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

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

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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
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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 spa
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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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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
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Ding, Chensen. "Isogeometric independent coefficients method for fast reanalysis of structural modifications." Engineering Computations 37, no. 4 (2019): 1341–68. http://dx.doi.org/10.1108/ec-03-2019-0121.

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Purpose This paper aims to provide designers/engineers, in engineering structural design and analysis, approaches to freely and accurately modify structures (geometric and/or material), and then quickly provide real-time capability to obtain the numerical solutions of the modified structures (designs). Design/methodology/approach The authors propose an isogeometric independent coefficients (IGA-IC) method for a fast reanalysis of structures with geometric and material modifications. Firstly, the authors seamlessly integrate computer-aided design (CAD) and computer-aided engineering (CAE) by ca
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Abdelmoety, Ahmed K., Taha H. A. Naga, and Youssef F. Rashed. "Isogeometric boundary integral formulation for Reissner’s plate problems." Engineering Computations 37, no. 1 (2019): 21–53. http://dx.doi.org/10.1108/ec-11-2018-0507.

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Purpose This paper aims to develop a new isogeometric boundary element formulation based on non-uniform rational basis splines (NURBS) curves for solving Reissner’s shear-deformable plates. Design/methodology/approach The generalized displacements and tractions along the problem boundary are approximated as NURBS curves having the same rational B-spline basis functions used to describe the geometrical boundary of the problem. The source points positions are determined over the problem boundary by the well-known Greville abscissae definition. The singular integrals are accurately evaluated usin
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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
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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
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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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Dissertations / Theses on the topic "Spline theory. Computer-aided design. Engineering design"

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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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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 descrevemo
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Garcia, Jordan. "DESIGN AND PROCESS OF 3D-PRINTED PARTS USING COMPOSITE THEORY." UKnowledge, 2019. https://uknowledge.uky.edu/me_etds/144.

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3D printing is a revolutionary manufacturing method that allows the productions of engineering parts almost directly from modeling software on a computer. With 3D printing technology, future manufacturing could become vastly efficient. However, it is observed that the procedures used in 3D printing differ substantially among the printers and from those used in conventional manufacturing. In this thesis, the mechanical properties of engineering products fabricated by 3D printing were comprehensively evaluated and then compared with those made by conventional manufacturing. Three open-source 3D
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McCulloch, Thomas L. "Feasible Form Parameter Design of Complex Ship Hull Form Geometry." ScholarWorks@UNO, 2018. https://scholarworks.uno.edu/td/2552.

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This thesis introduces a new methodology for robust form parameter design of complex hull form geometry via constraint programming, automatic differentiation, interval arithmetic, and truncated hierarchical B- splines. To date, there has been no clearly stated methodology for assuring consistency of general (equality and inequality) constraints across an entire geometric form parameter ship hull design space. In contrast, the method to be given here can be used to produce guaranteed narrowing of the design space, such that infeasible portions are eliminated. Furthermore, we can guarantee that
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Ribeiro, Carlos Fernando Morgado. "Development of computational tools for Isogeometric Analysis (IGA)." Master's thesis, Universidade de Aveiro, 2014. http://hdl.handle.net/10773/14421.

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Mestrado em Engenharia Mecânica<br>A few years ago drawings were made in the drawing boards and using pencils on vellum. There were no computers helping the designers in the parts modeling. After designing the object, the design was passed to the analysts. The designers and analysts were in constant communication. Nowadays, the designers used Computer Aided Design (CAD) tools in the parts modeling. For application the analysis at the geometries, initially a mesh to approximate the geometries is generated. After this, on the mesh the Finite Element Method (FEM) was applied. In complex en
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Books on the topic "Spline theory. Computer-aided design. Engineering design"

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

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Gray, C. Thomas. Wave Pipelining: Theory and CMOS Implementation. Springer US, 1994.

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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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Vankka, Jouko. Direct Digital Synthesizers: Theory, Design and Applications. Springer US, 2001.

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Drechsler, Rolf. Binary Decision Diagrams: Theory and Implementation. Springer US, 1998.

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service), SpringerLink (Online, ed. The Language of Design: Theory and Computation. Springer London, 2009.

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Roberto, Moreno-Díaz, Pichler, Franz, Ing., Dr. phil., and Quesada Arencibia Alexis, eds. Computer aided systems theory -- EUROCAST 2005: 10th International Conference on Computer Aided Systems Theory, Las Palmas de Gran Canaria, Spain, February 7-11, 2005 : revised selected papers. Springer, 2005.

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International Workshop on Computer Aided Systems Theory (2nd 1991 Krems an der Donau, Austria). Computer aided systems theory, EUROCAST '91: A selection of papers from the Second International Workshop on Computer Aided Systems Theory, Krems, Austria, April 15-19, 1991 : proceedings. Springer-Verlag, 1992.

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Roberto, Moreno-Díaz, and Pichler Franz 1936-, eds. Computer aided systems theory--EUROCAST 2003: 9th International Workshop on Computer Aided Systems Theory, Las Palmas de Gran Canaria, Spain, February 24-28, 2003 : revised selected papers. Springer-Verlag, 2003.

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Book chapters on the topic "Spline theory. Computer-aided design. Engineering design"

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Pichler, Franz. "CAST-modelling approaches in engineering design." In Computer Aided Systems Theory — EUROCAST '89. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/3-540-52215-8_5.

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Wymore, A. Wayne. "SYNERGY: The design of a systems engineering system, I." In Computer Aided Systems Theory — CAST '94. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/3-540-61478-8_66.

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Zou, Dingxiang. "Blasting Models and Computer-Aided Design for Bench Blasting." In Theory and Technology of Rock Excavation for Civil Engineering. Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-1989-0_12.

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"Computer-Aided Chemical Engineering." In Computer Aided Molecular Design: Theory and Practice. Elsevier, 2003. http://dx.doi.org/10.1016/s1570-7946(13)70754-5.

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Rong, Ben Guang, Andrzej Kraslawski, and Lars Nyström. "Creative design of distillation flowsheets based on theory of solving inventive problems." In Computer Aided Chemical Engineering. Elsevier, 2000. http://dx.doi.org/10.1016/s1570-7946(00)80106-6.

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Ramos, Manuel, Marianne Boix, Didier Aussel, Ludovic Montastruc, and Serge Domenech. "Optimal design of water exchanges in eco-industrial parks through a game theory approach." In Computer Aided Chemical Engineering. Elsevier, 2016. http://dx.doi.org/10.1016/b978-0-444-63428-3.50201-0.

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Elhamraoui, Ahmed, Elhassane Abdelmounim, Hamid Bennis, and Mohamed Latrach. "Printed Antenna for UHF and SHF RFID Applications." In Advances in Computer and Electrical Engineering. IGI Global, 2019. http://dx.doi.org/10.4018/978-1-5225-7539-9.ch009.

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In this chapter, new microstrip antennas for RFID system are presented. The chapter is split into two sections. The first section deals with the design of two dual-band antennas for handheld RFID readers, and the second section is dedicated to antennas for RFID tag. In the first section, the authors describe theory and principle characteristics of microstrip antenna and the fundamentals of multiband behavior. The two proposed antennas are designed to operate in the ISM (industrial, scientific, and medical) band at 2.45 and 5.8 GHz bands. In the second section, the authors present the principles of matching techniques for tag antenna design. Then, they present two examples of tag antenna. The first one is a flexible antenna mounted on paper substrate, and the second one is designed for the identification of metallic object.
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Zhou, Zude, Huaiqing Wang, and Ping Lou. "Intelligent Product Design." In Manufacturing Intelligence for Industrial Engineering. IGI Global, 2010. http://dx.doi.org/10.4018/978-1-60566-864-2.ch010.

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CAD (Computer Aided Design) is almost instead of classical designing method which drawing plan on paper nowadays. With the development of information technology, the traditional CAD technology becomes rather matured and is developing towards a modern direction of being further integrative, intelligent, and collaborative, namely ICAD (Intelligent CAD). ICAD is a complex system consist of multi agents or multi experts to design product. It can simulate expert in this area to help designer accomplish design. ICAD is based on some technology such as artificial intelligence, CAD technique, expert systems technique, modern mechanical design theory and database technique. In this chapter, the reason of ICAD proposing is given firstly, then some research and application is described on the second sector. Thirdly, some theory and technique about ICAD is discussed. Finally, a case study is presented.
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"Computer Aided Simulation of a 4BL Problem With MATHLAB." In Advanced Technology-Assisted Problem Solving in Engineering Education. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-0465-9.ch004.

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In this chapter, the synthesis and analysis of four link bar (4BL) mechanisms problem, which is a well-known classical design problem, is discussed. However, limitations to the classical theory of this problem potentially limit its application to certain real-world problems by virtue of the small number of precision points and unspecified order. A prototype of the problem was designed and simulated for visualizing a four-bar link (4BL – simple movable closed chain linkage) mechanism engineering problem using MATLAB software. The aim is to facilitate the analysis, dynamic simulation of the four-bar mechanisms. First, a brief review of some of the current computer-aided learning software for four-bar mechanisms is presented. These software packages provide two-dimensional visualization and computational capabilities necessary to synthesize and analyze four-bar mechanisms. The chapter also reviews the kinematics of four-bar mechanisms as they pertain to their geometric modelling followed by the design approach of the graphical MATLAB simulation for 4BL mechanisms. A preliminary validation test using pre- and posttest questionnaires and focus group discussion with student participation in using the MATLAB simulation has facilitated in visualizing the engineering concepts of 4BL mechanism at UNITEN.
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Biancolini, Marco Evangelos. "Mesh Morphing and Smoothing by Means of Radial Basis Functions (RBF)." In Handbook of Research on Computational Science and Engineering. IGI Global, 2012. http://dx.doi.org/10.4018/978-1-61350-116-0.ch015.

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Radial Basis Functions (RBF) mesh morphing, its theoretical basis, its numerical implementation, and its use for the solution of industrial problems, mainly in Computer Aided Engineering (CAE), are introduced. RBF theory is presented showing the mathematical framework for a basic RBF fit, its MathCAD implementation, and its usage. The equations required for a 2D case comparing RBF smoothing and pseudosolid smoothing based on Finite Elements Method (FEM) structural solution are given; RBF exhibits excellent performance and produces high quality meshes even for very large deformations. The industrial application of RBF morphing to Computational Fluid Dynamics (CFD) is covered presenting the RBF Morph software, its implementation, and a description of its working principles and performance. Practical examples include: physical problems that use CFD, shape parameterisation strategy, and modelling guidelines for setting-up a well posed RBF problem. Future directions explored are: transient shape evolution, fluid structure interaction modelling, and shape parameterization in multi-physics, multi-objective design optimization.
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Conference papers on the topic "Spline theory. Computer-aided design. Engineering design"

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Ge, Q. Jeffrey, and Pierre M. Larochelle. "Algebraic Motion Approximation With NURBS Motions and its Application to Spherical Mechanism Synthesis." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/mech-5881.

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Abstract 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
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Zhang, Andy S. J. "Teaching Computer Aided Product Design With Aesthetic Considerations." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85531.

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This paper presents a study on how to utilize the computer based 3-dimensional parametric solid modeling software to integrate aesthetics into the lectures of product design related courses of a mechanical engineering curriculum to improve teaching and learning. The study indicates that when aesthetics were properly introduced into the classrooms of product design related courses; it created an environment that stimulated students’ imagination and creativity therefore enhancing their learning experience. When teaching product design courses, instruction tends to be focused on the underlying en
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Daniels, Joel, Elaine Cohen, and David Johnson. "Converting Molecular Meshes Into Smooth Interpolatory Spline Solid Models." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85363.

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The study and understanding of molecules, once the domain of blackboards and stick-and-ball models, has become more and more exclusively linked to the use of computer-aided visualizations. Our project seeks to return the physical facsimile to the biologists, allowing the use of tactile senses while interacting with and manipulating a physical model, thus aiding educational and research endeavors. To increase the effectiveness of such a tool, the model is constructed such that multiple levels of information are viewable within the single physical form, stressing the interaction between the asso
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Flórez Guzmán, Horacio, and Raúl Manzanilla Morillo. "Automatic Unstructured Mesh Generation Around Two-Dimensional Domains Described by B-Spline Curves." 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/cie-21269.

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Abstract A computer code for the generation of unstructured two-dimensional triangular meshes around arbitrary complex geometries has been developed. The code is based on Delaunay triangulation with an automatic point insertion scheme and a smoothing technique. The geometrical definition of the domain to be meshed is prescribed by means of B-spline curves obtained from two approaches of interest in Computer-Aided Geometric Design named inverse design and interpolation problems. The presented scheme is based on an interpolation procedure along a B-spline curve proposed by the author in a recent
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Khan, Maqsood A., and Zezhong C. Chen. "An Effective Approach to Approximating 2-D Free-Form Curve Offsets for B-Spline NC Tool Paths With Offset Error Globally Bounded." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-29150.

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The topic of representing the offset of a 2-D B-spline curve in the same form has been under research for a long time, and it has many industrial applications, especially, in NC tool path generation for pocketing. For B-spline tool paths, it is often required that the tool paths have fewer control points, lower base function degree, and higher geometric accuracy. However, the existing methods often generate the offsets of 2-D free-form curves in the form of B-spline curves with high function degree and many control points. Although these offsets are useful in computer-aided design, they are in
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Aggarwal, A., V. S. Aguilar, C. H. Lee, et al. "Spline Based Microstructural Mapping for Soft Biological Tissues: Application to Aortic Valves." In ASME 2013 Summer Bioengineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/sbc2013-14265.

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Splines are the standard tools in computer aided design for geometric representations and have been recently integrated into the finite element analysis of structures and fluids [1]. As the biomedical engineering is making progress, there is a need for an integrated tool for expanding the geometrical representation to include the microstructural details specific to soft tissue, e.g. fiber alignment, orientation, crimp and stiffness. In this work, a spline-based method is presented for aortic valves which facilitates mapping of the fiber structure from any aortic valve specimen to any other aor
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Yanagisawa, Hideyoshi, and Shuichi Fukuda. "Global Feature Based Interactive Reduct Evolutional Computation for Aesthetic Design." In ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/detc2004-57651.

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In this paper, we verify the enhancement of IREC, which is a computer algorithm for interactive design support system, to support global design features as design attributes. IREC (Interactive Reduct Evolutional Computation) is a method to evolve designs based on users’ personal preferences. The method works through an interaction between the user and a computer system. The computer system with IREC generates design samples consisting of random attributes and the user evaluates and scores each samples depending on his/her psychological preferences. The system estimates the design attributes th
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Chen, Yi-Cheng, Yun-Hao Cheng, Jui-Tang Tseng, and Kun-Ju Hsieh. "Tooth Geometry Design and Two-Dimensional Finite Element Analysis for a Strain Wave Gear With Double-Circular-Arc Profile." 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/detc2019-97594.

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Abstract The mathematical model of a strain wave gear (SWG) composed of a flexspline (FS), an elliptical wave generator (WG), and a circular spline (CS) was developed and the performance was simulated by two-dimensional (2-D) finite element analysis. A rack cutter exhibiting a double-circular-arc normal section was utilized to generate the FS, and the conjugate CS was also developed based on the theory of gearing and enveloping equation. Computer program developed in Visual C++ was completed for the geometry and 2-D mesh generation. The performances as well as the rotational motion of the SWG
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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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Ravani, B., and J. W. Wang. "Computer Aided Geometric Design of Line Constructs." In ASME 1990 Design Technical Conferences. American Society of Mechanical Engineers, 1990. http://dx.doi.org/10.1115/detc1990-0030.

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Abstract 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 Plücker 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 complex
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