A new surface model based on a fibre bundle of 1-parameter groups

Abstract

In this paper, a new fibre bundle surface model is proposed for 3D object modeling. This fibre bundle model, consisting of local direct product of a base curve and a fibre curve, is able to represent arbitrary surfaces. In particular, the fibre bundle of 1-parameter groups, i.e. with fibres as 1-parameter groups are efficient in both synthesis and recognition. Indeed, the 1-parameter groups can be uniquely determined by six invariants of their Lie algebras. Besides the surfaces can be fastly generated by elementary function without numerical integration error. This model is also expected to be useful in object-based 3D image coding.