Introduction

Traditionally, 3D objects and virtual worlds are defined by lists of geometric primitives: cubes and spheres in a CSG tree, NURBS patches, a set of implicit functions, a soup of triangles, or just a cloud of points.

The term ‘generative modeling‘ describes a paradigm change in shape description, the generalization from objects to operations: A shape is described by a sequence of processing steps, rather than just the end result of applying operations. Shape design becomes rule design. This approach is very general and it can be applied to any shape representation that provides a set of generating functions, the ‘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 generating functions for meshes, operating on the half edge level.