A description and analysis of an interpolatory cubic spline curve is made for use in Computer Aided Geometric Design (CAGD). The cubic pieces are stitched together with a generalized continuity: the parameters in the description of this continuity provide a variety of shape control. This geometric cubic spline provides not only a computationally simple alternative to the exponential based spline under tension [Cline 74, Preuss'76, Schweikert' 66] and the rational spline methods [Gregory and Sarfraz' 90, Sarfraz' 92] but also recovers the well known existing GC2 or C1 methods like cubic v-spline of Nielson [Nielson' 86], y-splines of Boehm [Bohem' 85] and weighted v-splines [Foley' 87].