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 basedupon 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. Introduc...

We present an unstructured triangular mesh generation algorithm that approximates a set of mutually nonintersecting simple trimmed polynomial parametric surface patches within a user specified geometric tolerance. The proposed method uses numerically robust interval geometric representations/computations and also addresses the problem of topological consistency (homeomorphism) between the exact geometry and its approximation. Those are among the most important outstanding issues in geometry approximation problems. We also extract important differential geometric features of input geometry for use in the approximation. Our surface tessellation algorithm is based on the unstructured Delaunay mesh approach which leads to an efficient adaptive triangulation. A robust decision criterion is introduced to prevent possible failures in the conventional Delaunay triangulation. To satisfy the prescribed geometric tolerance, an adaptive node insertion algorithm is employed and furthermore, an efficient method to compute a tight upper bound of the approximation error is proposed. Unstructured triangular meshes for free-form surfaces frequently involve triangles with high aspect ratio and, accordingly, result in ill-conditioned meshing. Our proposed algorithm constructs 2D triangulation domains which sufficiently preserve the shape of triangles when mapped into 3D space and, furthermore, the algorithm provides an efficient method that explicitly controls the aspect ratio of the triangular elements.

This paper discusses the informational requirements of layered manufacturing (LM). The most common industrial use of LM today is for rapid prototyping, but we take a wider view of it as a flexible fabrication technology. Its use in building functional metallic parts under computer control has already been demonstrated in the research context. Commercial LM machines for building production parts are in prospect. We report on a study of current and proposed data formats for communication between the various stages of the LM process. They are compared, and attention is given to the issue of their extensibility to meet future needs. In this last respect, particular emphasis is given to materials-related and other nongeometric information needed for fabricating multi-material objects and objects with graded material properties. One conclusion is that the best way forward is the creation of a new Application Protocol for the international standard ISO 10303, specifically to handle layered ma...

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We present an unstructured triangular mesh generation algorithm that approximates a set of mutually non-intersecting simple trimmed rational B-spline surface patches within a user specified geometric tolerance. The proposed method uses numerically robust interval geometric representations/computations and also addresses the problem of topological consistency (homeomorphism) between the exact geometry and its approximation. Those are among the most important outstanding issues in geometry approximation problems. Our surface tessellation algorithm is based on the unstructured Delaunay mesh approach which leads to an efficient adaptive triangulation. A robust decision criterion is utilized to prevent possible failures in the conventional Delaunay triangulation. To satisfy the prescribed geometric tolerance, an adaptive node insertion algorithm is employed. Unstructured triangular meshes for free-form surfaces frequently involve triangles with high aspect ratio and accordingly, result in i...

This chapter surveys some recent work on the application of techniques from computational geometry to geometric problems arising in manufacturing processes such as layered manufacturing, mold design, and numerically controlled machining. Within each topic, we discuss problems that have benefited from the application of geometric

This paper reviews the emerging field of layered manufacturing. This field is little over 10 years old but a significant amount of research has been conducted and results to date are quite promising. We consider three broad topics namely, design systems for heterogeneous objects, layered manufacturing processes, and process planning techniques. Several applications/examples are included in the course of the survey and limitations of current technology identified. We conclude with some possibilities for the future. �DOI: 10.1115/1.1355029� 1