Computer graphics of kinematic surfaces

Abstract

This work deals with some problems of constructing and graphical displaying for a class of kinematic surfaces generated by mutual moving ruled surfaces touching one another along their common ruling in each position [1,2]. Exactly, we are dealing with the surfaces generated by movement of a cone fixed ruling during combined movement of the cone with respect to a torse surface [2]. The movement is defined as a cone rotating with simultaneous movement of the cone vortex along the torse edge-of-regression so that both surfaces, the torse and the cone, touch one another along the common ruling [3-5]. The methods and program modules developed allow using a wide range of curves as a torse edge-of-regression and a cone guiding line. Since the program modules are implemented using some numerical methods the application of a new-type curve is reduced to define the curve within the program module. This computer implementation includes cylindrical circular and elliptical helixes, and lines based on circular and elliptical helixes as the edge-of-regression, and circle and ellipse curves as the cone guiding line. Surfaces obtained are displayed on a screen in a ‘frame’ (Fig. 1) or ‘solid’ (Fig. 2) style in any user-selected projection.