Descriptive Geometry — the Base of Computer Graphics
About: This article is published in Geometry & Graphics.The article was published on 2016-06-18. It has received 32 citations till now. The article focuses on the topics: Descriptive geometry & Computer graphics.
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TL;DR: In technical inventions related to innovative developments, the role of one of the main components belongs to geometry, and in technical inventions the geometrical component is the determining one, this statement is proved by examples developed based on geometry of following inventions.
Abstract: In technical inventions related to innovative developments, the role of one of the main components belongs to geometry. A follow hypothesis has been adopted: in technical inventions the geometrical component is the determining one. This hypothesis applied to technical inventions can be confirmed by any copyright certificate, any patent both in Russia and abroad. In proposed paper this statement is proved by examples developed based on geometry of following inventions. 1. Screen feeder for sticky masses. Screen feeder’s grates are made in pairs, and between grate pairs there are gaps for screening of material’s size-defined fractions. In the screen-feeder has been proposed such geometry of grates that grates of each pair could clean each other, thereby preventing sticking on the surface and destroying the gaps between the pairs, which transforms the usual screen-feeder with cylindrical grates at an ordinary feeder. 2. Double-screw mixer for paste-like masses. The mixer consists of two contiguous worms. Their surfaces are the helical ones, in cross-section consisting of two quarters of circles stacked at the ends. Such cross-section allows homogenize the mixed paste-like material in the best way, and also deliver it under higher pressure in an extrusion head, that improves a final product. 3. Machine for processing of multi-faceted surfaces. This invention serves for manufacture of worms with a cross-section composed of two, three, etc. pieces of circles of the same radius and angle. Worms, made with this machine, are designed for the above mentioned two-screw mixer. 4. Method of mechanical processing. This method is also intended to manufacture of worms for two-screw mixer.
26 citations
19 citations
TL;DR: In this article, the authors considered the issue related to complex training in the area of graphic disciplines for students of technical high educational institutions, and proposed a method to train a general course of descriptive geometry and engineering graphics taking into account the professional orientation and relevant competencies.
Abstract: In connection with transition of the higher education system to the bachelor's degree, a number of difficulties has arisen e in the student’s educational schedule. The question is especially acute for disciplines of general education, and a rather large reduction in classroom time has happened. Taking into account the rather low level of students training in the area of drawing, and sometimes its complete absence, due to the abolition of the subject of drawing from the mandatory school program, teachers are faced with more and more tasks on the formation of educational and methodical complexes [3; 6; 15–17; 23]. In this paper has been considered the issue related to complex training in the area of graphic disciplines for students of technical high educational institutions. These disciplines, as is known, are the basis of many special engineering disciplines, such as machine parts, theory of mechanisms and machines and so on. The fundamental component is the design documentation, the possession of which is necessary for a future engineer. Studying the general course of descriptive geometry and engineering graphics is not enough, training should be carried out taking into account the professional orientation and relevant competencies. However, despite the global automation in all areas, it is not necessary to completely abandon the traditional methods of training, for example, in descriptive geometry’s section. This course allows develop students' spatial reasoning [12–14; 19]. Work on descriptive geometry’s tasks gives for a student the opportunity to more clearly understand the projection principles, methods of drawings transformation, formation of complex surfaces, obtaining of visual images by constructing of axonometric projections or performing of a technical drawing. Another question in our opinion is the order for studying the section of engineering graphics, which is more appropriate to study using modern graphics programs [10; 11].
18 citations
TL;DR: Recommendations have been given for further research in this field, and measures are proposed on changing the learning process aimed at personalizing and building an individual learning trajectory in order to increase the educational process’s efficiency.
Abstract: Engineering practice cannot and will never be successful without spatial imagination and thinking, deep knowledge of geometric methods and ways for solution of engineering problems, comprehensive understanding of specificity and geometric features of technical objects and their images, understanding of labor organization impact on these processes etc. In this paper has been described the social and pedagogical investigation of question related to students’ substantive readiness to study higher educational institution’s graphic disciplines, and this question’s basis is contradiction between requirements to the initial level of students’ knowledge and skills and the level of students’ substantive readiness on the course of school training. In this paper have been performed analysis and generalization of existing pedagogical experience on issues related to graphic training. A method and a scheme for monitoring the degree of students’ competence on the school geometry course using Google forms have been proposed. Selective testing of students by the proposed way has been performed. Statistical processing of data obtained during this testing has been carried out, the density function of correct responses has been built, field of testing results correlation with total score of Unified State Exam (USE) results has been carried out, cluster analysis of obtained results has been performed by Varda method. Using the theory of latent variables and the Rush model an analysis of test tasks, aimed at optimizing the test structure, has been carried out. Based on the performed investigation, recommendations have been given for further research in this field, and measures are proposed on changing the learning process aimed at personalizing and building an individual learning trajectory in order to increase the educational process’s efficiency.
13 citations
TL;DR: In this article, the loci (L) equally spaced from a sphere and a straight line, and from a conic surface and a plane, are considered, and the following options have been considered: the straight line passes through the center of the sphere (a = 0), at the same time completely at spheres' positive radiuses a surface of rotation is obtained, forming which the parabola is, and a rotation axis, this straight line.
Abstract: The loci (L) equally spaced from a sphere and a straight line, and from a conic surface and a plane, are considered. The following options have been considered. The straight line passes through the center of the sphere (a = 0), at the same time completely at spheres’ positive radiuses a surface of rotation is obtained, forming which the parabola is, and a rotation axis – this straight line. The parabola’s top forms the biggest parallel on the site points of intersection of the parabola’s forming with the rotation axis. Let's call such paraboloid a perpendicular paraboloid of rotation. The straight line crosses the sphere, but does not pass through the center (0 < a < R/2) – a perpendicular paraboloid, at that the surface is also completely obtained at radiuses’ positive values. The straight line is tangent to the sphere (a = R/2) – a surface which projections are parabolas, lemniscates and circles, and a piece from a tangency point to the sphere center – at radiuses positive values; a beam from the sphere center, perpendicular to this straight line – at radiuses negative values, at that the beam and the piece belong to one straight line. The straight line lies out of the sphere (α > R/2) – two different surfaces, having the general properties with a hyperbolic paraboloid, are obtained, one of which is obtained at radius positive values, and another one – at radius negative values. It has been noticed that loci, equally spaced from a sphere and a straight line, and from a cylinder and a point, coincide at equal radiuses and distances from axes to points and straight lines if to take into account the surfaces obtained both at positive, and negative values of radiuses. Locus, equally spaced from the conic surface of rotation and the plane, are two elliptic conic surfaces which in case 7.4.1 degenerate in the conic surfaces of rotation. In cases 7.4.3 and 7.4.4 one elliptic conic surface degenerates in a plane and a parabolic cylinder respectively.
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12 citations