Surface as an Object of Computer Geometric Modelling

AbstractThe geometric model of a surface is formed taking into consideration the set of functional, structural, technological, economic, and aesthetic requirements. These requirements are formulated in terms of geometry and are expressed through the surface parameters. The surface is modeled with the help of either the kinematic method or the two-dimensional interpolation method. In accordance with the kinematic method, the surface is formed as a continuous one-parameter set of curves which forms the simulated surface. The kinematic method studied in the article is based on the curves of the second order with variable eccentricity. In order to control the shape of the constructed surface, directing ruled surfaces are used. The authors develop a computer program which determines the eccentricity of the forming curves depending on the boundary conditions. The program allows plotting a curve of the second order assigned by the arbitrary set of five coplanar points and tangents. When modeling a surface passing through a close circuit, this circuit is mapped in four-dimensional space. The abovementioned mapping gives a larger control over the shape of the surface. It is shown that the kinematic method of computer surface modeling has more technological advantages compared to the interpolation method