Representation of Developable Surfaces and Achievement of the Algorithm

2006 ◽  
Vol 532-533 ◽  
pp. 813-816
Author(s):  
Min Zhou ◽  
Zheng Lin Ye ◽  
Guo Hua Peng ◽  
Yun Qing Yang ◽  
Hong Chan Zheng
Keyword(s):  
Efficient Method ◽  
Computer Aided Design ◽  
Control Parameter ◽  
Geometric Design ◽  
B Spline ◽  
Developable Surfaces ◽  
Computer Aided ◽  
Aided Design ◽  
Traditional Approaches

In order to overcome the difficulties in representation of developable surfaces utilizing traditional approaches, and resolve the problems in adjusting and controlling the position and shape of developable surfaces that often faced in Engineering. In this paper, we propose a directly explicit and efficient method of computer-aided design for developable surfaces based on triangle-B spline. The shapes of developable surfaces can be adjusted using a control parameter. Meanwhile, we show that the techniques for the geometric design of developable surfaces in this paper have all the characteristics of existing approaches for curves design. The algorithms are explained in detail, and demonstrated with the examples in the paper.

Computer Aided Geometric Design of Two-Parameter Freeform Motions

1999 ◽  
Vol 121 (4) ◽  
pp. 502-506 ◽  
Author(s):  
Q. J. Ge ◽  
M. Sirchia
Keyword(s):  
Computer Aided Design ◽  
Control Structure ◽  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
Kinematic Control ◽  
Computer Aided ◽  
Cad Cam ◽  
Aided Design ◽  
Two Parameter ◽  
And Robotics

This paper brings together the notion of analytically defined two-parameter motion in Theoretical Kinematics and the notion of freeform surfaces in Computer Aided Geometric Design (CAGD) to develop methods for computer aided design of two-parameter freeform motions. In particular, a rational Be´zier representation for two-parameter freeform motions is developed. It has been shown that the trajectory surface of such a motion is a tensor-product rational Be´zier surface and that such a kinematically generated surface has a geometric as well as a kinematic control structure. The results have not only theoretical interest in CAGD and kinematics but also applications in CAD/CAM and Robotics.

An approach for designing a developable and minimal ruled surfaces using the curvature theory

2020 ◽  
Vol 18 (01) ◽  
pp. 2150015
Author(s):  
Fatma Güler
Keyword(s):  
Computer Graphics ◽  
Computer Aided Design ◽  
Research Topic ◽  
Ruled Surfaces ◽  
Developable Surfaces ◽  
Computer Aided ◽  
Curvature Theory ◽  
Active Research ◽  
Aided Design

Developable surfaces are defined to be locally isometric to a plane. These surfaces can be formed by bending thin flat sheets of material, which makes them an active research topic in computer graphics, computer aided design, computational origami and manufacturing architecture. We obtain condition for developable and minimal ruled surfaces using rotation frame. Also, the validity of the theorems is illustrated with examples.

scholarly journals Computer-Aided Sketching: Incorporating the Locus to Improve the Three-Dimensional Geometric Design

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1181 ◽  
Author(s):  
José Ignacio Rojas-Sola ◽  
David Hernández-Díaz ◽  
Ricardo Villar-Ribera ◽  
Vicente Hernández-Abad ◽  
Francisco Hernández-Abad
Keyword(s):  
Computational Geometry ◽  
Computer Aided Design ◽  
Three Dimensional ◽  
Geometric Design ◽  
Curved Surfaces ◽  
Two Dimensional ◽  
Technical Design ◽  
Computer Aided ◽  
Aided Design

This article presents evidence of the convenience of implementing the geometric places of the plane into commercial computer-aided design (CAD) software as auxiliary tools in the computer-aided sketching process. Additionally, the research considers the possibility of adding several intuitive spatial geometric places to improve the efficiency of the three-dimensional geometric design. For demonstrative purposes, four examples are presented. A two-dimensional figure positioned on the flat face of an object shows the significant improvement over tools currently available in commercial CAD software, both vector and parametric: it is more intuitive and does not require the designer to execute as many operations. Two more complex three-dimensional examples are presented to show how the use of spatial geometric places, implemented as CAD software functions, would be an effective and highly intuitive tool. Using these functions produces auxiliary curved surfaces with points whose notable features are a significant innovation. A final example provided solves a geometric place problem using own software designed for this purpose. The proposal to incorporate geometric places into CAD software would lead to a significant improvement in the field of computational geometry. Consequently, the incorporation of geometric places into CAD software could increase technical-design productivity by eliminating some intermediate operations, such as symmetry, among others, and improving the geometry training of less skilled users.

Computer Aided Geometric Design of Line Constructs

1991 ◽  
Vol 113 (4) ◽  
pp. 363-371 ◽  
Author(s):  
B. Ravani ◽  
J. W. Wang
Keyword(s):  
Computer Aided Design ◽  
Geometric Design ◽  
Numerical Control ◽  
Ruled Surfaces ◽  
Motion Generation ◽  
Computer Aided ◽  
Nc Milling ◽  
On Line ◽  
Tool Motion ◽  
Aided Design

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.

Newer Theory and More Robust Algorithms for Computer-Aided Design of Developable Surfaces

2005 ◽  
Vol 42 (03) ◽  
pp. 71-79
Author(s):  
B. Konesky
Keyword(s):  
Computer Aided Design ◽  
Developable Surface ◽  
Robust Algorithms ◽  
Developable Surfaces ◽  
Space Curves ◽  
Surface Areas ◽  
C Programming ◽  
Computer Aided ◽  
Reliable Solution ◽  
Aided Design

The use of developable surfaces in design is of engineering importance because of the relative ease with which they can be manufactured. The problem of how to make surfaces developable is not new. The usual technique is by using two space curves, defining the edges of the surface. These are first created, and then a set of rulings are constructed between the space curves under the constraint of being developable. A problem with existing algorithms for designing developable surfaces is the tendency to include nondevelopable portions of the surface: areas of regression. A more reliable solution to the problem of creating a developable surface is presented. The key to the method is to define the developable surface in terms of a normal directrix. The shape of the normal directrix defines the resulting developable surface. Algorithms are defined to compute the shape of a normal directrix from a pair of space curves. Intersecting adjacent developable surfaces and generating the flat plate layouts were also accomplished. This paper presents research and development that started around 1987. The algorithms were implemented using ANSI C++ programming language and commercial computer-aided design and manufacturing (CAD and CAM) software programs.

Computer Aided Geometric Design of Line Constructs

1990 ◽  
Author(s):  
B. Ravani ◽  
J. W. Wang
Keyword(s):  
Computer Aided Design ◽  
Geometric Design ◽  
Numerical Control ◽  
Ruled Surfaces ◽  
Motion Generation ◽  
Computer Aided ◽  
Nc Milling ◽  
On Line ◽  
Tool Motion ◽  
Aided Design

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 complexes. The methods presented are general and allow utilization of different basis functions such as Bézier, 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.

Geometric Issues in Computer Aided Design/Computer Aided Engineering Integration

2011 ◽  
Vol 11 (2) ◽  
Author(s):  
Vadim Shapiro ◽  
Igor Tsukanov ◽  
Alex Grishin
Keyword(s):  
Computer Aided Design ◽  
Computer Aided Engineering ◽  
Geometric Design ◽  
Engineering Analysis ◽  
Engineering Applications ◽  
Fully Integrated ◽  
Computer Aided ◽  
Geometric Representations ◽  
Engineering Integration ◽  
Aided Design

The long-standing goal of computer aided design (CAD)/computer aided engineering (CAE) integration demands seamless interfaces between geometric design and engineering analysis/simulation tasks. The key challenge to this integration stems from the distinct and often incompatible roles geometric representations play, respectively, in design and analysis. This paper critically examines and compares known mesh-based and meshfree approaches to CAD/CAE integration, focusing on the basic tasks and components required for building fully integrated engineering applications. For each task, we identify the fundamental requirements and challenges and discuss how they may be met by known techniques and proposed solutions.

Review on Non Uniform Rational B-Spline (NURBS): Concept and Optimization

2014 ◽  
Vol 903 ◽  
pp. 338-343
Author(s):  
Ali Munira ◽  
Nur Najmiyah Jaafar ◽  
Abdul Aziz Fazilah ◽  
Z. Nooraizedfiza
Keyword(s):  
Image Processing ◽  
Literature Review ◽  
Computer Aided Design ◽  
B Spline ◽  
B Splines ◽  
Curves And Surfaces ◽  
Geometry Design ◽  
Nurbs Curves ◽  
Computer Aided ◽  
Aided Design

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.

Ideal Compliant Joints and Integration of Computer Aided Design and Analysis

2014 ◽  
Author(s):  
Ashraf M. Hamed ◽  
Paramsothy Jayakumar ◽  
Michael D. Letherwood ◽  
David J. Gorsich ◽  
Antonio M. Recuero ◽  
...  
Keyword(s):  
Computer Aided Design ◽  
Large Scale ◽  
Algebraic Equations ◽  
B Spline ◽  
Constraint Equations ◽  
Compliant Joints ◽  
Linear Algebraic Equations ◽  
Dependent Variables ◽  
Computer Aided ◽  
Aided Design

This paper discusses fundamental issues related to the integration of computer aided design and analysis (I-CAD-A) by introducing a new class of ideal compliant joints that account for the distributed inertia and elasticity. The absolute nodal coordinate formulation (ANCF) degrees of freedom are used in order to capture modes of deformation that cannot be captured using existing formulations. The ideal compliant joints developed can be formulated, for the most part, using linear algebraic equations, allowing for the elimination of the dependent variables at a preprocessing stage, thereby significantly reducing the problem dimension and array storage needed. Furthermore, the constraint equations are automatically satisfied at the position, velocity, and acceleration levels. When using the proposed approach to model large scale chain systems, differences in computational efficiency between the augmented formulation and the recursive methods are eliminated, and the CPU times resulting from the use of the two formulations become similar regardless of the complexity of the system. The elimination of the joint constraint equations and the associated dependent variables also contribute to the solution of a fundamental singularity problem encountered in the analysis of closed loop chains and mechanisms by eliminating the need to repeatedly change the chain or mechanism independent coordinates. It is shown that the concept of the knot multiplicity used in computational geometry methods, such as B-spline and NURBS (Non-Uniform Rational B-Spline), to control the degree of continuity at the breakpoints is not suited for the formulation of many ideal compliant joints. As explained in this paper, this issue is closely related to the inability of B-spline and NURBS to model structural discontinuities. Another contribution of this paper is demonstrating that large deformation ANCF finite elements can be effective, in some MBS application, in solving small deformation problems. This is demonstrated using a heavily constrained tracked vehicle with flexible link chains. Without using the proposed approach, modeling such a complex system with flexible links can be very challenging. The analysis presented in this paper also demonstrates that adding significant model details does not necessarily imply increasing the complexity of the MBS algorithm.

Computer-Aided Design With Spatial Rational B-Spline Motions

1996 ◽  
Vol 118 (2) ◽  
pp. 193-201 ◽  
Author(s):  
B. Ju¨ttler ◽  
M. G. Wagner
Keyword(s):  
Computer Animation ◽  
Computer Aided Design ◽  
Control Structure ◽  
Basic Theory ◽  
Linear Control ◽  
Geometry Processing ◽  
B Spline ◽  
Computer Aided ◽  
Interpolation Techniques ◽  
Aided Design

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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