Russian Federation
A method for obtaining of polyhedral structures when modeling polyhedra using the projective graphic method by changing parameters of a convex polyhedron, taken as a kernel, is proposed in this paper. A process for obtaining a kernel of a tetrahedral symmetry group (tetrahedral 24-hedron) has been considered in detail. The kernel parameters influence on the shape change of corresponding polyhedral structures is analyzed. For this, the parameters V, G, and R are used, which are the lengths of radius vectors drawn from the center of the sphere circumscribed around the initial tetrahedron to the vertices, midpoints of the edges, and the centers of this tetrahedron’s facets. It has been shown that the influence quantity of the kernel shape on the shape of the three-dimensional object’s generated elements depends on the degree of proximity of this generated element to the kernel itself; moreover, this influence is such that the near regions depend on the kernel shape to a lesser extent than the distant ones. As examples, shape-forming solutions based on a tetrahedral 24-hedron have been obtained, which reflect a change in the central regions’ shape, and solutions reflecting a change in the shape of regions distant from the center. In addition, shape-forming solutions based on dihedral symmetry have been also considered. Varying the kernel parameters within certain limits by a developed computer program can serve as a tool for designing such forms of objects that are difficult to formalize in the traditional way. A visual analysis of projective graphic drawings for objects deformed in a certain way in order to obtain acceptable results on three-dimensional objects is carried out. In conclusion, a comparison of the proposed shape-forming method with alternative options for obtaining similar results without using projectography is given. The proposed technique can be used by architects and designers while constructing forms with predetermined properties.
shaping of polyhedral structures, projective-graphic method, kernels of tetrahedral and dihedral symmetry, influence of kernel parameters, variation of kernel parameters as designer’s tool
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