No abstract

No abstract

No 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.

Considering various ways of shaping, the paper analyzes and geometrically interprets the space-planning and process requirements posed to the frame of the designed architectural surface. It considers the issues of designingshells formed by various ways of extracting a frame from a set of lines. Astructural kinematic method is used as the main one, which allows us to depict a surface and show the points and lines belonging to it. The surface frame is extracted from a set of algebraic curved lines. Straight lines and second-order curves are more preferable. We proposed to use a focal second-order surface toextracta linear surface frame. Straight lines tangent to the second-order surface form a three-parameter set of straight lines (a complex of straight lines).To extract a one-parameter ruled surface from a three-parameter complex of straight lines, we proposed to use additional curvilinear guides allowing us to control the shape of the surface. The structural kinematic method allows us to design smooth architectural shells based on an arbitrary spatial contour. We considered examples of building smooth composite surfaces passing through a given contour and including a given compartment of a second-order focal surface. We proposed a design of a transitional ruled surface connecting the roof and dome of a church building. The working drawing of the transitional surface evolvent is made on the basis of the descriptive geometry methods. The surface frame is built using three-dimensional computer graphical means. An expedient combination of computer graphics and theoretical methods of descriptive geometry allows us to obtain surfaces meeting the preset geometric conditions.