The Algorithm for Crossing the N-dimensional Hyperquadric with N-1-dimensional Hyperspace

Abstract

In descriptive geometry, the problem of finding a surface curve section with a plane is common. One such surface curve is a quadric. Due to the increased demand for tasks related to quadric, the synthetic modeling method becomes relevant. In recent years, geometric constructions of dimensions of more than three began to be studied more and more often. Multidimensional geometric shapes in multidimensional space are typically constructed using geometric modeling software. However, without additional building automation tools, software does not sufficiently facilitate human labor. The larger the dimension of the constructions, the more cumbersome and time consuming the drawing process becomes. The increasing complexity of constructions requires automation of constructions that can be traditimatized. Geometric constructions made using automation tools make us rethink the process of structural geometric modeling in descriptive geometry. Within the framework of the article, the algorithm for crossing the N-dimensional hyperquadric with N-1-dimensional hyperspace is presented. Special cases of this geometric construction are also considered: intersection of a three- dimensional quadric with a plane and intersection of a four-dimensional hyperquadric with a three-dimensional space. The implementation of the developed algorithm is carried out using the Simplex system and the built-in interpreter of the prolog logical programming language.