An introduction to splines for use in computer graphics & geometric modeling

1992 ◽  
Vol 9 (3) ◽  
pp. 278
Author(s):  
J.J.S.P. Cabral
Author(s):  
Denis Voloshinov ◽  
K. Solomonov ◽  
Lyudmila Mokretsova ◽  
Lyudmila Tishchuk

The application of constructive geometric modeling to pedagogical models of teaching graphic disciplines today is a promising direction for using computer technology in the educational process of educational institutions. The essence of the method of constructive geometric modeling is to represent any operation performed on geometric objects in the form of a transformation, as a result of which some constructive connection is established, and the transformation itself can be considered as a result of the action of an abstract cybernetic device. Constructive geometric modeling is a popular information tool for information processing in various applied areas, however, this tool cannot be appreciated without the presence of appropriate software systems and developed design techniques. Traditionally, constructive geometric modeling is used in the design of mechanical engineering, energy, aircraft and shipbuilding facilities, in architectural and design engineering. The need to study descriptive geometry at the university in recent years has something in common with the issues of mastering graphic packages of computer programs in the framework of the new discipline "Engineering and Computer Graphics". The well-known KOMPAS software product is considered the simplest and most attractive for training. It should be noted the important role of graphic packages in the teaching of geometric disciplines that require a figurative perception of the material by students. Against the background of a reduction in classroom hours, computer graphics packages are practically the only productive teaching methodology, successfully replacing traditional tools - chalk and blackboard.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mehwish Bari ◽  
Ghulam Mustafa ◽  
Abdul Ghaffar ◽  
Kottakkaran Sooppy Nisar ◽  
Dumitru Baleanu

AbstractSubdivision schemes (SSs) have been the heart of computer-aided geometric design almost from its origin, and several unifications of SSs have been established. SSs are commonly used in computer graphics, and several ways were discovered to connect smooth curves/surfaces generated by SSs to applied geometry. To construct the link between nonstationary SSs and applied geometry, in this paper, we unify the interpolating nonstationary subdivision scheme (INSS) with a tension control parameter, which is considered as a generalization of 4-point binary nonstationary SSs. The proposed scheme produces a limit surface having $C^{1}$ C 1 smoothness. It generates circular images, spirals, or parts of conics, which are important requirements for practical applications in computer graphics and geometric modeling. We also establish the rules for arbitrary topology for extraordinary vertices (valence ≥3). The well-known subdivision Kobbelt scheme (Kobbelt in Comput. Graph. Forum 15(3):409–420, 1996) is a particular case. We can visualize the performance of the unified scheme by taking different values of the tension parameter. It provides an exact reproduction of parametric surfaces and is used in the processing of free-form surfaces in engineering.


2021 ◽  
Author(s):  
Fuhua Cheng ◽  
Lee Johnson ◽  
Anastasia Kazadi ◽  
Ethan Toney ◽  
Jonathan Watson ◽  
...  

2020 ◽  
pp. short28-1-short28-8
Author(s):  
Vitaly Karabchevsky

Computer technologies of graphic education of students studying programming and information technologies are considered. Particular attention is paid to the joint use of descriptive geometry methods and three-dimensional geometric modeling tools in the creation and study of models of geometric shapes. A basic set of competencies has been identified, allowing to solve the main types of computer graphics tasks, methods for achieving these competencies are considered.


2018 ◽  
Vol 193 ◽  
pp. 03022
Author(s):  
Dmitry V. Nesnov

Field theory is widely represented in spherical and cylindrical coordinate systems, since the mathematical apparatus of these coordinate systems has been thoroughly studied. Sources of field with more complex structures require new approaches to their study. The purpose of this research is to adapt the field theory referred to curvilinear coordinates and represent it in normal toroidal coordinates. Another purpose is to develop the foundations of geometric modeling with the use of computer graphics for visualizing the level surfaces. The dependence of normal toroidal coordinates on rectangular Cartesian coordinates and Lame coefficients is shown in this scientific paper. Differential characteristics of scalar and vector fields in normal toroidal coordinates are obtained: scalar and vector field laplacians, divergence, and rotation of vector field. The example shows the technique of modeling the field and its further computer visualization. The technique of reading the internal equation of the surface is presented and the influence of the values of the parameters on the shape of the surface is shown. For the first time, expressions of scalar and vector field characteristics in normal toroidal coordinates are obtained, the fundamentals of geometric modeling of fields with the use of computer graphics tools are developed for the purpose of providing visibility for their study.


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