We describe a method for generating arbitrary sweep objects, where the object being swept may be a 2D contour or a 3D object. The path taken by the object as it is swept can include arbitrary affine transformations, for example stretching and rotating. Thus we can produce effects such as tapering and twisting with ease. The method described composites the object being swept into a volume model at a number of points along its defined path. The points at which the object is composited are determined adaptively.