Kinematical ruled surfaces based on interrelated movements in triads of contacted axoids
Date issued
2016
Journal Title
Journal ISSN
Volume Title
Publisher
Václav Skala - UNION Agency
Abstract
Kinematical ruled surfaces are constructed by generating the line's motion of a moving ruled surface during its
movement along a fixed ruled surface [Spr02a]. The main condition of constructing kinematical ruled surfaces is
that a moving axoid contacts with a fixed axoid along their common generating line in each of their positions
during the movement of one axoid along another. A lot of well-known kinematical ruled surfaces are
constructed on the base of certain pairs of contacted axoids such as “plane – cylinder”, “plane – cone”, “cylinder
– cylinder”, “cone – cone”, etc. [Kri06a]. A new model of constructing kinematical ruled surfaces based on
interrelated movements in the triads of contacted axoids is proposed in this research. Geometrical models,
analytical representations, and computer visualization of the new constructed kinematical surfaces for some
cases of triads of contacted axoids “plane – cylinder – cylinder”, “plane – cone – cone”, “cylinder – cylinder –
cylinder”, “cone – cone – cone” (Fig. 1), and for matched triads of one-sheet hyperboloids of revolution are
developed in this paper. Figures of the triads of contacted axoids and corresponding constructed kinematical
ruled surfaces have been developed with the help of the software application AMG (“ArtMathGraph”)
[Con07a].
Description
Subject(s)
geometrické modelování, počítačová grafika, kinematické povrchy
Citation
WSCG '2016: short communications proceedings: The 24th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision 2016 in co-operation with EUROGRAPHICS: University of West Bohemia, Plzen, Czech RepublicMay 30 - June 3 2016, p. 293-297.