The dual drawing method of the hyperbolic paraboloid and the screen representation of the ruling

Ruled surface design and its applications are widely used in CAGD(Computer Aid Geometric Design) and industrial areas. In this paper, the hyperbolic paraboloid is a particular ruled surface, which is drawn by using the dual De Casteljau algorithm [15]. The characteristics of the hyperbolic paraboloid are analysed in order to match the requirement of the dual De Casteljau algorithm. A new method for the screen representation of the ruling is introduced. The new method presents the ruling as a clipped line segment on the screen in order to show the proportion of the ruled surface on the screen. The two new methods represent the universal approach to draw ruled surfaces by a combination of the theoretical and practical aspects of dual methods.Rena Ding and Yan Zhan