K. Polke's Theorem in Computer Model Space in 2D Modeling

Abstract

The application of Polke's theorem in the search for a coordinate system for an electronic geometric model in the model space of a computer in 2D geometric modeling is considered. The possibility of creating an electronic geometric model in a system of axonometric axes in 2D modeling for scientific and educational purposes using a coordinate method is shown. It is possible to solve problems on axonometric coordinate planes that do not provide solutions in a rectangular coordinate system. In the computer model space, it has become possible to solve classical problems of descriptive geometry, the solution of which is associated only with the method of projecting space onto the projection plane. Secondary axonometry in the system of axonometric coordinate axes in 2D modeling has allowed us to solve a number of problems that do not have a solution in a rectangular coordinate system: • simulate the parallel (oblique) direction of the correspondence of two related shapes; • move the shape in space by rotating around the axonometric coordinate axes; • the construction of an arbitrary relationship of two affine corresponding figures with mutual perpendicularity of the axis of kinship and the direction of kinship; • switch to the coordinate solution method instead of projecting on the projection plane; • vased on the numerical equality of isometric coordinates with natural ones, it is possible to switch from one coordinate system to another right in the process of solving problems. A new reading of Polke's theorem expands the possibilities of the model space of personal computers for solving scientific and educational problems. However, a necessary condition for the implementation of these capabilities is the availability of isometric constructions by software. The possibility of learning how to create an electronic drawing from a full-scale part in the educational process is shown. In this case, it is advisable to use an isometric image as an electronic model, as it has visibility in a single-picture view and simplicity of drawing in a coordinate way. According to the constructed axonometric view, rectangular views are programmatically obtained using rectangular coordinates. A rectangular electronic drawing is formed from these types. If the purpose of its creation is to build a 3D geometric model of an object, then the construction can be continued, considering the created electronic drawing as the initial conditions for building a 3D model of the object