Pi-surfaces: products of implicit surfaces towards constructive composition of 3D objects

Implicit functions provide a fundamental basis to model 3D objects, no matter they are rigid or deformable, in computer graphics and geometric modeling. This paper introduces a new constructive scheme of implicitly-defined 3D objects based on products of implicit functions. This scheme is in contrast with popular approaches like blobbies, meta balls and soft objects, which rely on the sum of specific implicit functions to fit a 3D object to a set of spheres.