This paper describes an approach to computer-based sculpting concerned with the creation and modification of digital models based on physical abstract sculptures. The authors begin by presenting a survey of current methods for the creation of computer-based sculpted artifacts. They proceed to present some original methods and tools based on the Function Representation of geometric models. They introduce a specialized computer language, called Hyper Fun, that facilitates the modeling of complex objects. In addition to presenting computer-generated textured and animated models of pre-existing sculptures, they also show how novel shapes can be generated using the Hyper-Fun system. Finally they outline two advanced projects concerned with creating a sculpture-based augmented reality that allows for the interactive participation of the observer.