BUILDING MODELS OF DYNAMIC CANAL SURFACES VIA GEOMETRY CONSTRUCTIONS LANGUAGE

Abstract

Building computer models of dynamic canal surfaces is a special case when implemented in CAD-systems since existing methods of surface modeling of such type are concentrated mostly on obtaining analytical expressions such as equations for the surface itself or its sections. The article introduces a constructive method of building models based on plane and spatial geometric constructions. The paper provides the analysis of given surface parameters, constructive algorithms for setting up a geometric correspondence between the graph of the cross-sectional area and the directrix, constructing of cross-section for the given point on the cross-section area graph as well as placement the cross-sections in three dimensions and determining spatial coordinates of the points on the surface. This allows to build a structured point cloud of a dynamic canal surface of required density and build a model of it in CAD-systems. Suggested constructive algorithms are applied with the help of GC language commands. The paper provides fragments of construction subroutines as well as examples of created models of dynamic canal surfaces. The approach proposed provides for automation of building models of surfaces in CAD-systems, moreover it is flexible to adjust according to the given parameters such as a directrix shape, cross-section area graph, a cross-section shape, etc.