This work was submitted in partial fulfillment of the requirements for the degree of doctor of philosophy to the senate of the Technion - Israel Institute of Technology in May 2003. The research thesis was supervised by professor Gershon Elber under auspices of the Applied Mathematics Department. In this work, we examine different aspects of continuous deformations that can be applied to freeform rational curves and surfaces. One very popular type of such deformations is known as metamorphosis or morphing. Morphing is the gradual and continuous transformation of one shape into another. The process is characterized by finding correspondence between the shapes and interpolation between the shapes, and we study both aspects. We aim at defining a completely automatic algorithm that finds a good looking and intuitive metamorphosis sequence.