Constructing shells and their visualization in system "MathCad" on basis of vector equations of surfaces

7th International Symposium Actual Problems of Computational Simulation in Civil Engineering

土木建筑工程;计算机科学

Ivanov, V.N.^1

Department of Architecture and Construction, Engineering Academy Peoples' Friendship University of Russia, Russia Miclukho-Maklaya str. 6, Moscow

117198, Russia^1

关键词: Cartesian systems;    English languages;    Modern architectures;    Program visualization;    Scalar equations;    Spatial construction;    Surface formation;    Vector functions;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/456/1/012018/pdf
DOI  :  10.1088/1757-899X/456/1/012018

来源: IOP

【 摘 要 】

One of the tasks of modern architecture and building is creation of new forms of civil and sport buildings. In world practice it is possible to see the examples of original forms of sport, exhibition, trade and other types of constructions. For creating new complex forms of spatial constructions it is necessary to have equations of middle surfaces of these constructive forms. Certainly, there are many sources of classic literature and articles on geometry of the surfaces including sources in Internet. "Encyclopedia of analytical surfaces" was published in 2012, Encyclopedia was published in English language in 2016. 35 classes of surfaces, more than 500 types of surfaces, are described in Encyclopedia. On the basis of the types of surfaces given at the encyclopedias it is possible to form various spatial forms. For the same time it is desirable to have a possibility to create other forms of surfaces. In 2016 the monograph was published. At the monographs vector equation of surfaces with the system of flat coordinate curves is given. Even knowing the law of surface formation, having its equation, it is not always possible to present the type of surface on all areas of change of coordinates at the certain values of parameters of surface. It is therefore important to use program facilities for constructing and visualizing compartments of surfaces. Presently there are many programmatic complexes, allowing reproducing the drafts of constructions, space graphic and surface. One of such complexes is a complex "MathCad". In this complex it is necessary to use equations of surfaces in the projections of the Cartesian system of coordinates. But the most comfortable form of equations of surfaces of complex forms are vector equations. Scalar self-reactance equations of complex surfaces usually are very bulky. It is difficult to set the method of formation of surfaces on scalar equations of surfaces of complex form. Vector equations are made with introduction of special additional vector-functions that shows the method of motion a formative curve. Methodology of development of program visualization of surfaces is shown in a complex "MathCad" with the use of vector equation.