Qin, KaihuaiSun, JiaguangWang, Xuefu2014-10-212014-10-2119921467-8659http://dx.doi.org/10.1111/1467-8659.1150285In this paper, a new method is presented for representing conics precisely using NURBS of degree two. The method requires only four control vertices to represent a full circle using the full circumscribing square-based representation, which is less than the number required with the other methods using the square control vertex configuration.9, 10, 13 The paper also derives a new condition for NURBS to represent conics precisely and shows the sufficient and necessary conditions for representation of a circular arc, and gives the definition and the knot vector formulae of a periodic NURBS curve.10.1111/1467-8659.1150285285-291