Unfolding Groups, II

Abstract

Selection is a profound phenomenon in generativity: In many situations, it is necessary for an agent to be able to select part of an existing structure and perform generative operations with respect to only that part. Examples are as follows: (1) Navigation: It is often the case that a path is defined as progressing from one of the surfaces of a scene, while ignoring other surfaces, which might be moving independently. For example, a path might be defined with respect to a wall but not an opening door in the wall; or conversely the manipulation of a door-handle might be defined with respect to the opening door rather than the wall. (2) Computer-Aided Design: During the design process, one frequently needs to modify only part of the existing design; e.g., move a block face with respect to the rest of the block, rotate only a subset of nodes in a facial animation. (3) Computer vision: The representation of a scene can often involve the creation of a tree of relationships through the scene, such that any particular branch selectively connects only some of the objects and not others. (4) Science: A causal trajectory might depend on a property that only a specific class of objects in the situation possess, e.g., those that are not electrically neutral. (5) Biology: The limbs on a body emerge at only specific points. (6) Music: Marsella & Schmidt [103] have identified structures in which there is dependency selectively between a part in one hierarchy and a part in another hierarchy.