A Numerical Proposal of an Extended Solid Modeling System

This thesis has been carried out at the Department of Mathematics of the University of Bologna and at the Company HyperLean s.r.l. spin-off of the University Polytechnic of Marche, as part of a collaborative project on "Theoretical and numerical aspects of a hybrid geometric modeling system". The key observation that motivates the interest in this topic is that in different application contexts you have the need to create virtual solid models that integrate real data acquired by 3D scanning, represented by polygonal meshes, with synthetic models, designed by parametric/analytical multi-patches. The research topic covered the study of theoretical and numerical aspects of solid modeling and the development of suitable solutions as part of a "hybrid geometric solid modeling system". In particular, the involvement as regards the professional side of the project covered the development of algorithms for the optimization of the 3D geometry of solid objects and boolean operations between polygonal meshes to improve the LeanCost software (HyperLean's proprietary software). Concerning the academic side, we investigated many aspects of solid modeling, focusing on the B-Rep models and introducing the new paradigm "Extended B-Rep" which is able to integrate "mesh-faces" as part of a B-rep model. To manage the quality of the built model we studied a notion of continuity and join between parametric and discrete representations and we proposed a set of methods that guarantee that the models can be manipulated while maintaining predetermined continuity constraints among the constituent parts. We generalized the most important tools of solid modeling to the Extended B-Reps and proposed solutions to extend the geometric kernels of standard solid modeling systems tobe able to deal with Extended B-rep models. The new geometric solid modeling kernel has been realized in a software supported by the OpenCascade library.