Abstract

A mathematical model for geometric modelling is presented in this work. This model is based on the concept of *extended simplicial chain*. Solids are defined by means of simple algebraic operations (additions and subtractions) performed on what we call *extended cells*. In like manner, by using the operations defined for extended simplicial chains, we obtain the traditional Boolean operations in geometric modelling. Thus, we define a new model which allows us to represent and operate with free-form solids, particularised for the case of solids whose boundaries are free-form surfaces expressed as a set of low degree algebraic patches. However, the concept of extended simplicial chain is more general and wide both in the dimension in which the solid is defined and in the type of surface used for its representation.

**Keywords:** formal methods in computer graphics, mathematical models, free-form solid modelling, Boolean operations.