Metamorphosis

Animation:

Metamorphosis (shape transformation, morphing) between two functionally represented objects can be described by the interpolation between their defining functions. Such interpolation procedure defines a homotopy map in n+1-dimensional space. This makes possible metamorphosis between a blobby object and a constructive solid (frames shown above).

A picture shown above illustrates metamorphosis between four “key objects” normally modeled in different representational styles, but unified by F-rep here:

CSG solid
Swept spiral
Volumetric teapot
Blobby object

More details and a program code for this example can be found in the paper:

Pasko A.A., Adzhiev V.D., Sourin A.I., Savchenko V.V. “Function representation in geometric modeling: concepts, implementation and applications”, The Visual Computer, vol.11, No.8, 1995, pp.429-446. Electronic version: PostScript (467K) and PostScript + gzip (112K)