Before revision:  We show a generalization of this result on Hausdorff distances and middle shapes, and various related properties. We also show that a generalization of such middle shapes implies a morph with a bounded rate of change  .
After revision:  We show that our result can be generalised to give an interpolated shape between A and B for any interpolation variable \alpha between 0 and 1, and prove that the resulting morph has a bounded rate of change .