This paper describes a new approach to interactive geometric modelling, based on the application of an agent-oriented modelling technique. Our methods are conceived with exploratory modelling that involves experiment and observation particularly in mind. Our geometric modelling system is based on CSG principles and uses R-functions for implementing sets of operations over functionally defined objects. This supplies a high-level symbolic description of the n-dimensional geometric model being updated during the modelling process. Our approach to building a definitive geometric language to allow incremental and extensible modelling is described. An agent-oriented notation is used to describe both the interaction of the user with the geometric modelling system and the interactions between the principal components of the system itself. A case-study that involves exploratory modelling of morphing between two CSG objects is introduced. The future development of an agent-oriented approach to geometric modelling is discussed.