scholarly journals ≈ g(1,2)*-CLOSED AND ≈ g(1,2)*-OPEN MAPS

2021 ◽  
pp. 234-240
Author(s):  
R. Vasanthi
Keyword(s):  
Particle Physics ◽  
Computer Aided Design ◽  
Quantum Physics ◽  
Molecular Design ◽  
Vital Role ◽  
Geometric Design ◽  
Digital Topology ◽  
Closed Sets ◽  
Computer Aided ◽  
Aided Design

General topology plays vital role in many fields of applied sciences as well as in all branches of mathematics. In reality it is used in data mining, computational topology for geometric design and molecular design, computer-aided design, computer-aided geometric design, digital topology, information systems, particle physics and quantum physics etc. By researching generalizations of closed sets, some new separation axioms have been founded and they turn out to be useful in the study of digital topology. Therefore, all bi-topological sets and functions defined will have many possibilities of applications in digital topology and computer graphics.

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.

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.

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.

Two Generalizations of the Isometric Projection in Geometric Design

1987 ◽  
Author(s):  
D. J. Wilde
Keyword(s):  
Computer Aided Design ◽  
Three Dimensional ◽  
Geometric Design ◽  
Structural Members ◽  
Rotation Matrices ◽  
Computer Aided ◽  
Drawing Board ◽  
Aided Design

Abstract The well-known pictorial drafting technique of isometric drawing is here generalized in two ways, called “isoclinal” and “axial”, or collectively, “symmetric”. Although the isoclinal projection preserves the useful property of foreshortening adjacent edges equally, and the axial projection foreshortens adjacent edges equally, the directions for these projections usually differ from that for isometric projection. Formulas are derived for the isoclinal and axial directions and their foreshortening factors and rotation matrices. Although intended for three-dimensional computer-aided design, the symmetric projections can also be performed on a drawing board with a protractor. Graphic examples involving design of non-rectangular connectors for three skew structural members and adjacent plates in space are presented.

New Methods of the Computer Aided Design of Roof Skeletons

2016 ◽  
Vol 4 (2) ◽  
pp. 3-7 ◽  
Author(s):  
Козневски ◽  
E. Kozniewski
Keyword(s):  
Information Technology ◽  
Computer Aided Design ◽  
Geometric Design ◽  
Efficient Design ◽  
Orthographic Projection ◽  
Logic Operation ◽  
New Methods ◽  
Computer Aided ◽  
The Times ◽  
Aided Design

The problem of efficient design of roofs is a topical area of research. This is confirmed by scientific studies [1–5, etс.]. Today, in the times of information technology in all areas of actively using the computer and specific programs [6; 12; 15, etc.]. The author presents a proposal of geometric design (geometric solutions) for roofs with restrictions, so-called "roof with its neighbors."Roofs are treated as a special class of polyhedral surfaces. Construction includes a corresponding attachment roof with restrictions on the roof on a simple connection of the polygon, designing a conventional roof and perform the appropriate logic operation. Fig. 1. The Boolean operations are useful tools in geometrical designing of roof skeletons. Solving roofs with neighbors is much easier if we bring them to solve simple roofs over simpleconnected polygon base. The difficulty comes to the design of an appropriate polygonal base. This method essentially involves applying geometric design of a regular roof to design a roof with constraints, which can be relatively easily performed with a CAD program [13]. The elements of a roof: a) a roof with its elements in the orthographic projection, b) the roof with its elements in a military axonometry, c) the line of disappearing ridges of the roof in the orthographic projection [9].

Application of computer-aided design in the Ontario Domed Stadium project

1988 ◽  
Vol 15 (1) ◽  
pp. 14-23 ◽  
Author(s):  
C. Michael Allen ◽  
Donald Duchesne ◽  
Jagmohan Humar
Keyword(s):  
Computer Graphics ◽  
Design Process ◽  
Computer Aided Design ◽  
Civil Engineering ◽  
Vital Role ◽  
Data Generation ◽  
Structure Generation ◽  
Roof Structure ◽  
Computer Aided ◽  
Aided Design

Application of computer-aided design (CAD) in civil engineering is most effective when the entire design process, from design and analysis to construction, is integrated. Owing to the complexity of civil engineering projects, complete integration of design has not been achieved as yet. However, even partial integration considerably improves the reliability and efficiency of the design process. This is illustrated in the paper through a case study on the application of CAD in the structural design of the Ontario Domed Stadium. The Ontario Domed Stadium, currently being constructed on a site near the Toronto harbour, will have a seating capacity of 55 000. A unique feature of the stadium is its fully retractable roof. The proposed roof has four separate steel space truss panels, three of which move along tracks and one of which is fixed. To handle the large volume of data involved in the design and analysis of the roof structure, generation of data files containing information on the geometry and topology of the roof structure was automated as much as possible. Special interfaces were developed to transfer this data to application programs for structural analysis, design, and production of working drawings. Computer graphics played a vital role in the design process, assisting in data generation, visual check of geometry and deflected shapes, and seating layout. Key words: computer-aided design, CAD, computer graphics, Ontario Domed Stadium, sight line studies, solids modelling.

Support Engineering Computer-Aided Design Systems and BIM Template

2014 ◽  
Vol 971-973 ◽  
pp. 1906-1911
Author(s):  
Y. Peng ◽  
L. Zheng ◽  
B.S. Ruan
Keyword(s):  
Computer Aided Design ◽  
Architectural Design ◽  
Design Method ◽  
Three Dimensional ◽  
Building Design ◽  
Vital Role ◽  
Computer Aided ◽  
New Thinking ◽  
Support Engineering ◽  
Aided Design

In computer-aided design meteoric rise in the field of architectural design , computers have become an important tool for architects work. The use of computers has changed a lot of work methods. Updated key architectural design methods, using new thinking tools by updating to assist architectural design ideas that can help us find new ways to architectural creation. We know that there is a convenient three-dimensional computer modeling, easy to modify and intuitive physical display. The concept of the future whether to play a vital role in the concept of the method, and eventually will change and affect the building design and construction. By using computer-aided design and design examples to make computer-aided design method building construction design process , the use of further explanation.

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.

Sign in / Sign up

Export Citation Format

Share Document