Volume modeling has become an important research topic. For many years people have been focusing on modeling homogeneous solid object. Because of the rapid hardware and technological development in volumetric data acquisition during the past decade, effectively modeling heterogeneous volumetric objects or datasets becomes imperative in solid modeling and 3D graphics. A heterogeneous model consists of a solid model and a number of spatially distributed material attributes. Heterogeneous object scalar modeling focuses on representing and capturing a broad range of complex appearances in solid model.Discrete representations such as voxels and regular or irregular grids have been predominating in scientific visualization and finite element analysis for the last thirty years. Prior state-of-the-art in continuous representations include B-splines and simplex splines, however, they either lack of local adaptivity and refinement, and hierarchical structure, or have irregular domain and the process of choosing partitioning into simplices is hard.To overcome these problems, in this thesis we advocate a continuous representation scheme for heterogeneous material modeling which built upon trivariate scalar T-splines, whose domain is principal-axis-aligned regular and control grids/lattice permit T-junctions. By using trivariate T-splines, lines of control points need not traverse the entire control grid and local adaptivity and refinement can be obtained. Moreover, heterogeneous volumetric objects can be adaptively refined in a hierarchical manner (hierarchical refinement) by this scalar modeling method.In addition to object modeling and material representation, we also design a volume rendering algorithm via ray-casting. Since trivariate T-splines afford a continuous representation, we can benefit from this precise and compact mathematical formulation that will facilitate the modeling and visualization tasks in engineering applications. Several techniques, such as empty space skipping, intersection refinement, adaptive sampling, and attribute integration have been proposed to get both efficient and accurate visualization results. We conduct experiments that have demonstrated the utility of our trivariate scalar T-splines in modeling, graphics, and visualization.