Given two or more objects of general topology, intermediate objects are constructed by a distance field metamorphosis. In the presented method the interpolation of the distance field is guided by a warp function controlled by a set of corresponding anchor points. Some rules for defining a smooth least-distorting warp function are given. To reduce the distortion of the intermediate shapes, the warp function is decomposed into a rigid rotational part and an elastic part. The distance field interpolation method is modified so that the interpolation is done in correlation with the warp function. The method provides the animator with a technique that can be used to create a set of models forming a smooth transition between pairs of a given sequence of key frame models. The advantage of the new approach is that it is capable of morphing between objects having a different topological genus where no correspondence between the geometric primitives of the models needs to be established. The desired correspondence is defined by an animator in terms of a relatively small number of anchor points.