Object Representation and Reasoning Using Halfspaces and Logic

Abstract

Shapes and objects represent important ways with which to perceive and reason about the world. This paper develops a framework which uniformly encompasses both planar and non-planar surfaces to represent graphical objects in three dimensions. Based on the concept of halfspaces this framework allows the representation of volumes as predicates in logic. This representation is applied to demonstrate object concepts associated with reasoning about the topology of objects as individuals as well as groups of objects at the early, conceptual phase of designing. The example shows how both planar and non-planar boundaries of objects are treated uniformly