Usual 3D file formats describe a virtual world in terms of geometric primitives. These may be cubes and spheres in a CSG tree, NURBS patches, a set of implicit functions, a triangle mesh, or just a cloud of points. The term "generative 3D modelling" describes a different paradigm for describing shape. The main idea is to replace 3D objects by object-generating operations: A shape is described by a sequence of processing steps, rather than the triangles which are the result of applying these operations. Shape design becomes rule design. The approach can be generally applied to any shape representation that provides a basic set of generating functions, called in this context 'elementary shape operators'. Its effectiveness has been demonstrated, e.g., in the field of procedural mesh generation, with Euler operators as complete and closed set of invertible shape generating functions for meshes, operating on the half-edge level.
