Dual space drawing methods for cones

Abstract

Ruled surface design and its applications are widely used in CAGD (Computer Aid Geometric Design) and industrial areas. In this paper, the cone is a particular ruled surface, which is drawn by using the dual methods based on the cylindrical shape [Ding 2003] with its same base curve. The underlying principle is the conversion from cylinders to cones by application of the dual displacement methods [Sprott and Ravani 1997]. Based on the dual methods, a comprehensive study is carried out for the creation of cones. The translation, which satisfies the condition of dual methods, from cylinders which have been created by using the dual De Casteljau algorithm [Ding 2003] to cones is investigated. During the process, a new theorem, the tangential interpolation line theorem is unveiled. This discovery lays the foundation for the conversion from cylinders to cones. The new methods are put forward to draw different cones, which have been successfully implemented by computer simulation.