J4  2013, Vol. 47 Issue (7): 1246-1252    DOI: 10.3785/j.issn.1008-973X.2013.07.017
Designing  developable surface pencil through  given curve as its common asymptotic curve
LIU Yu, WANG Guo-jin
Institute of Computer Images and Graphics, Zhejiang University, Hangzhou 310027, China

Abstract

Both the general and rational developable surface pencils through an arbitrary parametric curve as its common asymptotic curve were analyzed. By employing the parametric representation of a developable surface pencil taking a given curve as its asymptotic curve, the expression for the case that the pencil is developed was presented and the type of the designed developable surface was discussed. The rational Bézier form of the developable surface pencil through a given Bézier curve as its asymptotic curve was given. Programming examples for the general and rational developable surfaces through a circular helix, conical helix or Bézier curve as its asymptotic curve were illustrated to verify the correctness and effectivity of the algorithm．

Published: 01 July 2013
 CLC: TP 391
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