Free-form solid modelling based on extended simplicial chains using triangular Bézier patches

We present a mathematical model for geometric modelling based on the concept of extended simplicial chain (ESC) defined in previous works. With this model, a solid is defined by means of an algebraic sum of non− disjoint extended cells, applying the divide and conquer concept. This allows us to obtain the traditional Boo− lean operations in geometric modelling through the operations defined for ESC’s. The model enables us to represent free−form solids whose boundaries are free−form surfaces represented by a set of low degree triangular Bézier patches and operate with them. In fact, this model allows us to solve basic problems in solid modelling, like the point−in−solid test. In this case we make use of the generality of the definition of ESC to particularize it to the use of triangular Bézier patches in 3D.