Neste trabalho, propusemos uma nova estrutura de dados para representar sincronamente curvas e superfícies em modelagem de sólidos B-Rep. Esta nova estrutura baseia-se na estrutura unificada. Ela separa duas funções principais atribuídas à face: fechar o contorno do sólido topologicamente, e representar a forma geométrica do fechamento. Estas duas funções não são consistentes entre si, pois existem situações em que a face possui três ou cinco lados, e neste caso é necessário dividi-la para que todas as faces possuam apenas quatro lados. Este processo, geralmente, é feito de modo automático pelo sistema CAD. Neste caso, a estrutura de dados proposta separa as informações relativas às intenções do usuário dos elementos criados automaticamente pelo sistema CAD para satisfazer esta necessidade. Também foi definido um nível extra para suportar a definição de faces poligonais planas que aproximam a forma da geometria, e deste modo permitem que propriedades integrais sejam calculadas.

In this article a new data structure is defined based on non-manifold representation to support the representation of curves and surfaces in B-Rep solid models. This new data structure will support the synchronization between the geometry of the Geometric Model and an approximated polyhedral. An approximated polyhedral is obtained allowing the calculation of mass properties using several existent algorithms in the literature. And it is possible to reduce the approximated polyhedral for a minimum representation when necessary. The face, in commercial solid modelers, has two functions: represent the boundary of the solid and represent the geometrical shape of the contour. In this new structure, we will separate these two functions, one topological element will represent the boundary of the solid and another topological element will represent the geometrical shape as free form curves and surfaces. This mechanism facilitate the representation of irregular faces (faces with three, five or more sides). Since it is not common for a commercial CAD system to support the direct representation of a three-side surface, usually, those faces are subdivided in a number of four side faces. That fact is an inconsistency between topology and geometry, as the number of sides in a face is defined by topology and geometry usually "forces" a face to have four sides. In this article, we will propose two structures, the principal data structure contains the original solid model, and theauxiliary data structure represents an approximation of the solid model. In this mechanism, an automatic mode is defined that can determine the forms of the irregular faces separated to the mode that surfaces can be modified by users. To synchronize both data structures, we defined some algorithms maintaining the consistence of the data structure.