Amorphous computing is a recently introduced paradigm that favours geometrical configurations. The physical layout of an amorphous computer is based on a large number of simple processing components that are well-suited for handling spatial structures. It has come to our attention that the discipline of computational geometry could benefit from this approach and it seemed natural to refer to it by the notion of amorphous geometry. Although at this stage our exploration of this concept is fairly modest, we feel that our experiments are sufficiently convincing and merit further study. We are confident that amorphous geometry can deal with various classes of problems while providing a basis for useful applications.