scholarly journals Pembinaan lengkungan peralihan berbentuk C yang memuaskan Data Interpolasi Hermite G2

2020 ◽  
Vol 8 (2) ◽  
pp. 39-50
Author(s):  
Azhar Ahmad
Keyword(s):  
Computer Aided Design ◽  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
B Splines ◽  
Computer Aided ◽  
Aided Design

Makalah ini membincangkan satu kaedah pembinaan lengkungan peralihan berbentuk C yang memenuhi syarat-syarat data interpolasi Hermite Lengkungan peralihan ini dibina berasaskan gabungan dua pilin kuadratik nisbah Bezier atau gabungan bersama satu segmen garis lurus bagi mencapai keselanjaran pada keseluruhan binaan. Kaedah analisis geometri bersama syarat kemonotonan suatu lengkungan kuadratik nisbah Bezier telah digunakan bagi mencapai objektif kajian. Hasil kajian yang dicapai adalah satu teknik pembinaan yang membolehkan kita memperolehi lengkungan peralihan secara terus, mudah diaplikasikan serta tanpa perlu menggunakan sebarang prosedur tranformasi affin. Syarat untuk lengkungan peralihan ini terhasil ditentukan oleh data Hermite yang diberi dan kepelbagaiannya pula dikawal oleh panjang segmen garis lurus yang menghubungkan kedua-dua pilin berkenaan. Keupayaan memenuhi sifat-sifat interpolasi ini memberi banyak kelebihan dan amat sesuai untuk aplikasi tertentu di dalam CAGD (Computer Aided Geometric Design), umpamanya rekabentuk produk industri, trajektori robot non-holonomic, serta rekabentuk mendatar landasan keretapi dan lebuhraya. Oleh kerana kuadratik nisbah Bezier merupakan sebahagian daripada perwakilan NURBS (Nonuniform Rational B-splines) maka adalah mudah bagi kita mengabungjalinkan formulasi lengkungan peralihan yang dicadangkan ini ke dalam kebanyakan sistem pengaturcara CAD (Computer Aided Design).

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.

Computer Aided Geometric Design of Two-Parameter Freeform Motions

1998 ◽  
Author(s):  
Q. J. Ge ◽  
M. Sirchia
Keyword(s):  
Computer Aided Design ◽  
Control Structure ◽  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
Computer Aided ◽  
Cad Cam ◽  
Rational Bézier Surface ◽  
Aided Design ◽  
Two Parameter ◽  
And Robotics

Abstract 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 Bézier 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 Bézier 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.

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.

Polygon-to-Object Boundary Clipping in Object Space for Hidden Surface Removal in Computer-Aided Design

1995 ◽  
Vol 117 (3) ◽  
pp. 374-389 ◽  
Author(s):  
Wei-Hua Chieng ◽  
D. A. Hoeltzel
Keyword(s):  
Computer Aided Design ◽  
Geometric Design ◽  
Design System ◽  
Boundary Contour ◽  
Object Boundary ◽  
Computer Aided Geometric Design ◽  
Object Space ◽  
Computer Aided ◽  
Hidden Surface Removal ◽  
Surface Removal

Since techniques for both polygon-to-polygon clipping and polygon-to-object boundary (contour) clipping have been developed, it appears that the visibility problem may exhibit potential for improvement in its time complexity. This paper provides some insight and results concerning the performance of an object-space hidden surface removal algorithm based on polygon-to-object boundary (contour) clipping. The applicability of these results to the graphic rendering of partially visible objects in an incremental computer-aided geometric design system, such as that used in mechanical design, is demonstrated. The polygon-to-object boundary clipping algorithm is compared with the more conventional polygon-to-polygon approach to clipping for hidden surface removal. Examples are included which demonstrate the potential for improving the performance of software-based hidden surface removal algorithms used in computer-aided geometric design applications.

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.

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