Second order surfaces in architecture and construction

[摘要] The modern means of computer graphics allow designing a wide variety of architectural forms. An architect's fantasy is not limited by the difficulties of the technical implementation of the project, nor by the materials, nor by the complexity of the design calculations. Of particular interest are the technical problems associated with second-order surfaces (quadrics). Two problems are considered in the paper: the problem of reconstructing a quadric given by nine points, and the problem of joining two quadrics by means of a flat welded seam. To solve these problems, modern computer graphics is used in combination with classical methods of descriptive and projective geometry. The reconstruction task was solved on the basis of the well-known algorithm proposed by German mathematicians Rohn, Papperitz (1896). The algorithm can be practically realized with the help of 3D computer graphics. The problem of a planar compound of quadrics is solved on the basis of Theorem 1 (parabolic cylinders with parallel planes of symmetry intersect along a plane curve) and Theorem 2 (quadrics of rotation with the coincident pair of focal points are in imaginary double contact). The results obtained can be used in construction and architectural design.

[发布机构] Department of Engineering and Computer Graphics, South Ural State University, Lenin Avenue, 76, Chelyabinsk; 454080, Russia^1

[学科分类] 土木及结构工程学

[关键词] 3D computer graphics;Classical methods;Design calculations;Parabolic cylinder;Parallel planes;Planar compounds;Projective geometry;Technical implementation