ABSTRACT M.C. Escher's artwork has inspired and arguably even informed computer science, as well as geometric and shape modeling. Even today, much of his work poses challenges to conventional digital shape modeling systems. The authors introduce several interesting problems presented by Escher's graphic artworks and describe their use of a novel approach, based on implicit surfaces and their extension (Function Representation), to produce 2D, 2.5D and 3D computer models. They also discuss several physical objects or sculptures based on these models, crafted using digital fabrication processes.

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.