. This is achieved by minimizing a shape-preserving objective function which covers all the factors in the deformation process such as bending, stretching and spring effects. The resulting surface maintains a NURBS representation and, hence, is compatible with most of the current data-exchange standards. Test results on several car parts with trimming curves are included. The, quality of the resulting surfaces is examined using the highlight line model.
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Song, Hai-Chuan, Kan-Le Shi, Jun-Hai Yong, Xin Qiao, and Yang Lu. "Parameter Estimation of Point Projection on NURBS Curves and Surfaces." In 2015 14th International Conference on Computer-Aided Design and Computer Graphics (CAD/Graphics). IEEE, 2015. http://dx.doi.org/10.1109/cadgraphics.2015.37.

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Krishnamurthy, Adarsh, Rahul Khardekar, and Sara McMains. "Direct evaluation of NURBS curves and surfaces on the GPU." In the 2007 ACM symposium. New York, New York, USA: ACM Press, 2007. http://dx.doi.org/10.1145/1236246.1236293.

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Urick, Benjamin, Richard H. Crawford, Thomas J. R. Hughes, Elaine Cohen, and Richard F. Riesenfeld. "Reconstruction of Gap-Free Intersections for Trimmed NURBS Surfaces." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-98372.

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Abstract The modern engineering technologies of Computer-Aided Design (CAD), Computer-Aided Engineering (CAE) and Computer-Aided Manufacturing (CAM) are ubiquitous in engineering design. They are focused on creating, analyzing, and fabricating objects represented as geometric models. Historically, these technologies developed independently, such that their geometric representations are customized to the needs of the technology. As a result, combined use of these technologies has led to differences in data structures, file formats, software constraints, and user knowledge and practice, requiring translation of representations between systems to support interoperability. Complicating this situation is the approximate nature of modeling operations in CAD systems, which can result in gaps at the boundary curves between mating trimmed surfaces of a model. The research presented here is aimed at removing the gaps between trimmed surfaces, resulting in a “watertight” model that is suitable for use directly by downstream applications. A three-step algorithm is presented that includes analysis of the parametric space of the trimming curves, reparameterization to create a global parameter space, and reconstruction of the intersecting surfaces to ensure continuity at the trimming curve.
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Ohbuchi, Masuda, and Aono. "A shape-preserving data embedding algorithm for NURBS curves and surfaces." In Proceedings Computer Graphics International CGI-99. IEEE, 1999. http://dx.doi.org/10.1109/cgi.1999.777952.

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Varanasi, Srinivasa P., and Athamaram H. Soni. "Approximate Degree Reduction of NURBS Curves and Surfaces: An Integrated Approach." In ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/detc1994-0368.

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Abstract Data exchange between different CAD systems usually requires conversion between different representations of free-form curves and surfaces. Also, trimmed surfaces give rise to high degree boundary curves. Accurate conversion of these forms becomes necessary for reliable data transfer. Also important is the issue of shape control, specially in the aircraft industry. The objective of this paper is to investigate conversion methods and effect of shape control on the design and choice of such methods.
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Lu, Chunjin, and Kwun-Lon Ting. "Weight Function Based Direct Manipulation of NURBS Curves." In ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/detc2002/cie-34476.

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Direct shape manipulation allows one to specify constraints on curves or surfaces to modify their shapes. This paper presents a new and simple method of direct manipulation of NURBS curves accomplished through the use of a weight function. Within a marked boundary, the curve can be forced to pass through given discrete points by using a synthesized weight function instead of repositioning control points. By introducing four additional derivative constraints to construct the weight function, exact locality and continuity can be easily obtained without knot insertion. B-spline interpolation is used to generate the weight function in the paper. The algorithms are easy to implement and can be used for interactive shape design systems.
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Elber, Gershon. "On Self Intersections of Freeform Curves and Surfaces." In ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2008. http://dx.doi.org/10.1115/esda2008-59330.

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The computations of curve-curve and surface-surface intersections are considered difficult problems in geometric design. Numerous results were annually published on these topics for the last several decades. Moreover, the detection and more so the computation and even elimination of self-intersections in freeform curves and surfaces is viewed by many as a far more challenging problem, with much fewer satisfactory results. In recent years, several methods were developed to robustly detect, compute and even eliminate self intersections in general freeform (typically NURBs) curves and surfaces, exploiting intrinsic and/or geometric properties, on one side, and the algebraic structure of the shape, on the other. Other methods are specific and employ special properties of the problem in hand, as is the case of offset computation. In this work, we will survey some of our results and others, and provide a birds view of the current state-of-the-art research, on the self-intersections problem, in the freeform domain.
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El-Komy, Mohamed A., and Sayed M. Metwalli. "Optimum 3D Rapping of CAD Models Using Single NURBS." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-36736.

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Non-Uniform Rational B-Splines (NURBS) can represent curves and surfaces of any degree. Usually in the same curve, however, the degree is unique. The goal of this work is to identify single and exact corner point of lines represented by cubic or other NURBS. The combination of arcs and lines can then be represented by one NURBS with error not to exceed (10−12). The developed procedure can represent any NURBS curve and surface of any degree with full control on all parameters, control points, weights, knot vectors, and number of segments representing the curve or surface, in addition to, the basis functions examination. The optimization identifies the parameters and geometry to insure any required level of accuracy to represent singular corner solid models to allow a single cubic or other NURBS representing the whole solid. It is concluded that the singular corner point can be identified with cubic NURBS. Applications to several 3D solid CAD models are used to verify such a technique.
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10

Yang, Jingzhou, Karim Abdel-Malek, and Jim Cremer. "An Approach to Sweeping NURBS." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/dac-21150.

Full text
Abstract:
Abstract This paper presents a method of determining the swept volume of Non-Uniform rational B-Spline (NURBS) curves and surfaces. Characteristic (also called singular) points or curves are determined by obtaining local and global maxima points at discrete frames during the motion and with respect to a local moving coordinate system. This coordinate system is calculated in reference to the direction of motion of the rigid body as determined from its composite velocity vector. The aim is to develop a rigorous method for identifying and visualizing a NURBS swept volume. NURBS have become the industry standard for the representation, design, and data exchange of geometric information processed by computers. On the other hand, sweeping operations are valuable tools for the CAD user to shape and create primitives. In this paper, we extend our previous method used in determining the swept volume of implicit and parametric surfaces and those that are as a result of multiple sweeping. The method and numerical algorithm are illustrated through examples.
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