Using Topological Transformations to Construct the Intercepting Lines

What is it about?

The use of topological transformations in solving the problems of descriptive geometry is that these transformations carry out the non-uniform deformation of space, enabling one to map the non-closed curve on the line and the closed curve on the circumference. The problem is solved with the participation of projections of deformed figures, and then the result is returned to the original projection. For practical use of topical transformations, it is necessary to establish the graphically represented compatibility for each corresponding point of the transformed and initial spaces. The following positional problems are solved in the paper: (1) Any frontal contour surface having same or similarly located elliptical intersections and the triangular prism are represented. Construct their intercepting line; (2) Any frontal contour surface having identical or similarly located elliptical intersections and the horizontally projected plane are represented. Construct their intercepting line; (3) The elliptic paraboloid and frontally projected cylinder are represented. Construct their intercepting line. The results of the paper can be used to solve technical and constructive problems.

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