Most 3D animation packages use graphical representations called motion graphs to represent the variation in time of the motion parameters. Many use two-dimensional B-splines as animation curves because of their power to represent free-form curves. In this project, we investigate the possibility of using One-dimensional Non-Uniform Rational B-Spline (NURBS) curves for the interactive construction of animation control curves. One-dimensional NURBS curves present the potential of solving some problems encountered in motion graphs when two-dimensional B-splines are used. The study focuses on the properties of One-dimensional NURBS mathematical model. It also investigates the algorithms and shape modification tools devised for two-dimensional curves and their port to the One-dimensional NURBS model. It also looks at the issues related to the user interface used to interactively modify the shape of the curves.