Solid Freeform Fabrication SFF processes have demonstrated the ability to produce parts with locally controlled composition. In the limit, processes such as 3D Printing can create parts with composition control on a length scale of 100 m. To exploit this potential, new methods to model, exchange, and process parts with local composition control need to be developed. An approach to modeling a part's geometry, topology, and composition is presented. This approach is based on subdividing the solid model into sub-regions and associating analytic composition blending functions with each region. These blending functions de ne the composition throughout the model as mixtures of the primary materials available to the SFF machine. Design tools based u p on distance functions are also introduced, such as the speci cation of composition as a function of the distance from the surface of a part. Finally, the role of design rules restricting maximum and minimum concentrations is discussed.

Methods to represent and exchange parts consisting of Functionally Graded Material (FGM) for Solid Freeform Fabrication (SFF) with Local Composition Control (LCC) are evaluated based on their memory requirements. Data structures for representing FGM objects as heterogeneous models are described and analyzed, including a voxel-based structure, finite-element mesh-based approach, and the extension of the Radial-Edge and Cell-Tuple-Graph data structures with Material Domains representing spatially varying composition properties. The storage cost for each data structure is derived in terms of the number of instances of each of its fundamental classes required to represent an FGM object. In order to determine the optimal data structure, the storage cost associated with each data structure is calculated for several hypothetical models. Limitations of these representation schemes are discussed and directions for future research also recommended.

Solid Freeform Fabrication (SFF) processes have demonstrated the ability to produce parts with locally controlled composition. In the limit, processes such as Three-Dimensional Printing(3DP) can create parts with composition to the length scale of 100 μm. To exploit this potential, new methods for automatic design of Functionally Gradient Material (FGM) parts need to be developed. This paper presents an efficient method for design and composition interrogation of FGM solids. The design tool based on the distance function from the surface of the part requires enhanced efficiency, and so does the interrogation of the part. The approach for improving efficiency includes preprocessing the model with bucket sorting and 3D digital distance transform, and an efficient point classification algorithm. Based on these tools, an efficient algorithm for distance function computation is developed for the design of FGM through distance to the surface of the part or distance to an .STL surface boundary. An efficient algorithm to evaluate composition at a point, along a ray or on a plane is also presented.

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