Using the above definitions and facts, the convex hull of a Bézier curve is the boundary of the intersection of all the convex sets containing all vertices or the intersection of the half spaces generated by taking three vertices at a time to construct a plane and having all other vertices on one side. The convex hull can also be conceptualized at the shape of a rubber band in 2-D or a sheet in 3-D stretched taut over the polygon vertices . The entire curve is contained within the convex hull of the control points as shown in Fig. 1.3 (b). The convex hull property is useful in intersection problems (see Fig. 1.4), in detection of absence of interference and in providing estimates of the position of the curve through simple and efficiently computable bounds.