A Quadratic Trigonometric Nu Spline with Shape Control

2017 ◽  
Vol 17 (03) ◽  
pp. 1750015 ◽  
Author(s):  
Muhammad Sarfraz ◽  
Shamaila Samreen ◽  
Malik Zawwar Hussain
Keyword(s):  
Computer Aided Design ◽  
Geometric Modeling ◽  
Shape Control ◽  
Partition Of Unity ◽  
Control Points ◽  
Geometric Continuity ◽  
Spline Method ◽  
Shape Effects ◽  
Curve Modeling ◽  
Aided Design

A significant curve modeling technique has been introduced with a view to its applications in geometric modeling, computer graphics and computer-aided design. It is a new spline method using quadratic trigonometric functions with well-controlled shape influences of parameters introduced through geometric continuity of order two. The proposed curve model owns the best possible geometric properties such as convex hull, partition of unity, affine invariance and variation diminishing. A quadratic normally has three control points giving lesser flexibility to one piece of curve. However, a cubic has four control points giving higher flexibility to one piece of curve. In the proposed scheme, we have introduced a quadratic trigonometric with four control points. Thus, the proposed quadratic trigonometric has embedded geometric features of cubic/cubic trigonometric. The proposed spline method, constrained with Nu spline like GC2 smoothness, produces a quadratic trigonometric Nu spline (QTNS) with interesting shape control locally and globally. The method is helpful for a variety of shape effects, like point tension, interval tension or global tension. It also produces a quadratic trigonometric alternative to cubic/cubic trigonometric spline because of having four control points in its piecewise description.

scholarly journals Advances in Engineering Graphics: Improvements and New Proposals

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 827
Author(s):  
José Ignacio Rojas-Sola
Keyword(s):  
Computer Animation ◽  
Computer Aided Design ◽  
Geometric Modeling ◽  
Correct Interpretation ◽  
Special Issue ◽  
Engineering Graphics ◽  
Communication Techniques ◽  
Graphic Communication ◽  
Graphic Language ◽  
Aided Design

The study of graphic communication techniques that engineers, architects, and designers use to express ideas and concepts, or the graphic expression applied to the design process, is becoming increasingly important. The correct interpretation of graphic language allows the development of skills in the training of an engineer or architect. For this reason, research on this topic is especially valuable in finding improvements or new proposals that help toward a better understanding of those techniques. This Special Issue shows the reader some examples of different disciplines available, such as engineering graphics, industrial design, geometric modeling, computer-aided design, descriptive geometry, architectural graphics and computer animation.

scholarly journals Explicit Continuity Conditions for G1 Connection of S-λ Curves and Surfaces

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1359 ◽  
Author(s):  
Gang Hu ◽  
Huinan Li ◽  
Muhammad Abbas ◽  
Kenjiro T. Miura ◽  
Guoling Wei
Keyword(s):  
Computer Aided Design ◽  
Linear Independence ◽  
Basis Functions ◽  
Geometric Continuity ◽  
Complex Curves ◽  
Curves And Surfaces ◽  
Computer Aided ◽  
Cad Cam ◽  
Geometric Representations ◽  
Aided Design

The S-λ model is one of the most useful tools for shape designs and geometric representations in computer-aided geometric design (CAGD), which is due to its good geometric properties such as symmetry, shape adjustable property. With the aim to solve the problem that complex S-λ curves and surfaces cannot be constructed by a single curve and surface, the explicit continuity conditions for G1 connection of S-λ curves and surfaces are investigated in this paper. On the basis of linear independence and terminal properties of S-λ basis functions, the conditions of G1 geometric continuity between two adjacent S-λ curves and surfaces are proposed, respectively. Modeling examples imply that the continuity conditions proposed in this paper are easy and effective, which indicate that the S-λ curves and surfaces can be used as a powerful supplement of complex curves and surfaces design in computer aided design/computer aided manufacturing (CAD/CAM) system.

Filling N-Sided Holes With Trimmed B-Spline Surfaces Based on Energy-Minimization Method

2015 ◽  
Vol 15 (1) ◽  
Author(s):  
Xiaodong Liu
Keyword(s):  
Energy Minimization ◽  
Computer Aided Design ◽  
Control Points ◽  
Minimization Method ◽  
B Spline ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Key Issues ◽  
Complex Constraints ◽  
Aided Design

Using a trimmed rectangular B-Spline surface to fill an n-sided hole is a much desired operation in computer aided design (CAD), but few papers have addressed this issue. Based on an energy-minimization or variational B-Spline technique, the paper presents the technique of using one single trimmed rectangular B-Spline surface to fill an n-sided hole. The method is efficient and robust, and takes a fraction of a second to fill n-sided holes with high-quality waterproof B-Spline surfaces under complex constraints. As the foundation of filling n-sided holes, the paper also presents the framework and addresses the key issues on variational B-Spline technique. Without any precalculation, the variational B-Spline technique discussed in this paper can solve virtually any B-Spline surface with up to 20,000 control points in real time, which is much more efficient and powerful than previous work in the variational B-Spline field. Moreover, the result is accurate and satisfies CAD systems' high-precision requirements.

Computer-Aided Modeling and Manufacturing of Spherical Mechanisms via a Novel Web Tool

2007 ◽  
Vol 7 (4) ◽  
pp. 339-346 ◽  
Author(s):  
J. Schuler ◽  
J. Ketchel ◽  
P. Larochelle
Keyword(s):  
Dynamic Simulation ◽  
Computer Aided Design ◽  
Geometric Modeling ◽  
Three Dimensional ◽  
Software Tool ◽  
Web Based ◽  
Spherical Mechanisms ◽  
Computer Aided ◽  
Manufacturing Software ◽  
Aided Design

In this paper, we present a novel web-based computer-aided modeling and manufacturing software tool for spherical mechanisms. Our purpose is to facilitate the analysis, dynamic simulation, and manufacture of one degree of freedom spherical four-bar mechanisms. First, a brief review of some of the current computer-aided design software for spherical four-bar mechanisms is presented. These software packages provide the three-dimensional visualization and computational capabilities necessary to synthesize and analyze spherical four-bar mechanisms. However, to date, no readily available and effective tools exist to aid in the modeling and manufacture of spherical mechanisms. Next, the kinematics of spherical four-bar mechanisms are reviewed as they pertain to their geometric modeling and manufacture. Finally, we present our web-based implementation of a computer-aided modeling, simulation, and manufacturing methodology for spherical four-bar mechanisms called SFBDESIGNER (for spherical four-bar designer). SFBDESIGNER facilitates the design, dynamic simulation, prototyping, and manufacture of spherical four-bar mechanisms.

A New Developed Interface for CAD/MCNP Data Conversion

2006 ◽  
Author(s):  
Noha Shaaban ◽  
Fukuzo Masuda ◽  
Hesham Nasif ◽  
Masao Yamada ◽  
Hidenori Sawamura ◽  
...  
Keyword(s):  
Computer Aided Design ◽  
Geometric Modeling ◽  
Input Data ◽  
Fusion Reactor ◽  
Computer Code ◽  
Data Conversion ◽  
Input File ◽  
Cell Geometry ◽  
Cad System ◽  
Aided Design

In a complex and huge system as in ITER fusion reactor, the creation of the geometrical input data of Monte Carlo (MC) codes such as MCNP is a highly exhausting task. Accordingly, it is a general approach to shift the geometric modeling into a computer aided design (CAD) system and to use an interface, which performs the exchange of CAD data into a representation appropriate for MC code. We have developed efficient algorithms and computer code, which are used to convert Parasolid format CAD files including solid and void data into MCNP input data. The CAD-MCNP conversion processes include creating surface equations; determining surface senses; constructing cell geometry and creating MCNP input file. This paper describes the basic algorithms used for the CAD/MCNP interface along with some applications for different geometries.

scholarly journals Geodetic Determining of Stockpile Volume of Mineral Excavated in Open Pit Mine/ Geodetické Určenie Objemu Vyťažiteľných Zásob Nerastu V Povrchovom Lome

2013 ◽  
Vol 59 (1) ◽  
pp. 30-40 ◽  
Author(s):  
Slavomír Labant ◽  
Hana Staňková ◽  
Roland Weiss
Keyword(s):  
Spatial Data ◽  
Computer Aided Design ◽  
3D Modelling ◽  
Open Pit Mine ◽  
Open Pit ◽  
Mountain Range ◽  
Control Points ◽  
Design Software ◽  
Aided Design ◽  
Geodetic Surveying

Abstract In the contemporary geodetic practice it is practically a must to use modern geodetic apparatuses and a variety of the CAD (Computer Aided Design) software for processing and visualising spatial data. The present paper deals with geodetic surveying of Kecerovce open pit mine to determine, for the purpose of mine reopening and commencing with mining of andesite, the volume of non-extracted volumes of andesite. The open pit mine is situated on the foot of Slanské vrchy mountain range. Determining of the auxiliary survey control points and the quarry vicinity was performed by GNSS technology and RTK method. Detailed surveying of the open pit mine was performed through an electronic total station. By measurements attained spatial data were processed by pertinent proprietary software. Subsequently, the determined spatial coordinated were imported into the graphiccalculating softwares for further processing and visualisation. These graphical-calculating applications make possible not only 3D modelling and visualising of surfaces but also their analysing, especially then determining the volumetric data that represent various aspects necessary to assess as activities within the related branches so possible future development.

scholarly journals Methods of geometric modeling and computer graphics based on the WorldSkills Occupational Standards “Engineering CAD Software”

2021 ◽  
pp. 1-12
Author(s):  
Elena Sergeevna Reshetnikova ◽  
Irina Aleksandrovna Savelyeva ◽  
Ekaterina Anatolyevna Svistunova
Keyword(s):  
Computer Aided Design ◽  
Geometric Modeling ◽  
Educational Process ◽  
Professional Activity ◽  
Distinct Advantage ◽  
Successful Implementation ◽  
Highly Qualified ◽  
Modern Computer ◽  
Occupational Standards ◽  
Aided Design

This article examines the questions of preparation of students of technical specialties in the higher educational institutions based on the WorldSkills Occupational Standards “Engineering CAD Software”. The relevance of implementation of 3D modeling standards in modern computer-aided design systems into the educational process is substantiated by the need in preparation of highly qualified internationally recognized specialists in different industry fields. The author analyzed competitive tasks of the WorldSkills championships, as well as assesses the importance of graphic training for the development of competences of a modern specialist, who use CAD in their professional activity. The article examines the methodology of geometric-graphic preparation of students of the specialty 15.05.01 Design of Technological Machines and Complexes, specialization in the Design of Metallurgical Machines and Complexes, implemented in the Magnitogorsk State Technical University. A distinct advantage of this methodology is the use of various CAD software and development of the skills for manual sketching of details of mechanical engineering within the framework of studying engineering graphics. The results are acquired of successful implementation of competitive tasks of the Worldskills championships in the educational process. The author concludes that the use of the developed methodology in educational process allowed improving the efficiency of preparation of students.

scholarly journals Approximation of Generalized Ovals and Lemniscates towards Geometric Modeling

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3325
Author(s):  
Valery Ochkov ◽  
Inna Vasileva ◽  
Ekaterina Borovinskaya ◽  
Wladimir Reschetilowski
Keyword(s):  
Computer Aided Design ◽  
Geometric Modeling ◽  
Three Dimensional ◽  
Numerical Data ◽  
Closed Curves ◽  
B Splines ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling ◽  
High Smoothness ◽  
Aided Design

This paper considers an approach towards the building of new classes of symmetric closed curves with two or more focal points, which can be obtained by generalizing classical definitions of the ellipse, Cassini, and Cayley ovals. A universal numerical method for creating such curves in mathematical packages is introduced. Specific aspects of the provided numerical data in computer-aided design systems with B-splines for three-dimensional modeling are considered. The applicability of the method is demonstrated, as well as the possibility to provide high smoothness of the curvature profile at the specified accuracy of modeling.

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