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

## TL;DR

This paper introduces Pi-surfaces, a novel constructive method for modeling 3D objects using products of implicit functions, offering an alternative to traditional sum-based approaches like blobbies and meta balls.

## Contribution

It proposes a new scheme for implicit 3D object modeling based on products of implicit functions, differing from existing sum-based methods.

## Key findings

- Provides a new constructive scheme for 3D modeling
- Offers an alternative to sum-based implicit methods
- Enables modeling of both rigid and deformable objects

## Abstract

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.