【摘要】The needs of modern (additive) manufacturing (AM) technologies can be satisfied no longer by boundary representations (B-reps), as AM requires the representation and manipulation of interior fields and (graded) materials as well. Further, while the need for a tight coupling between design and analysis has been recognized as crucial almost since geometric modeling (GM) has been conceived, contemporary GM systems only offer a loose link between the two, if at all.For about half a century, (trimmed) Non Uniform Rational B-spline (NURBs) surfaces has been the B-rep of choice for virtually all the GM industry. Fundamentally, B-rep GM has evolved little during this period. In this talk, we seek to examine an extended (trimmed) NURBs volumetric representation (V-rep) that successfully confronts existing and anticipated design, analysis, and manufacturing foreseen challenges. We extend all fundamental B-rep GM operations, such as primitive and surface constructors and Boolean operations, to trimmed trivariate V-reps. This enables the much-needed tight link to (Isogeometric) analysis (IGA) on one hand and the full support of (heterogeneous and anisotropic) additive manufacturing on the other. Special V-rep capabilities toward the support of modern AM and the support of IGA will also be presented, that enable robust queries over V-reps, including planar slicing of heterogeneous geometries, precise contact analysis, maximal penetration depth, and accurate integration over trimmed domains. Examples and applications of V-rep GM, including AM and (heterogeneous) microstructure synthesis will also be demonstrated.