Relevant bibliographies by topics / Computer-aided design. Computer graphics. Spline theory

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

Academic literature on the topic 'Computer-aided design. Computer graphics. Spline theory'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 February 2022

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Journal articles on the topic "Computer-aided design. Computer graphics. Spline theory"

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Ju¨ttler, B., and M. G. Wagner. "Computer-Aided Design With Spatial Rational B-Spline Motions." Journal of Mechanical Design 118, no. 2 (1996): 193–201. http://dx.doi.org/10.1115/1.2826869.

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Using rational motions it is possible to apply many fundamental B-spline techniques to the design of motions. The present paper summarizes the basic theory of rational motions and introduces a linear control structure for piecewise rational motions suitable for geometry processing. Moreover it provides algorithms for the calculation of the surface which is swept out by a moving polyhedron and examines interpolation techniques. The methods presented in this paper can be applied to various problems in computer animation as well as in robotics.
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Ravani, B., and J. W. Wang. "Computer Aided Geometric Design of Line Constructs." Journal of Mechanical Design 113, no. 4 (1991): 363–71. http://dx.doi.org/10.1115/1.2912791.

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This paper develops a mathematical foundation for Computer Aided Design (CAD) of sculptured shapes based on line geometry. First, a new representation is presented for a line based on Plu¨cker coordinates that would allow specification of a line segment (rather than an infinite line) in an elegant manner and suitable for computational purposes. Then, methods are presented for geometric design of shape patches (here referred to as line constructs) by interpolating or approximating a set of control lines (rather than control points) using ruled surfaces, line congruences, and line complexes. The methods presented are general and allow utilization of different basis functions such as Be´zier, Cardinal, and B-spline bases. As Computer Aided Manufacturing (CAM) application of the theory, methods are developed for generation of offsets of ruled surfaces useful in Numerical Control (NC) milling and tool motion generation in the Wire Cut Electric Discharge Machining (EDM) operation.
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Ge, Q. Jeffrey, and P. M. Larochelle. "Algebraic Motion Approximation With NURBS Motions and Its Application to Spherical Mechanism Synthesis." Journal of Mechanical Design 121, no. 4 (1999): 529–32. http://dx.doi.org/10.1115/1.2829493.

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In this work we bring together classical mechanism theory with recent works in the area of Computer Aided Geometric Design (CAGD) of rational motions as well as curve approximation techniques in CAGD to study the problem of mechanism motion approximation from a computational geometric viewpoint. We present a framework for approximating algebraic motions of spherical mechanisms with rational B-Spline spherical motions. Algebraic spherical motions and rational B-spline spherical motions are represented as algebraic curves and rational B-Spline curves in the space of quaternions (or the image space). Thus the problem of motion approximation is transformed into a curve approximation problem, where concepts and techniques in the field of Computer Aided Geometric Design and Computational Geometry may be applied. An example is included at the end to show how a NURBS motion can be used for synthesizing spherical four-bar linkages.
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Bodduluri, R. M. C., and B. Ravani. "Geometric Design and Fabrication of Developable Bezier and B-spline Surfaces." Journal of Mechanical Design 116, no. 4 (1994): 1042–48. http://dx.doi.org/10.1115/1.2919485.

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In this paper we study Computer Aided Geometric Design (CAGD) and Manufacturing (CAM) of developable surfaces. We develop a direct representation of developable surfaces in terms of plane geometry. It uses control planes to determine a surface which is a Bezier or a B-spline interpolation of the control planes. In the Bezier case, a de Casteljau type construction method is presented for geometric design of developable Bezier surfaces. In the B-spline case, de Boor type construction for the geometric design of the developable surface and Boehm type knot insertion algorithm are presented. In the area of manufacturing or fabrication of developable surfaces, we present simple methods for both development of a surface into a plane and bending of a flat plane into a desired developable surface. The approach presented uses plane and line geometries and eliminates the need for solving differential equations of Riccatti type used in previous methods. The results are illustrated using an example generated by a CAD/CAM system implemented based on the theory presented.
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WALTON, D. J. "Spiral Spline Curves for Highway Design." Computer-Aided Civil and Infrastructure Engineering 4, no. 2 (2008): 99–106. http://dx.doi.org/10.1111/j.1467-8667.1989.tb00012.x.

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Moroni, Giovanni, and Marco Rasella. "Application of Regression Spline to Reverse Modeling." Journal of Computing and Information Science in Engineering 7, no. 1 (2006): 95–101. http://dx.doi.org/10.1115/1.2424245.

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When dealing with inspection or reverse modeling, the problem of free-form curves and surfaces reconstruction has to be faced starting from a set of measured points. Because in point sampling the acquisition error is unavoidable, curves and surfaces fitting should be based on a rigorous diagnostic phase. We consider statistical regression analysis in which, treating error as a variable of the problem, we distinguish between the systematic behavior of measured points and noise in the reconstruction of curves and surfaces. The model we introduce for a regression based free-form reconstruction is the so-called regression spline. It is a well known model in the literature, with a consolidated theory and applications in fields such as chemical, econometric, and biomedical. Our purpose is to discuss the application of this powerful and flexible approach in a reverse modeling environment.
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Cotrina-Navau, J., N. Pla-Garcia, and M. Vigo-Anglada. "A Generic Approach to Free Form Surface Generation." Journal of Computing and Information Science in Engineering 2, no. 4 (2002): 294–301. http://dx.doi.org/10.1115/1.1559579.

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A theoretical approach to construct free form surfaces is presented. We develop the concepts that arise when a free form surface is generated by tracing a mesh, using differentiable manifold theory, and generalizing the B-spline scheme. This approach allows us to define a family of practical schemes. Four different applications of the generic approach are also presented in this paper.
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Wang, Yan. "Weighted Rational Quartic Spline Interpolation." Journal of Information and Computational Science 10, no. 9 (2013): 2651–58. http://dx.doi.org/10.12733/jics20101820.

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Hsieh, Chiu-Fan, and Yii-Wen Hwang. "Study on the High-Sealing of Roots Rotor With Variable Trochoid Ratio." Journal of Mechanical Design 129, no. 12 (2006): 1278–84. http://dx.doi.org/10.1115/1.2779897.

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Vacuum pump plays an important role in the vacuum system. In this paper, a new method is proposed to design the Roots rotor that was the trochoidal curve with variable trochoid ratio. The fifth-order polynomial and cubic spline functions are used to generate smoothly trochoid ratio functions and thus a regular addendum curve for Roots rotor will be generated. Based on the addendum curve, the tooth profile for the complete Roots rotor is derived by the gearing theory. In order to improve the sealing between the rotor tip and the chamber, a design procedure is also developed for roots rotor with high sealing and high area efficiency. In addition, the undercutting equation is used to study the constraints of design parameters and the center of curvature is used to check the occurrence of the carryover on the tooth profile. Finally, some design examples are presented to show the feasibility of the proposed method.
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McClarty, D. V. B., D. G. Fredlund, and S. L. Barbour. "Use of Spline Interpolation in Slope Stability Analysis." Computer-Aided Civil and Infrastructure Engineering 8, no. 6 (2008): 439–52. http://dx.doi.org/10.1111/j.1467-8667.1993.tb00228.x.

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Dissertations / Theses on the topic "Computer-aided design. Computer graphics. Spline theory"

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Cardon, David L. "T-Spline Simplification." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1813.pdf.

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Ipson, Heather. "T-spline Merging." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd804.pdf.

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Myles, Ashish. "Linear programming approach to fitting splines through 3D channels." [Gainesville, Fla.] : University of Florida, 2004. http://purl.fcla.edu/fcla/etd/UFE0006260.

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Finnigan, Gordon Thomas. "Arbitrary Degree T-Splines." Diss., CLICK HERE for online access, 2008. http://contentdm.lib.byu.edu/ETD/image/etd2453.pdf.

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Freitas, Lucas Batista. "Modelagem geológica por simplóides de Bézier." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/275754.

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Orientador: Stolfi Jorge, Martin Tygel<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Computação<br>Made available in DSpace on 2018-08-18T10:11:18Z (GMT). No. of bitstreams: 1 Freitas_LucasBatista_D.pdf: 3567527 bytes, checksum: d7c6af3cd4ddab0e7eacc837ade4b106 (MD5) Previous issue date: 2010<br>Resumo: A exploração e monitoramento de um reservatório de petróleo ou gás natural exige conhecimento bastante detalhado das estruturas geológicas da região de interesse. A representação matemática e computacional desse conhecimento é um modelo geofísico. Nesta tese descrevemos um sistema geral para modelagem geofísica baseado em elementos finitos polinomiais de graus arbitrários. Adotamos uma abordagem comum na indústria, em que a geometria e as propriedades das formações geológicas são representadas por funções definidas por partes, ou splines, que consistem da justaposição de tais elementos. Neste contexto, apresentamos contribuições teóricas e computacionais. A principal contribuição teórica é uma teoria unificada dos elementos simploidais de Bézier, que incluem os tipos de elementos finitos mais comuns na modelagem por malhas - tais como arcos de Bézier, retalhos de Bézier triangulares e retangulares, blocos de Bézier tetraédricos, prismáticos e hexaédricos, e suas generalizações para dimensões arbitrárias, com graus independentes em cada eixo e cada componente. Como parte testa teoria, desenvolvemos fórmulas genéricas explícitas para conversão entre estes vários tipos de blocos, bem como diferenciação, reparametrização afim e elevação de grau. As contribuições computacionais desta tese incluem a implementação dessa teoria na forma de uma biblioteca (BezEl) que permite a representação e manipulação eficiente de malhas de elementos de Bézier simplodais com dimensões e graus arbitrários. Outra contribuição original desta tese é uma metodologia para realizar o traçado eficiente de raios em malhas de elementos simploidais<br>Abstract: The exploration and monitoring of a hydrocarbon reservoir demand a very detailed knowledge about the geological structures of the target area. The mathematical and computation representation of this knowledge is a geophysical model. In this thesis, we describe a general system for geophysical modeling based on polynomial finite elements of arbitrary degree. We adopted an approach that is popular in industry, whereby both the geometry and the physical properties of the geological formations are represented by piecewise-defined functions, or splines, that are obtained by the assembly of many such elements. In this context, we present both theoretical and computational contributions. The main theoretical contribution is a unified theory of simploidal Bézier elements, which include the element types most common in mesh based modeling - such as Bézier arcs, triangular and rectangular Bézier patches, tetrahedral, prismatic and hexahedral Bézier blocks, and their generalizations to arbitrary dimensions with independent degrees on each axis and each component. As part of this theory, we developed general explicit formulas for the conversion between these various block types, as well as differentiation, affine reparametrization and degree raising. The computational contributions of this thesis include the implementation of this theory as a library (BezEl) that allows efficient representation and manipulation of meshes of simploidal Bézier elements with arbitrary dimension and degree. Another original contribution of this thesis is a methodology for performing efficient ray tracing in meshes of such simploidal elements<br>Doutorado<br>Computação Grafica<br>Doutor em Ciência da Computação
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Loop, Charles Teorell. "Generalized B-spline surfaces of arbitrary topological type /." Thesis, Connect to this title online; UW restricted, 1992. http://hdl.handle.net/1773/6888.

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Tjung, Jie Wen. "Projection, design, and representation of curves on B-spline surfaces /." This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-03042009-040805/.

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Tjung, Jie Wen. "Projection, design, and representation of curves on B-spline surfaces." Thesis, Virginia Tech, 1992. http://hdl.handle.net/10919/41412.

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Tang, Chi-Ming. "B-spline surface techniques for solid modeling : an application to computer-aided geometric design /." Online version of thesis, 1988. http://hdl.handle.net/1850/10216.

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Magoon, Jason. "Application of the B-spline collocation method to a geometrically non-linear beam problem /." Online version of thesis, 2010. http://hdl.handle.net/1850/11587.

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Books on the topic "Computer-aided design. Computer graphics. Spline theory"

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1928-, Boehm Wolfgang, and Paluszny Marco 1950-, eds. Bézier and B-spline techniques. Springer, 2002.

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Bartels, Richard H. An introduction to splines for use in computer graphics and geometric modeling. M. Kaufmann Publishers, 1987.

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1942-, Tiller Wayne, ed. The NURBS book. 2nd ed. Springer, 1997.

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Piegl, Les A. The NURBS book. Springer, 1995.

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Prautzsch, Hartmut. Bézier and B-Spline Techniques. Springer Berlin Heidelberg, 2002.

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Thalmann, Nadia Magnenat. Computer Animation: Theory and Practice. Springer Japan, 1990.

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Magnenat-Thalmann, Nadia. Image Synthesis: Theory and Practice. Springer Japan, 1987.

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E, Farin Gerald, ed. NURBS: From projective geometry to practical use. 2nd ed. A.K. Peters, 1999.

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

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Stra€er, Wolfgang. Theory and Practice of Geometric Modeling. Springer Berlin Heidelberg, 1989.

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Conference papers on the topic "Computer-aided design. Computer graphics. Spline theory"

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Zhang, Ting, Xingce Wang, Qianqian Jiang, Zhongke Wu, Mingquan Zhou, and Hock Soon Seah. "G2-Continuity Extension Algorithm for Disk B-Spline Curve." In 2013 International Conference on Computer-Aided Design and Computer Graphics (CAD/Graphics). IEEE, 2013. http://dx.doi.org/10.1109/cadgraphics.2013.73.

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Jiang, Qianqian, Zhongke Wu, Ting Zhang, Xingce Wang, Mingquan Zhou, and Hock Soon Seah. "G2-Continuity Blending of Ball B-Spline Curve Using Extension." In 2013 International Conference on Computer-Aided Design and Computer Graphics (CAD/Graphics). IEEE, 2013. http://dx.doi.org/10.1109/cadgraphics.2013.54.

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Wu, Xiaoqun, Yiyu Cai, and Jianmin Zheng. "TV-L1 Optimization for B-Spline Surface Reconstruction with Sharp Features." In 2013 International Conference on Computer-Aided Design and Computer Graphics (CAD/Graphics). IEEE, 2013. http://dx.doi.org/10.1109/cadgraphics.2013.13.

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Changqi Hu and Zhouwang Yang. "A fitting approach with dynamic algebraic spline curves." In Proceedings. Ninth International Conference on Computer Aided Design and Computer Graphics. IEEE, 2005. http://dx.doi.org/10.1109/cad-cg.2005.3.

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Zhang, Sen, Zhigang Li, Hui Zhang, and Junhai Yong. "Multi-resolution Mesh Fitting by B-spline Surfaces for Reverse Engineering." In 2011 12th International Conference on Computer-Aided Design and Computer Graphics (CAD/Graphics). IEEE, 2011. http://dx.doi.org/10.1109/cad/graphics.2011.65.

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Wu, Xiaoqin, Xuli Han, and Shanmin Luo. "Quadratic Trigonometric Spline Curves with Multiple Shape Parameters." In 2007 10th IEEE International Conference on Computer-Aided Design and Computer Graphics. IEEE, 2007. http://dx.doi.org/10.1109/cadcg.2007.4407918.

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Yang, Huaiping, and Bert Juttler. "3D Shape Metamorphosis Based on T-spline Level Sets." In 2007 10th IEEE International Conference on Computer-Aided Design and Computer Graphics. IEEE, 2007. http://dx.doi.org/10.1109/cadcg.2007.4407834.

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Wu, Zhongke, Hock Soon Seah, and Mingquan Zhou. "Skeleton Based Parametric Solid Models: Ball B-Spline Surfaces." In 2007 10th IEEE International Conference on Computer-Aided Design and Computer Graphics. IEEE, 2007. http://dx.doi.org/10.1109/cadcg.2007.4407854.

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Wang, Qiang, and Jieqing Tan. "Multi-Focus Image Fusion Algorithm Based on Rational Spline." In 2007 10th IEEE International Conference on Computer-Aided Design and Computer Graphics. IEEE, 2007. http://dx.doi.org/10.1109/cadcg.2007.4407885.

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Wu, Zhongke, Hock Soon Seah, and Mingquan Zhou. "Skeleton Based Parametric Solid Models: Ball B-Spline Curves." In 2007 10th IEEE International Conference on Computer-Aided Design and Computer Graphics. IEEE, 2007. http://dx.doi.org/10.1109/cadcg.2007.4407920.

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