This paper proposes a constructive representation scheme for heterogeneous objects (or FGMs). In particular, this scheme focuses on the construction of complicated heterogeneous objects, guaranteeing desired material continuities at all the interfaces. In order to create various types of heterogeneous primitives, we first describe methods for specifying material composition functions such as geometry-independent, geometry-dependent functions, and multiple sets of these functions. Constructive Material Composition (CMC) and corresponding heterogeneous Boolean Operators (e.g., material union, difference, intersection, and partition) are then proposed to illustrate how material continuities are dealt with. Finally, we will describe the model hierarchy and data structure for computer representation. Even though the constructive representation alone is sufficient for modeling heterogeneous objects, the proposed scheme pursues a hybrid representation between decomposition and construction. That is because hybrid representation can avoid unnecessary growth of binary trees.
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