Geometric Transformations in Engineering Geometry

• Main Authors: I. F. Borovikov, G. S. Ivanov
• Format: Article
• Language: Russian
• Published: MGTU im. N.È. Baumana 2015-01-01
• Series: Nauka i Obrazovanie
• Subjects: the descriptive geometry; engineering geometry; geometrical transformations; modeling of surfaces; interfacing a surface; position and metric tasks
• Online Access: http://technomag.edu.ru/jour/article/view/302

<p>Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.</p><p>The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.</p><p>The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant) straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".</p><p>Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry, raising the level of engineering and geometrical training and, as a consequence, provide quality assurance of training specialists.</p>