Using Parametric Blocks for Construction of Flat Algebraic Curves in AutoCAD by the Example of Cassini Ovals

Designing surfaces of complex shape is in demand in various industries. Forms of such surfaces are flat curves. However, the variety of these curves remains unclaimed by constructors, architects, designers due to the lack of tools for the rapid construction of these curves in modern graphical systems AutoCAD, Inventor, Revit, KOMPAS, etc. The article suggests a convenient and generally available method for constructing any curves defined by mathematical methods in AutoCAD by creating parametric blocks. For example, the lines obtained by the section of the torus by a plane parallel to the axis are chosen (curves of the fourth order are Cassini's ovals). In the process of investigation, the features of fourth-order curves are analyzed as a result of the intersection of the torus by planes parallel to the rotation axis of the torus, the shape dependence of the shape of the curves on the ratio of the parameters. We consider the problem of reconstructing the tonic metric and forming a model of a spatial object along the contours of the obtained sections by the methods of descriptive geometry and using 3-d modeling. On the basis of the obtained curves, surfaces with generators or guides, which are Cassini ovals, are constructed.