Free-Form Solid Modellíng Based on Extended Simplícial Chains Using Triangular Bézier Patches

Abstract

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 nondisjoint extended cells, applying the divide and conquer concept. This allows us to obtain the traditional Boolean 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 swfaces represented by a set of low degree triangular Bézier patches and operate with them. ln fact, this model allows us to solve basic problems in solid modelling, like the point-in-solid test. ln 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.