Smooth quasi-developable surfaces bounded by smooth curves

Computing a quasi-developable strip surface bounded by design curves finds wide industrial applications. Existing methods compute discrete surfaces composed of developable lines connecting sampling points on input curves which are not adequate for generating smooth quasi-developable surfaces. We propose the first method which is capable of exploring the full solution space of continuous input curves to compute a smooth quasi-developable ruled surface with as large developability as possible. The resulting surface is exactly bounded by the input smooth curves and is guaranteed to have no self-intersections. The main contribution is a variational approach to compute a continuous mapping of parameters of input curves by minimizing a function evaluating surface developability. Moreover, we also present an algorithm to represent a resulting surface as a B-spline surface when input curves are B-spline curves.Comment: 18 page

Analysis and design of developable surfaces for shipbuilding

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1997, and Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1997.Includes bibliographical references (p. 97-99).by Julie Steele Chalfant.M.S

Development of manufacturability constraints for press forming of sheet metal components

http://www.worldcat.org/oclc/2869757

08221 Abstracts Collection -- Geometric Modeling

From May 26 to May 30 2008 the Dagstuhl Seminar 08221 ``Geometric Modeling\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Parametric Spiral And Its Application As Transition Curve

Lengkung Bezier merupakan suatu perwakilan lengkungan yang paling popular digunakan di dalam applikasi Rekabentuk Berbantukan Komputer (RBK) dan Rekabentuk Geometrik Berbantukan Komputer (RGBK). The Bezier curve representation is frequently utilized in computer-aided design (CAD) and computer-aided geometric design (CAGD) applications. The curve is defined geometrically, which means that the parameters have geometric meaning; they are just points in three-dimensional space

Automatic mesh generation

The objective of this thesis project is a study of Pre-Processors and development of an Automatic Mesh Generator for Finite Element Analysis. The Mesh Generator developed in this thesis project can create triangular finite elements from the geometric database of Macintosh Applications. The user is required to give the density parameter to the program for mesh generation. The research is limited to Mesh Generators of planar surfaces. Delauny Triangulation method maximizes the minimum angles of a triangle. Watson\u27s Delauny Triangulation method can mesh only the \u27convex hull\u27 of a set of nodes. This algorithm has been modified to create triangular elements in convex and non-convex surfaces. The surfaces can have holes also. A node generation algorithm to place nodes on and inside a geometry has been developed in this thesis project. The mesh generation is very efficient and flexible. Geometric modeling methods have been studied to understand and integrate the Geometric Modeler with the Finite Element Mesh Generator. Expert Systems can be integrated with Finite Element Analysis. This will make Finite Element Method fully automatic. In this thesis project, Expert Systems in Finite Element Analysis are reviewed. Proposals are made for future approach for the integration of the two fields

A novel design framework for generation and parametric modification of yacht hull surfaces

This paper proposes a new design framework for the parametric design and shape modification of a yacht hull. In this framework, the hull is divided into three regions (entrance, middle and run) and each region is represented separately. In this way, a designer has better design flexibility so that higher design variations of the hull can be achieved. Each region consists of keel line(s), deck line, chine line(s) and station lines that are represented using Bezier curves and these lines are called feature curves. A 3D surface model of a yacht hull is obtained by generating Coons patches using feature curves. Shape operators are also introduced and implemented for the modification of the given hull shape while considering some quality criteria such as hull fairness. Experiments in this study show that a variety of hull shapes can be generated using the proposed design framework with the application of the shape operators

Computer-Aided Development of Shell Plates

Ship hulls and other curved shells, like gas tanks, aircraft bodies, and even clothes and shoes, offer a common difficulty in their manufacturing: it is necessary to produce them from a set of formerly plane elements. These plane elements, the raw materials like plates and fabric pieces, must be curved and assembled together to form the final product. The reverse of the forming process of these curved elements, is the map of the curved surface onto the plane, which is improperly known as development. To develop a surface, in a proper sense, is to unfold it onto the plane without stretching or bulging. This is not possible with all kinds of shapes, such as spherical and saddle surfaces. Some common developable surfaces are the conical and cylindrical ones. To form a non-developable shell requires much more work than to form an equivalent shell of developable shape. This increases the costs, the processing times and the defect content. Nevertheless, the fluid dynamists and the other designers are not always free to use developable shapes in their concepts; therefore, a pragmatic approach to the construction of curved shells has to cope with non-developable surfaces. These subjects are chiefly of an advanced mathematic nature, and the required background is too widely spread in the bibliography. Therefore the necessary mathematical results are compiled and presented in Chapter 2 - The Mathematics of Developable Surfaces, providing for a unified view of the concepts, the symbols and the nomenclature. Since the advent of the digital computer, the increasing availability of computing power enabled new methods for surface development and for developable surface definition. By examining and comparing the methods reported in the literature, CHAPTER 3 - Plate Development and Developable Surfaces provides a broad view of the surface development issues, along with the developability conditions and the technologies for the definition of developable surfaces. Given the absence of developability conditions in some areas of the shell, a number of methodologies are reported which produce a plate map onto the plane. In Chapter 4 - Concept and Implementation of an Algorithm, the concept and the implementation of a new development algorithm is described, analysed and applied to example cases. By geodesicaly mapping the surface onto the plane, this method avoids the implementation difficulties of both non- developable surfaces, and developable surfaces with ruling lines aligned in any direction. Therefore, the slightly non-developable plates, commonly found in actual ship hulls, are easily accommodated by this process, working as a map onto the plane. In Chapter 5 - Industrial Application of the Improper Geodesic Map, the user interface of the method is presented. The method provides information about the surface developability and fairness, which assists the user in the decision to develop or otherwise to take corrective measures, like re-fairing or editing of seams and butts. Results obtained from analytical plates, and comparisons with results from both a 1/10-scale electrostatic development jig, and a commercial software package, validate the method. Other results, obtained from actual ship plates, are also presented, further confirming the good accuracy of the method's developments and its good behaviour when processing non-developable plates. This method is in current use, as part of a shipyard system