Geometric Modeling of Construction Communications with Specified Dynamic Properties

Abstract

Abstract. Among many construction communications the pipelines designed for the organized supply or removal of liquid or loose working bodies are distinguished for their functional purpose. Such communications should have dynamic properties which allow one to reduce losses on friction and vortex formation. From the point of view of geometric modeling, the given dynamic properties of the projected communication mean the required degree of smoothness of its center line. To model the axial line (flat or spatial), it is proposed to use composite curve lines consisting of the curve arcs of the second order or from their quadratic images. The advantage of the proposed method is that the designer gets the model of a given curve not as a set of coordinates of its points but in the form of a matrix of coefficients of the canonical equations for each arc.

Study of the problem on constructing quadrics at the assigned tangent cones

“…In addition, a number of authors created an application to the system AutoCAD, which, on a purely constructive basis, makes it possible to perform the construction of conics under any conditions: actual, non-proper, imaginary and their combinations, and to solve complex geometric problems. This approach is presented in papers [11,12].…”