Projecting by conical screw lines with constant step

International Conference on Construction, Architecture and Technosphere Safety 2018

土木建筑工程

Denisova, E.V.^1 ; Voronina, M.V.^2 ; Tretyakova, Z.O.^2

Department of Descriptive Geometry and Engineering Graphics, Saint-Petersburg State University of Architecture and Civil Engineering, 2-ya Krasnoarmeiskaya st. 4, Saint Petersburg

199105, Russia^1

Department of Descriptive Geometry and Graphics, Saint-Petersburg Mining University, 21st Line 2, Saint Petersburg

199106, Russia^2

关键词: Analytical method;    Analytical theory;    Applied surface;    Arbitrary points;    Computer technology;    Methods of researches;    Non-traditional;    Surface requirements;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/451/1/012120/pdf
DOI  :  10.1088/1757-899X/451/1/012120

学科分类：土木及结构工程学

来源: IOP

【 摘 要 】

The relevance of the study: The formation of surfaces by analytical methods and their visualization using computer graphics is one of the topical problems of applied geometry. Purpose of the study is to investigate non-traditional projection systems, to select congruence parameters of conical helical lines that cover the entire complex of surface requirements, obtained by projecting with conic rays an arbitrary flat or spatial line and using computer graphics in visualization of the surface. Methods of research: The general analytical theory of applied surface molding, developed by prof. Skidan I A and a single unit, which is based on the mathematical support of computer technologies for designing and creating objects of complex shape. Results of the research: An example of an analytical interpretation of the image of curvilinear projection by conical screw lines of a constant step and an example of congruence of conical screw lines, located on coaxial cones with a common vertex and a variable angle of inclination of the generator to the axis. The properties are investigated, the parameters of the helical line of the congruence, passing through an arbitrary point of space that does not belong to the axis, are determined. A method is proposed for constructing spiral surfaces, the framework of which consists of rays projecting an arbitrary line.