Abstract
A fibre bundle model of shapes is proposed to describe a surface as a local direct product of a base curve and a fibre curve. With fibre curves as 1-parameter groups, this model is efficient in both synthesis and recognition. In fact, the 1-parameter groups can be uniquely determined by finite, e.g. six invariants of their Lie algebras. Besides the surfaces can be fastly generated by elementary function without numerical integration error. This model is then extended to fibres defined by high order ODE.